From 2e494884c53f31fc73dc91dda4a2dbfbce1a9752 Mon Sep 17 00:00:00 2001 From: Nicholas Clark Date: Mon, 4 Nov 2024 10:54:33 +1000 Subject: [PATCH] add update and residual_cor functions for jsdgams --- DESCRIPTION | 1 + NAMESPACE | 3 + NEWS.md | 3 +- R/jsdgam.R | 34 +- R/monotonic.R | 8 +- R/mvgam_setup.R | 17 +- R/residual_cor.R | 185 ++ R/residuals.mvgam.R | 1 + R/update.mvgam.R | 223 +- docs/news/index.html | 7 +- docs/reference/Rplot001.png | Bin 1011 -> 19506 bytes docs/reference/Rplot002.png | Bin 19219 -> 19379 bytes docs/reference/Rplot003.png | Bin 21349 -> 21070 bytes docs/reference/Rplot004.png | Bin 11811 -> 56645 bytes docs/reference/Rplot005.png | Bin 7075 -> 74483 bytes docs/reference/Rplot006.png | Bin 41439 -> 39959 bytes docs/reference/Rplot007.png | Bin 34967 -> 35061 bytes docs/reference/Rplot008.png | Bin 32017 -> 31748 bytes docs/reference/Rplot009.png | Bin 14374 -> 14614 bytes docs/reference/Rplot010.png | Bin 70346 -> 67515 bytes docs/reference/Rplot011.png | Bin 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docs/reference/update.mvgam.html | 268 +- man/jsdgam.Rd | 32 +- man/mvgam_marginaleffects.Rd | 2 + man/residual_cor.jsdgam.Rd | 111 + man/residuals.mvgam.Rd | 3 +- man/update.mvgam.Rd | 51 +- src/RcppExports.o | Bin 113491 -> 118706 bytes src/trend_funs.o | Bin 102172 -> 98386 bytes tests/testthat/Rplots.pdf | Bin 1958803 -> 1955825 bytes tests/testthat/test-jsdgam.R | 60 +- tests/testthat/test-update.R | 21 + 86 files changed, 2754 insertions(+), 2000 deletions(-) create mode 100644 R/residual_cor.R create mode 100644 docs/reference/residual_cor.jsdgam.html create mode 100644 man/residual_cor.jsdgam.Rd diff --git a/DESCRIPTION b/DESCRIPTION index 201006fd..cc090f74 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -43,6 +43,7 @@ Suggests: tweedie, splines2, extraDistr, + corpcor, wrswoR, xts, lubridate, diff --git a/NAMESPACE b/NAMESPACE index c76dad26..52213c42 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -56,6 +56,7 @@ S3method(print,mvgam) S3method(print,mvgam_conditional_effects) S3method(print,mvgam_prefit) S3method(print,mvgammodel) +S3method(residual_cor,jsdgam) S3method(residuals,mvgam) S3method(rhat,mvgam) S3method(score,mvgam_forecast) @@ -68,6 +69,7 @@ S3method(stancode,mvgam_prefit) S3method(standata,mvgam_prefit) S3method(summary,mvgam) S3method(summary,mvgam_prefit) +S3method(update,jsdgam) S3method(update,mvgam) S3method(variables,mvgam) export("%>%") @@ -142,6 +144,7 @@ export(predictions) export(prior) export(prior_) export(prior_string) +export(residual_cor) export(rhat) export(roll_eval_mvgam) export(s) diff --git a/NEWS.md b/NEWS.md index 9418880e..a327a559 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,6 +1,6 @@ # mvgam 1.1.4 (development version; not yet on CRAN) ## New functionalities -* Added function `jsdgam()` to estimate Joint Species Distribution Models in which both the latent factors and the observation model components can include any of mvgam's complex linear predictor effects. See `?mvgam::jsdgam` for details +* Added function `jsdgam()` to estimate Joint Species Distribution Models in which both the latent factors and the observation model components can include any of mvgam's complex linear predictor effects. Also added a function `residual_cor()` to compute residual correlation, covariance and precision matrices from `jsdgam` models. See `?mvgam::jsdgam` and `?mvgam::residual_cor` for details * Added a `stability.mvgam()` method to compute stability metrics from models fit with Vector Autoregressive dynamics (#21 and #76) * Added functionality to estimate hierarchical error correlations when using multivariate latent process models and when the data are nested among levels of a relevant grouping factor (#75); see `?mvgam::AR` for an example * Added `ZMVN()` error models for estimating Zero-Mean Multivariate Normal errors; convenient for working with non time-series data where latent residuals are expected to be correlated (such as when fitting Joint Species Distribution Models); see `?mvgam::ZMVN` for examples @@ -9,6 +9,7 @@ ## Bug fixes * Fixed a minor bug in the way `trend_map` recognises levels of the `series` factor * Bug fix to ensure `lfo_cv` recognises the actual times in `time`, just in case the user supplies data that doesn't start at `t = 1`. Also updated documentation to better reflect this +* Bug fix to ensure `update.mvgam` captures any `knots` or `trend_knots` arguments that were passed to the original model call # mvgam 1.1.3 ## New functionalities diff --git a/R/jsdgam.R b/R/jsdgam.R index c28c7426..36702dae 100644 --- a/R/jsdgam.R +++ b/R/jsdgam.R @@ -53,6 +53,10 @@ #'\code{Stan}'s `reduce_sum` function and have a slow running model that cannot be sped #'up by any other means. Currently works for all families when using \code{Cmdstan} #'as the backend +#'@param priors An optional \code{data.frame} with prior +#'definitions (in Stan syntax) or, preferentially, a vector containing +#' objects of class `brmsprior` (see. \code{\link[brms]{prior}} for details). +#' See [get_mvgam_priors] and for more information on changing default prior distributions #'@param ... Other arguments to pass to [mvgam] #'@author Nicholas J Clark #'@details Joint Species Distribution Models allow for responses of multiple species to be @@ -77,8 +81,8 @@ #' any of `mvgam`'s predictor effects, including random intercepts and slopes, multidimensional penalized #' smooths, GP effects etc... The factor loadings \eqn{\theta_j} are constrained for identifiability but can #' be used to reconstruct an estimate of the species' residual variance-covariance matrix -#' using \eqn{\theta \theta'} (see the example below -#' for an illustration of this). The latent factors are further modelled using: +#' using \eqn{\Theta \Theta'} (see the example below and [residual_cor()] for details). +#' The latent factors are further modelled using: #'\deqn{ #'u_i \sim \text{Normal}(Q_i\beta_{factor}, 1) \quad #'} @@ -86,10 +90,11 @@ #'constructed and modelled using `factor_formula`. Again, the effects that make up this linear #'predictor can contain any of `mvgam`'s allowed predictor effects, providing enormous flexibility for #'modelling species' communities. -#'@seealso [mvgam] +#'@seealso [mvgam()], [residual_cor()] #'@references Nicholas J Clark & Konstans Wells (2020). Dynamic generalised additive models (DGAMs) for forecasting discrete ecological time series. #'Methods in Ecology and Evolution. 14:3, 771-784. -#' +#' \cr +#' \cr #'David I Warton, F Guillaume Blanchet, Robert B O’Hara, Otso Ovaskainen, Sara Taskinen, Steven C #'Walker & Francis KC Hui (2015). So many variables: joint modeling in community ecology. #'Trends in Ecology & Evolution 30:12, 766-779. @@ -255,15 +260,18 @@ #' gratia::draw(mod, trend_effects = TRUE) #' } #' -#' # Calculate (median) residual spatial correlations -#' med_loadings <- matrix(apply(as.matrix(mod$model_output, 'lv_coefs'), -#' 2, median), -#' nrow = N_species, ncol = 4) -#' cormat <- cov2cor(tcrossprod(med_loadings)) -#' rownames(cormat) <- colnames(cormat) <- levels(dat$species) -#' -#' # A quick and dirty correlation matrix plot -#' image(cormat) +#' # Calculate residual spatial correlations +#' post_cors <- residual_cor(mod) +#' names(post_cors) + +#' # Look at lower and upper credible interval estimates for +#' # some of the estimated correlations +#' post_cors$cor[1:5, 1:5] +#' post_cors$cor_upper[1:5, 1:5] +#' post_cors$cor_lower[1:5, 1:5] + +#' # A quick and dirty plot of the posterior median correlations +#' image(post_cors$cor) #' #' # Posterior predictive checks and ELPD-LOO can ascertain model fit #' pp_check(mod, type = "ecdf_overlay_grouped", diff --git a/R/monotonic.R b/R/monotonic.R index 5f042e03..7ab18238 100644 --- a/R/monotonic.R +++ b/R/monotonic.R @@ -185,10 +185,10 @@ smooth.construct.moi.smooth.spec <- function(object, data, knots){ # Generate basis functions i_spline_basis <- splines2::iSpline(x, - knots = k, - degree = nk, - Boundary.knots = boundary, - intercept = TRUE) + knots = k, + degree = nk, + Boundary.knots = boundary, + intercept = TRUE) nbasis <- dim(i_spline_basis)[2] diff --git a/R/mvgam_setup.R b/R/mvgam_setup.R index 474195cf..3be13de2 100644 --- a/R/mvgam_setup.R +++ b/R/mvgam_setup.R @@ -11,19 +11,22 @@ mvgam_setup <- function(formula, maxit = 5) { if(missing(knots)){ - init_gam(formula(formula), - data = dat, - family = family) + out <- init_gam(formula(formula), + data = dat, + family = family) + attr(out, 'knots') <- NULL } else { if(!is.list(knots)){ stop('all "knot" arguments must be supplied as lists', call. = FALSE) } - init_gam(formula(formula), - data = dat, - family = family, - knots = knots) + out <- init_gam(formula(formula), + data = dat, + family = family, + knots = knots) + attr(out, 'knots') <- knots } + out } #' Generic JAGAM setup function diff --git a/R/residual_cor.R b/R/residual_cor.R new file mode 100644 index 00000000..81e55984 --- /dev/null +++ b/R/residual_cor.R @@ -0,0 +1,185 @@ +#' Extract residual correlations based on latent factors from a fitted jsdgam +#' +#' Compute residual correlation estimates from Joint Species Distribution +#' \code{jsdgam} models using latent factor loadings +#' +#' @name residual_cor.jsdgam +#' @inheritParams brms::residuals.brmsfit +#' @param object \code{list} object of class \code{mvgam} resulting from a call to [jsdgam()] +#' @param robust If `FALSE` (the default) the mean is used as a measure of central tendency. +#' If `TRUE`, the median is used instead. Only used if `summary` is `TRUE` +#' @param ... ignored +#' @return If `summary = TRUE`, a `list` with the following components: +#' \itemize{ +#' \item{cor, cor_lower, cor_upper}{: A set of \eqn{p \times p} correlation matrices, +#' containing either the posterior median or mean estimate, plus lower and upper limits +#' of the corresponding credible intervals supplied to `probs`} +#' \item{sig_cor}{: A \eqn{p \times p} correlation matrix containing only those correlations whose credible +#' interval does not contain zero. All other correlations are set to zero} +#' \item{prec, prec_lower, prec_upper}{: A set of \eqn{p \times p} precision matrices, +#' containing either the posterior median or mean estimate, plus lower and upper limits +#' of the corresponding credible intervals supplied to `probs`} +#' \item{sig_prec}{: A \eqn{p \times p} precision matrix containing only those precisions whose credible +#' interval does not contain zero. All other precisions are set to zero} +#' \item{cov}{: A \eqn{p \times p} posterior median or mean covariance matrix} +#' \item{trace}{: The median/mean point estimator of the trace (sum of the diagonal elements) +#' of the residual covariance matrix `cov`} +#' } +#' If `summary = FALSE`, this function returns a `list` containing the following components: +#' \itemize{ +#' \item{all_cormat}{: A \eqn{n_{draws} \times p \times p} `array` of posterior +#' residual correlation matrix draws} +#' \item{all_covmat}{: A \eqn{n_{draws} \times p \times p} `array` of posterior +#' residual covariance matrix draws} +#' \item{all_presmat}{: A \eqn{n_{draws} \times p \times p} `array` of posterior +#' residual precision matrix draws} +#' \item{all_trace}{: A \eqn{n_{draws}} `vector` of posterior covariance trace draws} +#' } +#' @details +#' Hui (2016) provides an excellent description of the quantities that this function calculates, so this passage +#' is heavily paraphrased from his associated `boral` package. +#' +#' In Joint Species Distribution Models, the residual covariance matrix is calculated +#' based on the matrix of latent factor loading matrix \eqn{\Theta}, where the residual covariance +#' matrix \eqn{\Sigma = \Theta\Theta'}. A strong residual covariance/correlation matrix +#' between two species can be interpreted as evidence of species interaction (e.g., +#' facilitation or competition), +#' missing covariates, as well as any additional species correlation not accounted for by shared +#' environmental captured in `formula`. +#' +#' The residual precision matrix (also known as partial correlation matrix, Ovaskainen et al., 2016) +#' is defined as the inverse of the residual correlation matrix. The precision matrix is often used to +#' identify direct or causal relationships between two species e.g., two species can have a zero +#' precision but still be correlated, which can be interpreted as saying that two species are not +#' directly associated, but they are still correlated *through* other species. In other words, they +#' are conditionally independent given the other species. It is important that the precision matrix +#' does not exhibit the exact same properties of the correlation e.g., the diagonal elements are +#' not equal to 1. Nevertheless, relatively larger values of precision imply a stronger +#' direct relationships between two species. +#' +#' In addition to the residual correlation and precision matrices, the median or mean point estimator +#' of trace of the residual covariance matrix is returned, +#' \eqn{\sum\limits_{j=1}^p [\Theta\Theta']_{jj}}. Often used in other areas of multivariate +#' statistics, the trace may be interpreted as the amount of covariation explained by the latent factors. +#' One situation where the trace may be useful is when comparing a pure latent factor model +#' (where no terms are suppled to `formula`) versus a model with latent +#' factors and some additional predictors in `formula` -- the proportional difference in trace +#' between these two models may be interpreted as the proportion of covariation between species explained +#' by the predictors in `formula`. Of course, the trace itself is random due to the MCMC sampling, and so it +#' is not always guaranteed to produce sensible answers. +#' @author Nicholas J Clark +#' @references +#' Francis KC Hui (2016). BORAL - Bayesian ordination and regression analysis of +#' multivariate abundance data in R. Methods in Ecology and Evolution. 7, 744-750. +#' \cr +#' \cr +#' Otso Ovaskainen et al. (2016). Using latent variable models to identify large networks of +#' species-to-species associations at different spatial scales. Methods in Ecology and Evolution, +#' 7, 549-555. +#' @seealso [jsdgam()] +#' @export +residual_cor <- function(object, ...){ + UseMethod("residual_cor", object) +} + +#' @rdname residual_cor.jsdgam +#' @method residual_cor jsdgam +#' @export +residual_cor.jsdgam <- function(object, + summary = TRUE, + robust = FALSE, + probs = c(0.025, 0.975), + ...) { + + insight::check_if_installed("corpcor") + + # Take draws of factor loadings + n_lv <- object$n_lv + p <- NCOL(object$ytimes) + sp_names <- levels(object$obs_data$series) + loadings <- as.matrix(object$model_output, 'lv_coefs') + + # Initiate array to store all posterior correlation and covariance matrices + all_cormat <- all_covmat <- all_precmat <- array(0, dim = c(nrow(loadings), p, p)) + all_trace_rescor <- numeric(NROW(loadings)) + + # Calculate posterior covariance, correlation, precision and trace estimates + for(i in 1:NROW(loadings)){ + lv_coefs <- matrix(loadings[i, ], nrow = p, ncol = n_lv) + + lambdalambdaT <- tcrossprod(lv_coefs) + all_covmat[i, , ] <- lambdalambdaT + all_trace_rescor[i] <- sum(diag(lambdalambdaT)) + all_cormat[i, , ] <- cov2cor(lambdalambdaT) + all_precmat[i, , ] <- corpcor::cor2pcor(lambdalambdaT) + } + + if(!summary){ + out <- list(all_cormat = all_cormat, + all_covmat = all_covmat, + all_precmat = all_precmat, + all_trace = all_trace_rescor) + } else { + + #### If summary, calculate summary statistics #### + # Initiate summary correlation and covariance matrices + sig_cormat <- cormat <- cormat_lower <- cormat_upper <- + sig_precmat <- precmat <- precmat_lower <- precmat_upper <- + covmat <- matrix(0, nrow = p, ncol = p) + + rownames(cormat) <- rownames(cormat_lower) <- rownames(cormat_upper) <- + rownames(sig_cormat) <- rownames(precmat) <- rownames(precmat_lower) <- + rownames(precmat_upper) <- rownames(sig_precmat) <- rownames(covmat) <- + colnames(cormat) <- colnames(cormat_lower) <- colnames(cormat_upper) <- + colnames(sig_cormat) <- colnames(precmat) <- colnames(precmat_lower) <- + colnames(precmat_upper) <- colnames(sig_precmat) <- colnames(covmat) <- + sp_names + + # Calculate posterior summaries + for (j in 1:p) { + for (j2 in 1:p) { + if (robust) { + covmat[j, j2] <- median(all_covmat[, j, j2]) + cormat[j, j2] <- median(all_cormat[, j, j2]) + precmat[j, j2] <- median(all_precmat[, j, j2]) + } else { + covmat[j, j2] <- mean(all_covmat[, j, j2]) + cormat[j, j2] <- mean(all_cormat[, j, j2]) + precmat[j, j2] <- mean(all_precmat[, j, j2]) + } + + sig_cormat[j, j2] <- cormat[j, j2] + cormat_lower[j, j2] <- quantile(all_cormat[, j, j2], probs = min(probs), na.rm = TRUE) + cormat_upper[j, j2] <- quantile(all_cormat[, j, j2], probs = max(probs), na.rm = TRUE) + if (0 > cormat_lower[j, j2] & 0 < cormat_upper[j, j2]) { + sig_cormat[j, j2] <- 0 + } + + sig_precmat[j, j2] <- precmat[j, j2] + precmat_lower[j, j2] <- quantile(all_precmat[, j, j2], probs = min(probs), na.rm = TRUE) + precmat_upper[j, j2] <- quantile(all_precmat[, j, j2], probs = max(probs), na.rm = TRUE) + if (0 > precmat_lower[j, j2] & 0 < precmat_upper[j, j2]) { + sig_precmat[j, j2] <- 0 + } + } + } + + if (robust) { + final_trace <- median(all_trace_rescor) + } else { + final_trace <- mean(all_trace_rescor) + } + + out <- list(cor = cormat, + cor_lower = cormat_lower, + cor_upper = cormat_upper, + sig_cor = sig_cormat, + cov = covmat, + prec = precmat, + prec_lower = precmat_lower, + prec_upper = precmat_upper, + sig_prec = sig_precmat, + trace = final_trace) + } + return(out) +} diff --git a/R/residuals.mvgam.R b/R/residuals.mvgam.R index ee035c77..2cddb0d0 100644 --- a/R/residuals.mvgam.R +++ b/R/residuals.mvgam.R @@ -6,6 +6,7 @@ #' #' @inheritParams brms::residuals.brmsfit #' @param object An object of class `mvgam` +#' @param ... ignored #' @details This method gives residuals as Dunn-Smyth (randomized quantile) residuals. Any #' observations that were missing (i.e. `NA`) in the original data will have missing values #' in the residuals diff --git a/R/update.mvgam.R b/R/update.mvgam.R index 5fbdf295..269c2996 100644 --- a/R/update.mvgam.R +++ b/R/update.mvgam.R @@ -9,12 +9,13 @@ #'@param formula Optional new `formula` object. Note, `mvgam` currently does not support dynamic formula #'updates such as removal of specific terms with `- term`. When updating, the entire formula needs #'to be supplied -#'@param ... Other arguments to be passed to \code{\link{mvgam}} +#'@param ... Other arguments to be passed to \code{\link{mvgam}} or \code{\link{jsdgam}} #'@return A \code{list} object of class \code{mvgam} containing model output, the text representation of the model file, #' the mgcv model output (for easily generating simulations at -#' unsampled covariate values), Dunn-Smyth residuals for each series and key information needed +#' unsampled covariate values), Dunn-Smyth residuals for each outcome variable and key information needed #' for other functions in the package. See \code{\link{mvgam-class}} for details. #' Use `methods(class = "mvgam")` for an overview on available methods. +#' @author Nicholas J Clark #' @examples #' \donttest{ #' # Simulate some data and fit a Poisson AR1 model @@ -48,6 +49,8 @@ update.mvgam = function(object, formula, trend_formula, + knots, + trend_knots, data, newdata, trend_model, @@ -99,6 +102,14 @@ update.mvgam = function(object, } } + if(missing(knots)){ + if(is.null(attr(object$mgcv_model, 'knots'))){ + knots <- missing_arg() + } else { + knots <- attr(object$mgcv_model, 'knots') + } + } + if(missing(share_obs_params)){ share_obs_params <- object$share_obs_params } @@ -111,6 +122,16 @@ update.mvgam = function(object, } } + if(!missing(trend_formula)){ + if(missing(trend_knots)){ + if(is.null(attr(object$trend_mgcv_model, 'knots'))){ + trend_knots <- missing_arg() + } else { + trend_knots <- attr(object$trend_mgcv_model, 'knots') + } + } + } + if(missing(trend_map)){ if(is.null(object$trend_map)){ trend_map <- missing_arg() @@ -161,10 +182,6 @@ update.mvgam = function(object, n_lv <- object$n_lv } - if(missing(n_lv)){ - n_lv <- object$n_lv - } - if(missing(family)){ family_char <- object$family family <- family_char @@ -183,6 +200,8 @@ update.mvgam = function(object, updated_mod <- mvgam(formula = formula, trend_formula = trend_formula, trend_map = trend_map, + knots = knots, + trend_knots = trend_knots, data = data_train, newdata = data_test, trend_model = trend_model, @@ -205,6 +224,8 @@ update.mvgam = function(object, updated_mod <- mvgam(formula = formula, trend_formula = trend_formula, trend_map = trend_map, + knots = knots, + trend_knots = trend_knots, data = data_train, trend_model = trend_model, use_lv = use_lv, @@ -227,3 +248,193 @@ update.mvgam = function(object, return(updated_mod) } + + +#'@rdname update.mvgam +#'@inheritParams jsdgam +#'@inheritParams update.mvgam +#'@param formula Optional new `formula` object. Note, `mvgam` currently does not support dynamic formula +#'updates such as removal of specific terms with `- term`. When updating, the entire formula needs +#'to be supplied +#'@param factor_formula Optional new `formula` object for the factor linear predictors +#'@return A \code{list} object of class \code{mvgam} containing model output, the text representation of the model file, +#' the mgcv model output (for easily generating simulations at +#' unsampled covariate values), Dunn-Smyth residuals for each series and key information needed +#' for other functions in the package. See \code{\link{mvgam-class}} for details. +#' Use `methods(class = "mvgam")` for an overview on available methods. +#' @author Nicholas J Clark +#'@export +update.jsdgam = function(object, + formula, + factor_formula, + knots, + factor_knots, + data, + newdata, + n_lv, + family, + share_obs_params, + priors, + chains, + burnin, + samples, + threads, + algorithm, + lfo = FALSE, + ...){ + + if(missing(chains)){ + chains <- object$model_output@sim$chains + } + + if(missing(burnin)){ + burnin <- object$model_output@sim$warmup + if(is.null(burnin)) burnin <- 0 + } + + if(missing(samples)){ + samples <- object$model_output@sim$iter - burnin + } + + if(missing(threads)){ + threads <- attr(object$model_data, 'threads') + if(is.null(threads)) threads <- 1 + } + + if(missing(algorithm)){ + algorithm <- object$algorithm + } + + if(!algorithm %in% 'sampling'){ + burnin <- 1 + } + + if(missing(formula)){ + formula <- object$call + + if(attr(object$mgcv_model, 'drop_obs_intercept')){ + formula <- update(formula, ~ . -1) + } + } + + if(missing(factor_formula)){ + factor_formula <- object$trend_call + } + + if(missing(knots)){ + if(is.null(attr(object$mgcv_model, 'knots'))){ + knots <- missing_arg() + } else { + knots <- attr(object$mgcv_model, 'knots') + } + } + + if(missing(factor_knots)){ + if(is.null(attr(object$trend_mgcv_model, 'knots'))){ + factor_knots <- missing_arg() + } else { + factor_knots <- attr(object$trend_mgcv_model, 'knots') + } + } + + if(missing(share_obs_params)){ + share_obs_params <- object$share_obs_params + } + + if(missing(data)){ + data_train <- object$obs_data + } else { + data_train <- data + } + + if(missing(priors)){ + if(!is.null(object$priors)){ + priors <- object$priors + } else { + priors <- rlang::missing_arg() + } + } + + if(!missing(newdata)){ + # If new testing data supplied, include as the test data + data_test <- newdata + include_fc <- TRUE + } else if(!is.null(object$test_data)){ + # only include test data when no new training data is supplied + if(missing(data)){ + include_fc <- TRUE + data_test <- object$test_data + } else { + include_fc <- FALSE + } + } else { + include_fc <- FALSE + } + + if(missing(n_lv)){ + n_lv <- object$n_lv + } + + if(missing(family)){ + family_char <- object$family + family <- family_char + if(family_char == 'negative binomial'){ + family <- nb() + } + if(family_char == 'beta'){ + family <- betar() + } + if(family_char == 'student'){ + family <- student_t() + } + } + + if(include_fc){ + updated_mod <- jsdgam(formula = formula, + factor_formula = factor_formula, + knots = knots, + factor_knots = factor_knots, + data = data_train, + newdata = data_test, + trend_model = trend_model, + n_lv = n_lv, + family = family, + share_obs_params = share_obs_params, + refit = TRUE, + lfo = lfo, + use_stan = ifelse(object$fit_engine == 'stan', TRUE, + FALSE), + priors = priors, + chains = chains, + burnin = burnin, + samples = samples, + algorithm = algorithm, + threads = threads, + ...) + } else { + updated_mod <- mvgam(formula = formula, + factor_formula = factor_formula, + knots = knots, + factor_knots = factor_knots, + data = data_train, + trend_model = trend_model, + n_lv = n_lv, + family = family, + share_obs_params = share_obs_params, + refit = TRUE, + lfo = lfo, + use_stan = ifelse(object$fit_engine == 'stan', TRUE, + FALSE), + priors = priors, + chains = chains, + burnin = burnin, + samples = samples, + algorithm = algorithm, + threads = threads, + ...) + } + + return(updated_mod) + +} + diff --git a/docs/news/index.html b/docs/news/index.html index c019db17..6b907c80 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -1,5 +1,5 @@ -Changelog • mvgamChangelog • mvgam @@ -52,7 +52,7 @@
@@ -60,7 +60,7 @@

mvgam 1.1.4 (development version; not yet on CRAN)

New functionalities

-
  • Added function jsdgam() to estimate Joint Species Distribution Models in which both the latent factors and the observation model components can include any of mvgam’s complex linear predictor effects. See ?mvgam::jsdgam for details
  • +
    • Added function jsdgam() to estimate Joint Species Distribution Models in which both the latent factors and the observation model components can include any of mvgam’s complex linear predictor effects. Also added a function residual_cor() to compute residual correlation, covariance and precision matrices from jsdgam models. See ?mvgam::jsdgam and ?mvgam::residual_cor for details
    • Added a stability.mvgam() method to compute stability metrics from models fit with Vector Autoregressive dynamics (#21 and #76)
    • Added functionality to estimate hierarchical error correlations when using multivariate latent process models and when the data are nested among levels of a relevant grouping factor (#75); see ?mvgam::AR for an example
    • Added ZMVN() error models for estimating Zero-Mean Multivariate Normal errors; convenient for working with non time-series data where latent residuals are expected to be correlated (such as when fitting Joint Species Distribution Models); see ?mvgam::ZMVN for examples
    • @@ -70,6 +70,7 @@

      New functionalitiesBug fixes

      • Fixed a minor bug in the way trend_map recognises levels of the series factor
      • Bug fix to ensure lfo_cv recognises the actual times in time, just in case the user supplies data that doesn’t start at t = 1. Also updated documentation to better reflect this
      • +
      • Bug fix to ensure update.mvgam captures any knots or trend_knots arguments that were passed to the original model call
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a/docs/reference/index.html b/docs/reference/index.html index beab101a..1c1fc25d 100644 --- a/docs/reference/index.html +++ b/docs/reference/index.html @@ -372,6 +372,11 @@

    All functionsresidual_cor() + +
    Extract residual correlations based on latent factors from a fitted jsdgam
    +

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  • + RW() AR() CAR() VAR()
    Specify autoregressive dynamic processes in mvgam
    @@ -403,7 +408,7 @@

    All functionsupdate(<mvgam>) + update(<mvgam>) update(<jsdgam>)
    Update an existing mvgam object

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zw>~};DzS2h7-LMM;gi$1?@=nyE@q#(x)zBs;JhLag~A#jAr%!BnY?-sh5{zn?H}mR zJbw>+nxciZdlvN;kev5zw?rg>k^!Pil*xYrd$~Bi9Q|qb8P?hNPaHTx>rb#oyY6<~ij3u(E3Ht^2-_J+XX=Lm+iXG6zF+cqf0;}AU5NK*fYfRT z67YD@X#lr3hEK6+2*YSGG g==y(tCsS*E7*YE&uMl?$CfSe!?tX5(yArgumentsprior for details). -See get_mvgam_priors and Details' for more information on changing default prior distributions

    +See get_mvgam_priors and for more information on changing default prior distributions

    n_lv
    @@ -340,8 +340,8 @@

    Detailsmvgam's predictor effects, including random intercepts and slopes, multidimensional penalized smooths, GP effects etc... The factor loadings \(\theta_j\) are constrained for identifiability but can be used to reconstruct an estimate of the species' residual variance-covariance matrix -using \(\theta \theta'\) (see the example below -for an illustration of this). The latent factors are further modelled using: +using \(\Theta \Theta'\) (see the example below and residual_cor() for details). +The latent factors are further modelled using: $$ u_i \sim \text{Normal}(Q_i\beta_{factor}, 1) \quad $$ @@ -353,14 +353,15 @@

    Details

    References

    Nicholas J Clark & Konstans Wells (2020). Dynamic generalised additive models (DGAMs) for forecasting discrete ecological time series. -Methods in Ecology and Evolution. 14:3, 771-784.

    -

    David I Warton, F Guillaume Blanchet, Robert B O’Hara, Otso Ovaskainen, Sara Taskinen, Steven C +Methods in Ecology and Evolution. 14:3, 771-784. +

    +David I Warton, F Guillaume Blanchet, Robert B O’Hara, Otso Ovaskainen, Sara Taskinen, Steven C Walker & Francis KC Hui (2015). So many variables: joint modeling in community ecology. Trends in Ecology & Evolution 30:12, 766-779.

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    See also

    - +

    Author

    @@ -456,7 +457,6 @@

    Examples # View the count distributions for each species library(ggplot2) -#> Warning: package ‘ggplot2’ was built under R version 4.3.3 ggplot(dat, aes(x = count)) + geom_histogram() + facet_wrap(~ species, scales = 'free') @@ -533,19 +533,6 @@

    Examples family = poisson(), chains = 2, silent = 2) -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5, -#> from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4, -#> from stan/lib/stan_math/stan/math/prim/prob.hpp:359, -#> from stan/lib/stan_math/stan/math/prim.hpp:16, -#> from stan/lib/stan_math/stan/math/rev.hpp:16, -#> from stan/lib/stan_math/stan/math.hpp:19, -#> from stan/src/stan/model/model_header.hpp:4, -#> from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc3f925043.hpp:2: -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)': -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers -#> 194 | if (cdf_n < 0.0) -#> | -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory # Plot species-level intercept estimates plot_predictions(mod, condition = 'species', @@ -567,15 +554,36 @@

    Examples} -# Calculate (median) residual spatial correlations -med_loadings <- matrix(apply(as.matrix(mod$model_output, 'lv_coefs'), - 2, median), - nrow = N_species, ncol = 4) -cormat <- cov2cor(tcrossprod(med_loadings)) -rownames(cormat) <- colnames(cormat) <- levels(dat$species) - -# A quick and dirty correlation matrix plot -image(cormat) +# Calculate residual spatial correlations +post_cors <- residual_cor(mod) +names(post_cors) +#> [1] "cor" "cor_lower" "cor_upper" "sig_cor" "cov" +#> [6] "prec" "prec_lower" "prec_upper" "sig_prec" "trace" +# Look at lower and upper credible interval estimates for +# some of the estimated correlations +post_cors$cor[1:5, 1:5] +#> species_1 species_2 species_3 species_4 species_5 +#> species_1 1.00000000 0.09346475 0.6393271 0.547931 0.1366726 +#> species_2 0.09346475 1.00000000 -0.3318063 -0.413929 -0.2074599 +#> species_3 0.63932709 -0.33180627 1.0000000 0.682426 0.1883235 +#> species_4 0.54793102 -0.41392901 0.6824260 1.000000 -0.3718930 +#> species_5 0.13667259 -0.20745989 0.1883235 -0.371893 1.0000000 +post_cors$cor_upper[1:5, 1:5] +#> species_1 species_2 species_3 species_4 species_5 +#> species_1 1.0000000 0.525394676 0.9352867 0.893813412 0.6375748 +#> species_2 0.5253947 1.000000000 0.2078931 0.004141424 0.1750635 +#> species_3 0.9352867 0.207893140 1.0000000 0.908985880 0.6385363 +#> species_4 0.8938134 0.004141424 0.9089859 1.000000000 0.1948296 +#> species_5 0.6375748 0.175063548 0.6385363 0.194829567 1.0000000 +post_cors$cor_lower[1:5, 1:5] +#> species_1 species_2 species_3 species_4 species_5 +#> species_1 1.0000000 -0.4361362 0.2168760 0.1650564 -0.2549159 +#> species_2 -0.4361362 1.0000000 -0.7445722 -0.7369653 -0.6293579 +#> species_3 0.2168760 -0.7445722 1.0000000 0.2784607 -0.2226831 +#> species_4 0.1650564 -0.7369653 0.2784607 1.0000000 -0.7276900 +#> species_5 -0.2549159 -0.6293579 -0.2226831 -0.7276900 1.0000000 +# A quick and dirty plot of the posterior median correlations +image(post_cors$cor) # Posterior predictive checks and ELPD-LOO can ascertain model fit @@ -588,18 +596,18 @@

    Examples#> Computed from 1000 by 600 log-likelihood matrix #> #> Estimate SE -#> elpd_loo -1942.0 41.6 -#> p_loo 351.5 23.9 -#> looic 3884.0 83.1 +#> elpd_loo -1953.6 42.3 +#> p_loo 367.6 25.2 +#> looic 3907.1 84.5 #> ------ #> Monte Carlo SE of elpd_loo is NA. #> #> Pareto k diagnostic values: #> Count Pct. Min. n_eff -#> (-Inf, 0.5] (good) 292 48.7% 81 -#> (0.5, 0.7] (ok) 171 28.5% 32 -#> (0.7, 1] (bad) 109 18.2% 14 -#> (1, Inf) (very bad) 28 4.7% 2 +#> (-Inf, 0.5] (good) 279 46.5% 10 +#> (0.5, 0.7] (ok) 174 29.0% 2 +#> (0.7, 1] (bad) 118 19.7% 1 +#> (1, Inf) (very bad) 29 4.8% 1 #> See help('pareto-k-diagnostic') for details. # Forecast log(counts) for entire region (site value doesn't matter as long diff --git a/docs/reference/mvgam-10.png b/docs/reference/mvgam-10.png index 65d6b581038b7136fd79f3ed4ddb8f7d27e54645..e68af813ded6412b49e80076b5ae04dfbb7ac76a 100644 GIT binary patch literal 163887 zcmeFYby$<(`#y}KqJm)2rG!W$B@KeaNa%p7+hCSE}-NZd2XH!^67+Qh2F>hj$%< zhll_A<_+ML>9~v?;OWL|CHa@YGw^jR(-a6i-EvXTcgMq{4f*qZC30!k5)bbY9_Zx@ zElA4dj1MHm8;Zsah@aY6@n=C%%|B1cx*ogUe+~O`=Vp*pRYeSptS5*}Xlo6VB9S7) zTAlZSK$Vd5eX5|;&l~y*Ngs-tc40r7%nfTT?NI_nR!!-Wa!+b`VRDt(yAx=n=S)1! zG4`|{8+YS$VKKe6?%Lm}{qK+ewZMNYAcUTI#2V0}9gFgEAv^st>z_`fxVKbC`|tg^ zv*p-_FpCHCu`mg)wbtD!^B#Xry66MRF0d#$f~kYW$U9~4Q~-7^ 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    -
    -
    - -
    -

    This function estimates the posterior distribution for Generalised Additive Models (GAMs) that can include -smooth spline functions, specified in the GAM formula, as well as latent temporal processes, -specified by trend_model. Further modelling options include State-Space representations to allow covariates -and dynamic processes to occur on the latent 'State' level while also capturing observation-level effects. -Prior specifications are flexible and explicitly encourage users to apply -prior distributions that actually reflect their beliefs. In addition, model fits can easily be assessed and -compared with posterior predictive checks, forecast comparisons and leave-one-out / leave-future-out cross-validation.

    -
    - -
    -

    Usage

    -
    mvgam(
    -  formula,
    -  trend_formula,
    -  knots,
    -  trend_knots,
    -  data,
    -  data_train,
    -  newdata,
    -  data_test,
    -  run_model = TRUE,
    -  prior_simulation = FALSE,
    -  return_model_data = FALSE,
    -  family = "poisson",
    -  share_obs_params = FALSE,
    -  use_lv = FALSE,
    -  n_lv,
    -  trend_map,
    -  trend_model = "None",
    -  drift = FALSE,
    -  noncentred = FALSE,
    -  chains = 4,
    -  burnin = 500,
    -  samples = 500,
    -  thin = 1,
    -  parallel = TRUE,
    -  threads = 1,
    -  priors,
    -  refit = FALSE,
    -  lfo = FALSE,
    -  residuals = TRUE,
    -  use_stan = TRUE,
    -  backend = getOption("brms.backend", "cmdstanr"),
    -  algorithm = getOption("brms.algorithm", "sampling"),
    -  autoformat = TRUE,
    -  save_all_pars = FALSE,
    -  max_treedepth = 12,
    -  adapt_delta = 0.85,
    -  silent = 1,
    -  jags_path,
    -  ...
    -)
    -
    - -
    -

    Arguments

    -
    formula
    -

    A character string specifying the GAM observation model formula. These are exactly like the formula -for a GLM except that smooth terms, s(), te(), ti(), t2(), as well as time-varying -dynamic() terms and nonparametric gp() terms, can be added to the right hand side -to specify that the linear predictor depends on smooth functions of predictors -(or linear functionals of these). In nmix() family models, the formula is used to -set up a linear predictor for the detection probability. Details of the formula syntax used by mvgam -can be found in mvgam_formulae

    - - -
    trend_formula
    -

    An optional character string specifying the GAM process model formula. If -supplied, a linear predictor will be modelled for the latent trends to capture process model evolution -separately from the observation model. Should not have a response variable specified on the left-hand side -of the formula (i.e. a valid option would be ~ season + s(year)). Also note that you should not use -the identifier series in this formula to specify effects that vary across time series. Instead you should use -trend. This will ensure that models in which a trend_map is supplied will still work consistently -(i.e. by allowing effects to vary across process models, even when some time series share the same underlying -process model). This feature is only currently available for RW(), AR() and VAR() trend models. -In nmix() family models, the trend_formula is used to set up a linear predictor for the underlying -latent abundance. Be aware that it can be very challenging to simultaneously estimate intercept parameters -for both the observation mode (captured by formula) and the process model (captured by trend_formula). -Users are recommended to drop one of these using the - 1 convention in the formula right hand side.

    - - -
    knots
    -

    An optional list containing user specified knot values to be used for basis construction. -For most bases the user simply supplies the knots to be used, which must match up with the k value supplied -(note that the number of knots is not always just k). Different terms can use different numbers of knots, -unless they share a covariate

    - - -
    trend_knots
    -

    As for knots above, this is an optional list of knot values for smooth -functions within the trend_formula

    - - -
    data
    -

    A dataframe or list containing the model response variable and covariates -required by the GAM formula and optional trend_formula. Most models should include columns:

    • series (a factor index of the series IDs; the number of levels should be identical -to the number of unique series labels (i.e. n_series = length(levels(data$series))))

    • -
    • time (numeric or integer index of the time point for each observation). -For most dynamic trend types available in mvgam (see argument trend_model), time should be -measured in discrete, regularly spaced intervals (i.e. c(1, 2, 3, ...)). However you can -use irregularly spaced intervals if using trend_model = CAR(1), though note that any -temporal intervals that are exactly 0 will be adjusted to a very small number -(1e-12) to prevent sampling errors. See an example of CAR() trends in CAR

    • -

    Note however that there are special cases where these identifiers are not needed. For -example, models with hierarchical temporal correlation processes (e.g. AR(gr = region, subgr = species)) -should NOT include a series identifier, as this will be constructed internally (see -mvgam_trends and AR for details). mvgam can also fit models that do not -include a time variable if there are no temporal dynamic structures included (i.e. trend_model = 'None' or -trend_model = ZMVN()). data should also include any other variables to be included in -the linear predictor of formula

    - - -
    data_train
    -

    Deprecated. Still works in place of data but users are recommended to use -data instead for more seamless integration into R workflows

    - - -
    newdata
    -

    Optional dataframe or list of test data containing the same variables -as in data. If included, the -observations in variable y will be set to NA when fitting the model so that posterior -simulations can be obtained

    - - -
    data_test
    -

    Deprecated. Still works in place of newdata but users are recommended to use -newdata instead for more seamless integration into R workflows

    - - -
    run_model
    -

    logical. If FALSE, the model is not fitted but instead the function will -return the model file and the data / initial values that are needed to fit the model outside of mvgam

    - - -
    prior_simulation
    -

    logical. If TRUE, no observations are fed to the model, and instead -simulations from prior distributions are returned

    - - -
    return_model_data
    -

    logical. If TRUE, the list of data that is needed to fit the -model is returned, along with the initial values for smooth and AR parameters, once the model is fitted. -This will be helpful if users wish to modify the model file to add -other stochastic elements that are not currently available in mvgam. -Default is FALSE to reduce -the size of the returned object, unless run_model == FALSE

    - - -
    family
    -

    family specifying the exponential observation family for the series. Currently supported -families are:

    • gaussian() for real-valued data

    • -
    • betar() for proportional data on (0,1)

    • -
    • lognormal() for non-negative real-valued data

    • -
    • student_t() for real-valued data

    • -
    • Gamma() for non-negative real-valued data

    • -
    • bernoulli() for binary data

    • -
    • poisson() for count data

    • -
    • nb() for overdispersed count data

    • -
    • binomial() for count data with imperfect detection when the number of trials is known; -note that the cbind() function must be used to bind the discrete observations and the discrete number -of trials

    • -
    • beta_binomial() as for binomial() but allows for overdispersion

    • -
    • nmix() for count data with imperfect detection when the number of trials -is unknown and should be modeled via a State-Space N-Mixture model. -The latent states are Poisson, capturing the 'true' latent -abundance, while the observation process is Binomial to account for -imperfect detection. -See mvgam_families for an example of how to use this family

    • -

    Note that only nb() and poisson() are available if using JAGS as the backend. -Default is poisson(). -See mvgam_families for more details

    - - -
    share_obs_params
    -

    logical. If TRUE and the family -has additional family-specific observation parameters (e.g. variance components in -student_t() or gaussian(), or dispersion parameters in nb() or betar()), -these parameters will be shared across all outcome variables. This is handy if you have multiple -outcomes (time series in most mvgam models) that you believe share some properties, -such as being from the same species over different spatial units. Default is FALSE.

    - - -
    use_lv
    -

    logical. If TRUE, use dynamic factors to estimate series' -latent trends in a reduced dimension format. Only available for -RW(), AR() and GP() trend models. Defaults to FALSE

    - - -
    n_lv
    -

    integer the number of latent dynamic factors to use if use_lv == TRUE. -Cannot be > n_series. Defaults arbitrarily to min(2, floor(n_series / 2))

    - - -
    trend_map
    -

    Optional data.frame specifying which series should depend on which latent -trends. Useful for allowing multiple series to depend on the same latent trend process, but with -different observation processes. If supplied, a latent factor model is set up by setting -use_lv = TRUE and using the mapping to set up the shared trends. Needs to have column names -series and trend, with integer values in the trend column to state which trend each series -should depend on. The series column should have a single unique entry for each series in the -data (names should perfectly match factor levels of the series variable in data). Note that -if this is supplied, the intercept parameter in the process model will NOT be automatically suppressed. -See examples for details

    - - -
    trend_model
    -

    character or function specifying the time series dynamics for the latent trend. Options are:

    • None (no latent trend component; i.e. the GAM component is all that contributes to the linear predictor, -and the observation process is the only source of error; similarly to what is estimated by gam)

    • -
    • ZMVN or ZMVN() (Zero-Mean Multivariate Normal; only available in Stan)

    • -
    • 'RW' or RW()

    • -
    • 'AR1' or AR(p = 1)

    • -
    • 'AR2' or AR(p = 2)

    • -
    • 'AR3' or AR(p = 3)

    • -
    • 'CAR1' or CAR(p = 1)

    • -
    • 'VAR1' or VAR()(only available in Stan)

    • -
    • 'PWlogistic, 'PWlinear' or PW() (only available in Stan)

    • -
    • 'GP' or GP() (Gaussian Process with squared exponential kernel; -only available in Stan)

    • -

    For all trend types apart from ZMVN(), GP(), CAR() and PW(), moving average and/or correlated -process error terms can also be estimated (for example, RW(cor = TRUE) will set up a -multivariate Random Walk if n_series > 1). It is also possible for many multivariate trends -to estimate hierarchical correlations if the data are structured among levels of -a relevant grouping factor. See mvgam_trends for more details and see ZMVN for an example.

    - - -
    drift
    -

    Deprecated. If you wish to estimate drift parameters, include parametric fixed effects -of 'time' in your formulae instead.

    - - -
    noncentred
    -

    logical Use the non-centred parameterisation for autoregressive -trend models? Setting to TRUE will reparameterise the model to avoid possible -degeneracies that can show up when estimating the latent dynamic random effects. For some -models, this can produce big gains in efficiency, meaning that fewer burnin and sampling -iterations are required for posterior exploration. But for other models, where the data -are highly informative about the latent dynamic processes, this can actually lead to worse -performance. Only available for certain trend models -(i.e. RW(), AR(), or CAR(), or for -trend = 'None' when using a trend_formula). Not yet available for moving average or -correlated error models

    - - -
    chains
    -

    integer specifying the number of parallel chains for the model. Ignored -if algorithm %in% c('meanfield', 'fullrank', 'pathfinder', 'laplace')

    - - -
    burnin
    -

    integer specifying the number of warmup iterations of the Markov chain to run -to tune sampling algorithms. Ignored -if algorithm %in% c('meanfield', 'fullrank', 'pathfinder', 'laplace')

    - - -
    samples
    -

    integer specifying the number of post-warmup iterations of the Markov chain to run for -sampling the posterior distribution

    - - -
    thin
    -

    Thinning interval for monitors. Ignored -if algorithm %in% c('meanfield', 'fullrank', 'pathfinder', 'laplace')

    - - -
    parallel
    -

    logical specifying whether multiple cores should be used for -generating MCMC simulations in parallel. If TRUE, the number of cores to use will be -min(c(chains, parallel::detectCores() - 1))

    - - -
    threads
    -

    integer Experimental option to use multithreading for within-chain -parallelisation in Stan. We recommend its use only if you are experienced with -Stan's reduce_sum function and have a slow running model that cannot be sped -up by any other means. Currently works for all families apart from nmix() and -when using Cmdstan as the backend

    - - -
    priors
    -

    An optional data.frame with prior -definitions (in JAGS or Stan syntax) or, preferentially, If using Stan, a vector containing -objects of class brmsprior (see. prior for details). -See get_mvgam_priors and Details' for more information on changing default prior distributions

    - - -
    refit
    -

    Logical indicating whether this is a refit, called using update.mvgam. Users should leave -as FALSE

    - - -
    lfo
    -

    Logical indicating whether this is part of a call to lfo_cv.mvgam. Returns a -lighter version of the model with no residuals and fewer monitored parameters to speed up -post-processing. But other downstream functions will not work properly, so users should always -leave this set as FALSE

    - - -
    residuals
    -

    Logical indicating whether to compute series-level randomized quantile residuals and include -them as part of the returned object. Defaults to TRUE, but you can set to FALSE to save -computational time and reduce the size of the returned object (users can always add residuals to -an object of class mvgam using add_residuals)

    - - -
    use_stan
    -

    Logical. If TRUE, the model will be compiled and sampled using -Hamiltonian Monte Carlo with a call to cmdstan_model or -a call to stan. Note that -there are many more options when using Stan vs JAGS

    - - -
    backend
    -

    Character string naming the package to use as the backend for fitting -the Stan model (if use_stan = TRUE). Options are "cmdstanr" (the default) or "rstan". Can be set globally -for the current R session via the "brms.backend" option (see options). Details on -the rstan and cmdstanr packages are available at https://mc-stan.org/rstan/ and -https://mc-stan.org/cmdstanr/, respectively

    - - -
    algorithm
    -

    Character string naming the estimation approach to use. -Options are "sampling" for MCMC (the default), "meanfield" for -variational inference with factorized normal distributions, -"fullrank" for variational inference with a multivariate normal -distribution, "laplace" for a Laplace approximation (only available -when using cmdstanr as the backend) or "pathfinder" for the pathfinder -algorithm (only currently available when using cmdstanr as the backend). -Can be set globally for the current R session via the -"brms.algorithm" option (see options). Limited testing -suggests that "meanfield" performs best out of the non-MCMC approximations for -dynamic GAMs, possibly because of the difficulties estimating covariances among the -many spline parameters and latent trend parameters. But rigorous testing has not -been carried out

    - - -
    autoformat
    -

    Logical. Use the stanc parser to automatically format the -Stan code and check for deprecations. Only for development purposes, so leave to TRUE

    - - -
    save_all_pars
    -

    Logical flag to indicate if draws from all -variables defined in Stan's parameters block should be saved -(default is FALSE).

    - - -
    max_treedepth
    -

    positive integer placing a cap on the number of simulation steps evaluated during each iteration when -use_stan == TRUE. Default is 12. Increasing this value can sometimes help with exploration of complex -posterior geometries, but it is rarely fruitful to go above a max_treedepth of 14

    - - -
    adapt_delta
    -

    positive numeric between 0 and 1 defining the target average proposal acceptance probability -during Stan's adaptation period, if use_stan == TRUE. Default is 0.8. In general you should not need to change adapt_delta -unless you see a warning message about divergent transitions, in which case you can increase adapt_delta from the default -to a value closer to 1 (e.g. from 0.95 to 0.99, or from 0.99 to 0.999, etc). -The step size used by the numerical integrator is a function of adapt_delta in that increasing -adapt_delta will result in a smaller step size and fewer divergences. Increasing adapt_delta will -typically result in a slower sampler, but it will always lead to a more robust sampler

    - - -
    silent
    -

    Verbosity level between 0 and 2. If 1 (the default), most of the informational -messages of compiler and sampler are suppressed. If 2, even more messages are suppressed. The -actual sampling progress is still printed. Set refresh = 0 to turn this off as well. If using -backend = "rstan" you can also set open_progress = FALSE to prevent opening additional -progress bars.

    - - -
    jags_path
    -

    Optional character vector specifying the path to the location of the JAGS executable (.exe) to use -for modelling if use_stan == FALSE. If missing, the path will be recovered from a call to findjags

    - - -
    ...
    -

    Further arguments passed to Stan. -For backend = "rstan" the arguments are passed to -sampling or vb. -For backend = "cmdstanr" the arguments are passed to the -cmdstanr::sample, cmdstanr::variational, -cmdstanr::laplace or -cmdstanr::pathfinder method

    - -
    -
    -

    Value

    - - -

    A list object of class mvgam containing model output, the text representation of the model file, -the mgcv model output (for easily generating simulations at -unsampled covariate values), Dunn-Smyth residuals for each series and key information needed -for other functions in the package. See mvgam-class for details. -Use methods(class = "mvgam") for an overview on available methods.

    -
    -
    -

    Details

    -

    Dynamic GAMs are useful when we wish to predict future values from time series that show temporal dependence -but we do not want to rely on extrapolating from a smooth term (which can sometimes lead to unpredictable and unrealistic behaviours). -In addition, smooths can often try to wiggle excessively to capture any autocorrelation that is present in a time series, -which exacerbates the problem of forecasting ahead. As GAMs are very naturally viewed through a Bayesian lens, and we often -must model time series that show complex distributional features and missing data, parameters for mvgam models are estimated -in a Bayesian framework using Markov Chain Monte Carlo by default. A general overview is provided -in the primary vignettes: vignette("mvgam_overview") and vignette("data_in_mvgam"). -For a full list of available vignettes see vignette(package = "mvgam") -

    Formula syntax: Details of the formula syntax used by mvgam can be found in -mvgam_formulae. Note that it is possible to supply an empty formula where -there are no predictors or intercepts in the observation model (i.e. y ~ 0 or y ~ -1). -In this case, an intercept-only observation model will be set up but the intercept coefficient -will be fixed at zero. This can be handy if you wish to fit pure State-Space models where -the variation in the dynamic trend controls the average expectation, and/or where intercepts -are non-identifiable (as in piecewise trends, see examples below) -

    Families and link functions: Details of families supported by mvgam can be found in -mvgam_families. -

    Trend models: Details of latent error process models supported by mvgam can be found in -mvgam_trends. -

    Priors: Default priors for intercepts and any scale parameters are generated -using the same practice as brms. Prior distributions for most important model parameters can be -altered by the user to inspect model -sensitivities to given priors (see get_mvgam_priors for details). -Note that latent trends are estimated on the link scale so choose priors -accordingly. However more control over the model specification can be accomplished by first using mvgam as a -baseline, then editing the returned model accordingly. The model file can be edited and run outside -of mvgam by setting run_model = FALSE and this is encouraged for complex -modelling tasks. Note, no priors are -formally checked to ensure they are in the right syntax for the respective -probabilistic modelling framework, so it is -up to the user to ensure these are correct (i.e. use dnorm for normal -densities in JAGS, with the mean and precision -parameterisation; but use normal for normal densities in Stan, with the mean -and standard deviation parameterisation) -

    Random effects: For any smooth terms using the random effect basis (smooth.construct.re.smooth.spec), -a non-centred parameterisation is automatically employed to avoid degeneracies that are common in hierarchical models. -Note however that centred versions may perform better for series that are particularly informative, so as with any -foray into Bayesian modelling, it is worth building an understanding of the model's assumptions and limitations by following a -principled workflow. Also note that models are parameterised using drop.unused.levels = FALSE in jagam -to ensure predictions can be made for all levels of the supplied factor variable -

    Observation level parameters: When more than one series is included in data and an -observation family that contains more than one parameter is used, additional observation family parameters -(i.e. phi for nb() or sigma for gaussian()) are -by default estimated independently for each series. But if you wish for the series to share -the same observation parameters, set share_obs_params = TRUE -

    Factor regularisation: When using a dynamic factor model for the trends with JAGS factor precisions are given -regularized penalty priors to theoretically allow some factors to be dropped from the model by squeezing increasing -factors' variances to zero. This is done to help protect against selecting too many latent factors than are needed to -capture dependencies in the data, so it can often be advantageous to set n_lv to a slightly larger number. However -larger numbers of factors do come with additional computational costs so these should be balanced as well. When using -Stan, all factors are parameterised with fixed variance parameters -

    Residuals: For each series, randomized quantile (i.e. Dunn-Smyth) residuals are calculated for inspecting model diagnostics -If the fitted model is appropriate then Dunn-Smyth residuals will be standard normal in distribution and no -autocorrelation will be evident. When a particular observation is missing, the residual is calculated by comparing independent -draws from the model's posterior distribution -

    Using Stan: mvgam is primarily designed to use Hamiltonian Monte Carlo for parameter estimation -via the software Stan (using either the cmdstanr or rstan interface). -There are great advantages when using Stan over Gibbs / Metropolis Hastings samplers, which includes the option -to estimate nonlinear effects via Hilbert space approximate Gaussian Processes, -the availability of a variety of inference algorithms (i.e. variational inference, laplacian inference etc...) and -capabilities to enforce stationarity for complex Vector Autoregressions. -Because of the many advantages of Stan over JAGS, -further development of the package will only be applied to Stan. This includes the planned addition -of more response distributions, plans to handle zero-inflation, and plans to incorporate a greater -variety of trend models. Users are strongly encouraged to opt for Stan over JAGS in any proceeding workflows -

    How to start?: The mvgam cheatsheet is a -good starting place if you are just learning to use the package. It gives an overview of the package's key functions and objects, -as well as providing a reasonable workflow that new users can follow. In general it is recommended to

    -
    -

    References

    -

    Nicholas J Clark & Konstans Wells (2020). Dynamic generalised additive models (DGAMs) for forecasting discrete ecological time series. -Methods in Ecology and Evolution. 14:3, 771-784.

    -
    - -
    -

    Author

    -

    Nicholas J Clark

    -
    - -
    -

    Examples

    -
    # \donttest{
    -# Simulate a collection of three time series that have shared seasonal dynamics
    -# and independent AR1 trends, with a Poisson observation process
    -set.seed(0)
    -dat <- sim_mvgam(T = 80,
    -                n_series = 3,
    -                mu = 2,
    -                trend_model = AR(p = 1),
    -                prop_missing = 0.1,
    -                prop_trend = 0.6)
    -
    -# Plot key summary statistics for a single series
    -plot_mvgam_series(data = dat$data_train, series = 1)
    -
    -
    -# Plot all series together
    -plot_mvgam_series(data = dat$data_train, series = 'all')
    -
    -
    -# Formulate a model using Stan where series share a cyclic smooth for
    -# seasonality and each series has an independent AR1 temporal process.
    -# Note that 'noncentred = TRUE' will likely give performance gains.
    -# Set run_model = FALSE to inspect the returned objects
    -mod1 <- mvgam(formula = y ~ s(season, bs = 'cc', k = 6),
    -             data = dat$data_train,
    -             trend_model = AR(),
    -             family = poisson(),
    -             noncentred = TRUE,
    -             use_stan = TRUE,
    -             run_model = FALSE)
    -
    -# View the model code in Stan language
    -stancode(mod1)
    -#> // Stan model code generated by package mvgam
    -#> data {
    -#>   int<lower=0> total_obs; // total number of observations
    -#>   int<lower=0> n; // number of timepoints per series
    -#>   int<lower=0> n_sp; // number of smoothing parameters
    -#>   int<lower=0> n_series; // number of series
    -#>   int<lower=0> num_basis; // total number of basis coefficients
    -#>   vector[num_basis] zero; // prior locations for basis coefficients
    -#>   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
    -#>   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
    -#>   matrix[4, 4] S1; // mgcv smooth penalty matrix S1
    -#>   int<lower=0> n_nonmissing; // number of nonmissing observations
    -#>   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
    -#>   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
    -#>   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
    -#> }
    -#> parameters {
    -#>   // raw basis coefficients
    -#>   vector[num_basis] b_raw;
    -#>   
    -#>   // latent trend AR1 terms
    -#>   vector<lower=-1, upper=1>[n_series] ar1;
    -#>   
    -#>   // latent trend variance parameters
    -#>   vector<lower=0>[n_series] sigma;
    -#>   
    -#>   // raw latent trends
    -#>   matrix[n, n_series] trend_raw;
    -#>   
    -#>   // smoothing parameters
    -#>   vector<lower=0>[n_sp] lambda;
    -#> }
    -#> transformed parameters {
    -#>   // basis coefficients
    -#>   vector[num_basis] b;
    -#>   
    -#>   // latent trends
    -#>   matrix[n, n_series] trend;
    -#>   trend = trend_raw .* rep_matrix(sigma', rows(trend_raw));
    -#>   for (s in 1 : n_series) {
    -#>     trend[2 : n, s] += ar1[s] * trend[1 : (n - 1), s];
    -#>   }
    -#>   b[1 : num_basis] = b_raw[1 : num_basis];
    -#> }
    -#> model {
    -#>   // prior for (Intercept)...
    -#>   b_raw[1] ~ student_t(3, 1.9, 2.5);
    -#>   
    -#>   // prior for s(season)...
    -#>   b_raw[2 : 5] ~ multi_normal_prec(zero[2 : 5], S1[1 : 4, 1 : 4] * lambda[1]);
    -#>   
    -#>   // priors for AR parameters
    -#>   ar1 ~ std_normal();
    -#>   
    -#>   // priors for smoothing parameters
    -#>   lambda ~ normal(5, 30);
    -#>   
    -#>   // priors for latent trend variance parameters
    -#>   sigma ~ student_t(3, 0, 2.5);
    -#>   to_vector(trend_raw) ~ std_normal();
    -#>   {
    -#>     // likelihood functions
    -#>     vector[n_nonmissing] flat_trends;
    -#>     flat_trends = to_vector(trend)[obs_ind];
    -#>     flat_ys ~ poisson_log_glm(append_col(flat_xs, flat_trends), 0.0,
    -#>                               append_row(b, 1.0));
    -#>   }
    -#> }
    -#> generated quantities {
    -#>   vector[total_obs] eta;
    -#>   matrix[n, n_series] mus;
    -#>   vector[n_sp] rho;
    -#>   vector[n_series] tau;
    -#>   array[n, n_series] int ypred;
    -#>   rho = log(lambda);
    -#>   for (s in 1 : n_series) {
    -#>     tau[s] = pow(sigma[s], -2.0);
    -#>   }
    -#>   
    -#>   // posterior predictions
    -#>   eta = X * b;
    -#>   for (s in 1 : n_series) {
    -#>     mus[1 : n, s] = eta[ytimes[1 : n, s]] + trend[1 : n, s];
    -#>     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
    -#>   }
    -#> }
    -#> 
    -#> 
    -
    -# View the data objects needed to fit the model in Stan
    -sdata1 <- standata(mod1)
    -str(sdata1)
    -#> List of 18
    -#>  $ y           : num [1:60, 1:3] 12 17 12 31 30 8 0 1 3 5 ...
    -#>  $ n           : int 60
    -#>  $ X           : num [1:180, 1:5] 1 1 1 1 1 1 1 1 1 1 ...
    -#>   ..- attr(*, "dimnames")=List of 2
    -#>   .. ..$ : NULL
    -#>   .. ..$ : chr [1:5] "X.Intercept." "V2" "V3" "V4" ...
    -#>  $ S1          : num [1:4, 1:4] 1.244 -0.397 0.384 0.619 -0.397 ...
    -#>  $ zero        : num [1:5] 0 0 0 0 0
    -#>  $ p_coefs     : Named num 0
    -#>   ..- attr(*, "names")= chr "(Intercept)"
    -#>  $ p_taus      : num 1.09
    -#>  $ ytimes      : int [1:60, 1:3] 1 4 7 10 13 16 19 22 25 28 ...
    -#>  $ n_series    : int 3
    -#>  $ sp          : Named num 0.368
    -#>   ..- attr(*, "names")= chr "s(season)"
    -#>  $ y_observed  : num [1:60, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
    -#>  $ total_obs   : int 180
    -#>  $ num_basis   : int 5
    -#>  $ n_sp        : num 1
    -#>  $ n_nonmissing: int 161
    -#>  $ obs_ind     : int [1:161] 1 2 3 4 5 6 7 8 9 10 ...
    -#>  $ flat_ys     : num [1:161] 12 17 12 31 30 8 0 1 3 5 ...
    -#>  $ flat_xs     : num [1:161, 1:5] 1 1 1 1 1 1 1 1 1 1 ...
    -#>   ..- attr(*, "dimnames")=List of 2
    -#>   .. ..$ : NULL
    -#>   .. ..$ : chr [1:5] "X.Intercept." "V2" "V3" "V4" ...
    -#>  - attr(*, "trend_model")= chr "AR1"
    -
    -# Now fit the model
    -mod1 <- mvgam(formula = y ~ s(season, bs = 'cc', k = 6),
    -              data = dat$data_train,
    -              trend_model = AR(),
    -              family = poisson(),
    -              noncentred = TRUE,
    -              chains = 2)
    -#> Compiling Stan program using cmdstanr
    -#> 
    -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
    -#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math.hpp:19,
    -#>                  from stan/src/stan/model/model_header.hpp:4,
    -#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc1a343381.hpp:2:
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
    -#>   194 |       if (cdf_n < 0.0)
    -#>       | 
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
    -#> Start sampling
    -#> Running MCMC with 2 parallel chains...
    -#> 
    -#> Chain 1 Iteration:   1 / 1000 [  0%]  (Warmup) 
    -#> Chain 2 Iteration:   1 / 1000 [  0%]  (Warmup) 
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    -#> Chain 2 Iteration: 1000 / 1000 [100%]  (Sampling) 
    -#> Chain 1 finished in 1.6 seconds.
    -#> Chain 2 finished in 1.5 seconds.
    -#> 
    -#> Both chains finished successfully.
    -#> Mean chain execution time: 1.6 seconds.
    -#> Total execution time: 1.8 seconds.
    -#> 
    -
    -# Extract the model summary
    -summary(mod1)
    -#> GAM formula:
    -#> y ~ s(season, bs = "cc", k = 6)
    -#> <environment: 0x0000016202170900>
    -#> 
    -#> Family:
    -#> poisson
    -#> 
    -#> Link function:
    -#> log
    -#> 
    -#> Trend model:
    -#> AR()
    -#> 
    -#> N series:
    -#> 3 
    -#> 
    -#> N timepoints:
    -#> 60 
    -#> 
    -#> Status:
    -#> Fitted using Stan 
    -#> 2 chains, each with iter = 1000; warmup = 500; thin = 1 
    -#> Total post-warmup draws = 1000
    -#> 
    -#> 
    -#> GAM coefficient (beta) estimates:
    -#>              2.5%    50%   97.5% Rhat n_eff
    -#> (Intercept)  1.80  2.000  2.1000 1.01   350
    -#> s(season).1  0.15  0.370  0.6000 1.01   199
    -#> s(season).2 -0.33 -0.091  0.1400 1.00   404
    -#> s(season).3 -1.00 -0.710 -0.4500 1.01   372
    -#> s(season).4 -0.52 -0.270 -0.0059 1.01   528
    -#> 
    -#> Approximate significance of GAM smooths:
    -#>            edf Ref.df Chi.sq p-value    
    -#> s(season) 3.69      4   26.7 1.1e-06 ***
    -#> ---
    -#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    -#> 
    -#> Latent trend parameter AR estimates:
    -#>             2.5%   50% 97.5% Rhat n_eff
    -#> ar1[1]    0.2400  0.73  0.98 1.01   274
    -#> ar1[2]   -0.9300 -0.36  0.18 1.01   147
    -#> ar1[3]    0.0021  0.38  0.92 1.02   149
    -#> sigma[1]  0.3900  0.53  0.73 1.00   314
    -#> sigma[2]  0.3900  0.55  0.77 1.00   267
    -#> sigma[3]  0.4300  0.59  0.78 1.00   309
    -#> 
    -#> Stan MCMC diagnostics:
    -#> n_eff / iter looks reasonable for all parameters
    -#> Rhat looks reasonable for all parameters
    -#> 0 of 1000 iterations ended with a divergence (0%)
    -#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%)
    -#> E-FMI indicated no pathological behavior
    -#> 
    -#> Samples were drawn using NUTS(diag_e) at Sat Nov 02 9:36:31 PM 2024.
    -#> For each parameter, n_eff is a crude measure of effective sample size,
    -#> and Rhat is the potential scale reduction factor on split MCMC chains
    -#> (at convergence, Rhat = 1)
    -
    -# Plot the estimated historical trend and forecast for one series
    -plot(mod1, type = 'trend', series = 1)
    -
    -plot(mod1, type = 'forecast', series = 1)
    -
    -
    -# Residual diagnostics
    -plot(mod1, type = 'residuals', series = 1)
    -
    -resids <- residuals(mod1)
    -str(resids)
    -#>  num [1:180, 1:4] 0.0319 -0.06 0.1531 0.5229 -0.0881 ...
    -#>  - attr(*, "dimnames")=List of 2
    -#>   ..$ : NULL
    -#>   ..$ : chr [1:4] "Estimate" "Est.Error" "Q2.5" "Q97.5"
    -
    -# Compute the forecast using covariate information in data_test
    -fc <- forecast(mod1, newdata = dat$data_test)
    -str(fc)
    -#> List of 16
    -#>  $ call              :Class 'formula'  language y ~ s(season, bs = "cc", k = 6)
    -#>   .. ..- attr(*, ".Environment")=<environment: 0x0000016202170900> 
    -#>  $ trend_call        : NULL
    -#>  $ family            : chr "poisson"
    -#>  $ family_pars       : NULL
    -#>  $ trend_model       :List of 7
    -#>   ..$ trend_model: chr "AR1"
    -#>   ..$ ma         : logi FALSE
    -#>   ..$ cor        : logi FALSE
    -#>   ..$ unit       : chr "time"
    -#>   ..$ gr         : chr "NA"
    -#>   ..$ subgr      : chr "series"
    -#>   ..$ label      : language AR()
    -#>   ..- attr(*, "class")= chr "mvgam_trend"
    -#>  $ drift             : logi FALSE
    -#>  $ use_lv            : logi FALSE
    -#>  $ fit_engine        : chr "stan"
    -#>  $ type              : chr "response"
    -#>  $ series_names      : Factor w/ 3 levels "series_1","series_2",..: 1 2 3
    -#>  $ train_observations:List of 3
    -#>   ..$ series_1: int [1:60] 12 17 12 31 30 8 0 1 3 5 ...
    -#>   ..$ series_2: int [1:60] 8 8 21 7 6 NA 1 8 9 3 ...
    -#>   ..$ series_3: int [1:60] 10 NA 7 2 1 11 4 NA 5 4 ...
    -#>  $ train_times       : int [1:60] 1 2 3 4 5 6 7 8 9 10 ...
    -#>  $ test_observations :List of 3
    -#>   ..$ series_1: int [1:20] 4 9 5 6 4 11 NA 3 8 11 ...
    -#>   ..$ series_2: int [1:20] 19 51 19 10 3 6 7 1 6 4 ...
    -#>   ..$ series_3: int [1:20] 10 NA 8 5 16 13 0 0 3 2 ...
    -#>  $ test_times        : int [1:20] 61 62 63 64 65 66 67 68 69 70 ...
    -#>  $ hindcasts         :List of 3
    -#>   ..$ series_1: num [1:1000, 1:60] 22 9 10 1 18 15 11 19 10 15 ...
    -#>   .. ..- attr(*, "dimnames")=List of 2
    -#>   .. .. ..$ : NULL
    -#>   .. .. ..$ : chr [1:60] "ypred[1,1]" "ypred[2,1]" "ypred[3,1]" "ypred[4,1]" ...
    -#>   ..$ series_2: num [1:1000, 1:60] 12 13 5 5 12 7 16 12 6 9 ...
    -#>   .. ..- attr(*, "dimnames")=List of 2
    -#>   .. .. ..$ : NULL
    -#>   .. .. ..$ : chr [1:60] "ypred[1,2]" "ypred[2,2]" "ypred[3,2]" "ypred[4,2]" ...
    -#>   ..$ series_3: num [1:1000, 1:60] 5 11 9 9 6 15 5 6 14 12 ...
    -#>   .. ..- attr(*, "dimnames")=List of 2
    -#>   .. .. ..$ : NULL
    -#>   .. .. ..$ : chr [1:60] "ypred[1,3]" "ypred[2,3]" "ypred[3,3]" "ypred[4,3]" ...
    -#>  $ forecasts         :List of 3
    -#>   ..$ series_1: int [1:1000, 1:20] 5 4 12 13 16 12 20 12 5 13 ...
    -#>   ..$ series_2: int [1:1000, 1:20] 23 13 7 7 4 3 3 30 7 7 ...
    -#>   ..$ series_3: int [1:1000, 1:20] 7 6 9 6 5 6 19 3 18 22 ...
    -#>  - attr(*, "class")= chr "mvgam_forecast"
    -plot(fc)
    -#> Out of sample DRPS:
    -#> 55.837128
    -
    -
    -# Plot the estimated seasonal smooth function
    -plot(mod1, type = 'smooths')
    -
    -
    -# Plot estimated first derivatives of the smooth
    -plot(mod1, type = 'smooths', derivatives = TRUE)
    -
    -
    -# Plot partial residuals of the smooth
    -plot(mod1, type = 'smooths', residuals = TRUE)
    -
    -
    -# Plot posterior realisations for the smooth
    -plot(mod1, type = 'smooths', realisations = TRUE)
    -
    -
    -# Plot conditional response predictions using marginaleffects
    -library(marginaleffects)
    -conditional_effects(mod1)
    -#> Warning: Removed 19 rows containing missing values or values outside the scale range
    -#> (`geom_point()`).
    -
    -plot_predictions(mod1, condition = 'season', points = 0.5)
    -#> Warning: Removed 19 rows containing missing values or values outside the scale range
    -#> (`geom_point()`).
    -
    -
    -# Generate posterior predictive checks using bayesplot
    -pp_check(mod1)
    -#> Using 10 posterior draws for ppc type 'dens_overlay' by default.
    -#> Warning: NA responses are not shown in 'pp_check'.
    -
    -
    -# Extract observation model beta coefficient draws as a data.frame
    -beta_draws_df <- as.data.frame(mod1, variable = 'betas')
    -head(beta_draws_df)
    -#>   (Intercept) s(season).1 s(season).2 s(season).3 s(season).4
    -#> 1     1.94416    0.394466 -0.06900860   -0.783359   -0.426288
    -#> 2     1.92798    0.271471 -0.00850006   -0.685065   -0.244868
    -#> 3     1.90193    0.230704 -0.04661740   -0.676646   -0.314741
    -#> 4     1.88637    0.430494 -0.30333200   -0.634353   -0.345208
    -#> 5     1.97914    0.322658  0.15346600   -0.703236   -0.263105
    -#> 6     2.02798    0.407478  0.05122050   -0.581718   -0.361806
    -str(beta_draws_df)
    -#> 'data.frame':	1000 obs. of  5 variables:
    -#>  $ (Intercept): num  1.94 1.93 1.9 1.89 1.98 ...
    -#>  $ s(season).1: num  0.394 0.271 0.231 0.43 0.323 ...
    -#>  $ s(season).2: num  -0.069 -0.0085 -0.0466 -0.3033 0.1535 ...
    -#>  $ s(season).3: num  -0.783 -0.685 -0.677 -0.634 -0.703 ...
    -#>  $ s(season).4: num  -0.426 -0.245 -0.315 -0.345 -0.263 ...
    -
    -# Investigate model fit
    -mc.cores.def <- getOption('mc.cores')
    -options(mc.cores = 1)
    -loo(mod1)
    -#> Warning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
    -#> 
    -#> Computed from 1000 by 161 log-likelihood matrix
    -#> 
    -#>          Estimate   SE
    -#> elpd_loo   -452.2  8.5
    -#> p_loo        91.6  4.8
    -#> looic       904.4 17.0
    -#> ------
    -#> Monte Carlo SE of elpd_loo is NA.
    -#> 
    -#> Pareto k diagnostic values:
    -#>                          Count Pct.    Min. n_eff
    -#> (-Inf, 0.5]   (good)     22    13.7%   131       
    -#>  (0.5, 0.7]   (ok)       61    37.9%   61        
    -#>    (0.7, 1]   (bad)      63    39.1%   19        
    -#>    (1, Inf)   (very bad) 15     9.3%   4         
    -#> See help('pareto-k-diagnostic') for details.
    -options(mc.cores = mc.cores.def)
    -
    -
    -# Example of supplying a trend_map so that some series can share
    -# latent trend processes
    -sim <- sim_mvgam(n_series = 3)
    -mod_data <- sim$data_train
    -
    -# Here, we specify only two latent trends; series 1 and 2 share a trend,
    -# while series 3 has it's own unique latent trend
    -trend_map <- data.frame(series = unique(mod_data$series),
    -                       trend = c(1, 1, 2))
    -
    -# Fit the model using AR1 trends
    -mod <- mvgam(y ~ s(season, bs = 'cc', k = 6),
    -             trend_map = trend_map,
    -             trend_model = AR(),
    -             data = mod_data,
    -             return_model_data = TRUE,
    -             chains = 2)
    -#> Compiling Stan program using cmdstanr
    -#> 
    -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
    -#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math.hpp:19,
    -#>                  from stan/src/stan/model/model_header.hpp:4,
    -#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc26e518ee.hpp:2:
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
    -#>   194 |       if (cdf_n < 0.0)
    -#>       | 
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
    -#> Start sampling
    -#> Running MCMC with 2 parallel chains...
    -#> 
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    -#> Chain 2 finished in 3.3 seconds.
    -#> 
    -#> Both chains finished successfully.
    -#> Mean chain execution time: 2.6 seconds.
    -#> Total execution time: 3.5 seconds.
    -#> 
    -
    -# The mapping matrix is now supplied as data to the model in the 'Z' element
    -mod$model_data$Z
    -#>      [,1] [,2]
    -#> [1,]    1    0
    -#> [2,]    1    0
    -#> [3,]    0    1
    -code(mod)
    -#> // Stan model code generated by package mvgam
    -#> data {
    -#>   int<lower=0> total_obs; // total number of observations
    -#>   int<lower=0> n; // number of timepoints per series
    -#>   int<lower=0> n_lv; // number of dynamic factors
    -#>   int<lower=0> n_sp; // number of smoothing parameters
    -#>   int<lower=0> n_series; // number of series
    -#>   matrix[n_series, n_lv] Z; // matrix mapping series to latent trends
    -#>   int<lower=0> num_basis; // total number of basis coefficients
    -#>   vector[num_basis] zero; // prior locations for basis coefficients
    -#>   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
    -#>   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
    -#>   matrix[4, 4] S1; // mgcv smooth penalty matrix S1
    -#>   int<lower=0> n_nonmissing; // number of nonmissing observations
    -#>   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
    -#>   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
    -#>   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
    -#> }
    -#> transformed data {
    -#>   
    -#> }
    -#> parameters {
    -#>   // raw basis coefficients
    -#>   vector[num_basis] b_raw;
    -#>   
    -#>   // latent factor SD terms
    -#>   vector<lower=0>[n_lv] sigma;
    -#>   
    -#>   // latent factor AR1 terms
    -#>   vector<lower=-1, upper=1>[n_lv] ar1;
    -#>   
    -#>   // dynamic factors
    -#>   matrix[n, n_lv] LV;
    -#>   
    -#>   // smoothing parameters
    -#>   vector<lower=0>[n_sp] lambda;
    -#> }
    -#> transformed parameters {
    -#>   // trends and dynamic factor loading matrix
    -#>   matrix[n, n_series] trend;
    -#>   
    -#>   // basis coefficients
    -#>   vector[num_basis] b;
    -#>   b[1 : num_basis] = b_raw[1 : num_basis];
    -#>   
    -#>   // derived latent trends
    -#>   for (i in 1 : n) {
    -#>     for (s in 1 : n_series) {
    -#>       trend[i, s] = dot_product(Z[s,  : ], LV[i,  : ]);
    -#>     }
    -#>   }
    -#> }
    -#> model {
    -#>   // prior for (Intercept)...
    -#>   b_raw[1] ~ student_t(3, 0, 2.5);
    -#>   
    -#>   // prior for s(season)...
    -#>   b_raw[2 : 5] ~ multi_normal_prec(zero[2 : 5], S1[1 : 4, 1 : 4] * lambda[1]);
    -#>   
    -#>   // priors for AR parameters
    -#>   ar1 ~ std_normal();
    -#>   
    -#>   // priors for smoothing parameters
    -#>   lambda ~ normal(5, 30);
    -#>   
    -#>   // priors for factor SD parameters
    -#>   sigma ~ student_t(3, 0, 2.5);
    -#>   
    -#>   // dynamic factor estimates
    -#>   LV[1, 1 : n_lv] ~ normal(0, sigma);
    -#>   for (j in 1 : n_lv) {
    -#>     LV[2 : n, j] ~ normal(ar1[j] * LV[1 : (n - 1), j], sigma[j]);
    -#>   }
    -#>   {
    -#>     // likelihood functions
    -#>     vector[n_nonmissing] flat_trends;
    -#>     flat_trends = to_vector(trend)[obs_ind];
    -#>     flat_ys ~ poisson_log_glm(append_col(flat_xs, flat_trends), 0.0,
    -#>                               append_row(b, 1.0));
    -#>   }
    -#> }
    -#> generated quantities {
    -#>   vector[total_obs] eta;
    -#>   matrix[n, n_series] mus;
    -#>   vector[n_sp] rho;
    -#>   vector[n_lv] penalty;
    -#>   array[n, n_series] int ypred;
    -#>   rho = log(lambda);
    -#>   penalty = 1.0 / (sigma .* sigma);
    -#>   
    -#>   matrix[n_series, n_lv] lv_coefs = Z;
    -#>   // posterior predictions
    -#>   eta = X * b;
    -#>   for (s in 1 : n_series) {
    -#>     mus[1 : n, s] = eta[ytimes[1 : n, s]] + trend[1 : n, s];
    -#>     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
    -#>   }
    -#> }
    -#> 
    -#> 
    -
    -# The first two series share an identical latent trend; the third is different
    -plot(mod, type = 'trend', series = 1)
    -
    -plot(mod, type = 'trend', series = 2)
    -
    -plot(mod, type = 'trend', series = 3)
    -
    -
    -
    -# Example of how to use dynamic coefficients
    -# Simulate a time-varying coefficient for the effect of temperature
    -set.seed(123)
    -N <- 200
    -beta_temp <- vector(length = N)
    -beta_temp[1] <- 0.4
    -for(i in 2:N){
    - beta_temp[i] <- rnorm(1, mean = beta_temp[i - 1] - 0.0025, sd = 0.05)
    -}
    -plot(beta_temp)
    -
    -
    -# Simulate a covariate called 'temp'
    -temp <- rnorm(N, sd = 1)
    -
    -# Simulate the Gaussian observation process
    -out <- rnorm(N, mean = 4 + beta_temp * temp,
    -             sd = 0.5)
    -
    -# Gather necessary data into a data.frame; split into training / testing
    -data = data.frame(out, temp, time = seq_along(temp))
    -data_train <- data[1:180,]
    -data_test <- data[181:200,]
    -
    -# Fit the model using the dynamic() formula helper
    -mod <- mvgam(out ~
    -              dynamic(temp,
    -                      scale = FALSE,
    -                      k = 40),
    -             family = gaussian(),
    -             data = data_train,
    -             newdata = data_test,
    -             chains = 2)
    -#> Compiling Stan program using cmdstanr
    -#> 
    -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
    -#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math.hpp:19,
    -#>                  from stan/src/stan/model/model_header.hpp:4,
    -#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc1b1bf3.hpp:2:
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
    -#>   194 |       if (cdf_n < 0.0)
    -#>       | 
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
    -#> Start sampling
    -#> Running MCMC with 2 parallel chains...
    -#> 
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    -#> Chain 1 finished in 1.4 seconds.
    -#> 
    -#> Both chains finished successfully.
    -#> Mean chain execution time: 1.4 seconds.
    -#> Total execution time: 1.6 seconds.
    -#> 
    -
    -# Inspect the model summary, forecast and time-varying coefficient distribution
    -summary(mod)
    -#> GAM formula:
    -#> out ~ gp(time, by = temp, c = 5/4, k = 40, scale = FALSE)
    -#> <environment: 0x0000016202170900>
    -#> 
    -#> Family:
    -#> gaussian
    -#> 
    -#> Link function:
    -#> identity
    -#> 
    -#> Trend model:
    -#> None
    -#> 
    -#> N series:
    -#> 1 
    -#> 
    -#> N timepoints:
    -#> 200 
    -#> 
    -#> Status:
    -#> Fitted using Stan 
    -#> 2 chains, each with iter = 1000; warmup = 500; thin = 1 
    -#> Total post-warmup draws = 1000
    -#> 
    -#> 
    -#> Observation error parameter estimates:
    -#>              2.5%  50% 97.5% Rhat n_eff
    -#> sigma_obs[1] 0.44 0.49  0.55    1  1179
    -#> 
    -#> GAM coefficient (beta) estimates:
    -#>                    2.5%       50% 97.5% Rhat n_eff
    -#> (Intercept)       4.000   4.0e+00 4.100 1.00  1235
    -#> gp(time):temp.1   0.740   3.3e+00 6.500 1.00   548
    -#> gp(time):temp.2  -2.400   1.5e+00 5.800 1.00   435
    -#> gp(time):temp.3  -5.700  -1.5e+00 3.800 1.00   573
    -#> gp(time):temp.4  -5.200  -1.2e+00 2.300 1.00   464
    -#> gp(time):temp.5  -2.900   4.5e-01 3.800 1.00   889
    -#> gp(time):temp.6  -2.300   1.6e-01 3.300 1.00   813
    -#> gp(time):temp.7  -3.400  -2.8e-01 2.200 1.00   839
    -#> gp(time):temp.8  -1.700   1.9e-01 2.700 1.00   794
    -#> gp(time):temp.9  -1.200   1.6e-01 2.700 1.00   920
    -#> gp(time):temp.10 -2.500  -2.5e-01 0.910 1.00   534
    -#> gp(time):temp.11 -1.900  -2.6e-02 1.200 1.00   832
    -#> gp(time):temp.12 -0.610   6.3e-02 1.800 1.00   671
    -#> gp(time):temp.13 -1.200   1.8e-09 1.200 1.00  1055
    -#> gp(time):temp.14 -1.400  -1.2e-03 0.690 1.00   667
    -#> gp(time):temp.15 -0.780   2.3e-18 1.000 1.00   841
    -#> gp(time):temp.16 -0.730   3.3e-06 0.860 1.00  1027
    -#> gp(time):temp.17 -0.810   5.1e-26 0.970 1.00  1103
    -#> gp(time):temp.18 -0.780   5.6e-29 0.670 1.00  1011
    -#> gp(time):temp.19 -1.000  -6.4e-06 0.320 1.00   833
    -#> gp(time):temp.20 -0.560   1.4e-19 0.590 1.00   997
    -#> gp(time):temp.21 -0.260   7.7e-12 0.910 1.00   669
    -#> gp(time):temp.22 -0.470  -6.6e-25 0.330 1.00  1345
    -#> gp(time):temp.23 -0.600  -4.1e-23 0.180 1.00   464
    -#> gp(time):temp.24 -0.220   1.8e-19 0.710 1.00  1152
    -#> gp(time):temp.25 -0.370   3.2e-33 0.310 1.00  1078
    -#> gp(time):temp.26 -0.610  -4.5e-21 0.096 1.00   448
    -#> gp(time):temp.27 -0.200   4.7e-39 0.360 1.00   764
    -#> gp(time):temp.28 -0.100   9.8e-21 0.320 1.00   938
    -#> gp(time):temp.29 -0.240  -5.7e-57 0.180 1.00  1000
    -#> gp(time):temp.30 -0.160   2.8e-82 0.230 1.00  1156
    -#> gp(time):temp.31 -0.160   2.6e-57 0.160 1.00   948
    -#> gp(time):temp.32 -0.130  -1.0e-60 0.170 1.00   772
    -#> gp(time):temp.33 -0.160  -1.7e-57 0.075 1.00   772
    -#> gp(time):temp.34 -0.066   8.3e-75 0.110 1.00   944
    -#> gp(time):temp.35 -0.038   1.6e-82 0.130 1.00   434
    -#> gp(time):temp.36 -0.085  3.4e-124 0.051 1.00   957
    -#> gp(time):temp.37 -0.062  7.2e-125 0.057 1.00   800
    -#> gp(time):temp.38 -0.046   4.0e-72 0.072 1.00  1389
    -#> gp(time):temp.39 -0.024  -4.0e-87 0.087 1.00   728
    -#> gp(time):temp.40 -0.062  -9.5e-73 0.019 1.00   902
    -#> gp(time):temp.41 -0.036  3.6e-126 0.029 1.01   754
    -#> 
    -#> GAM gp term marginal deviation (alpha) and length scale (rho) estimates:
    -#>                      2.5%   50%  97.5% Rhat n_eff
    -#> alpha_gp(time):temp  0.17  0.33   0.84 1.01   210
    -#> rho_gp(time):temp   11.00 32.00 100.00 1.01   135
    -#> 
    -#> Stan MCMC diagnostics:
    -#> n_eff / iter looks reasonable for all parameters
    -#> Rhat looks reasonable for all parameters
    -#> 63 of 1000 iterations ended with a divergence (6.3%)
    -#>  *Try running with larger adapt_delta to remove the divergences
    -#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%)
    -#> E-FMI indicated no pathological behavior
    -#> 
    -#> Samples were drawn using NUTS(diag_e) at Sat Nov 02 9:39:34 PM 2024.
    -#> For each parameter, n_eff is a crude measure of effective sample size,
    -#> and Rhat is the potential scale reduction factor on split MCMC chains
    -#> (at convergence, Rhat = 1)
    -plot(mod, type = 'smooths')
    -
    -fc <- forecast(mod, newdata = data_test)
    -plot(fc)
    -#> Out of sample CRPS:
    -#> 6.33897291368901
    -
    -
    -# Propagating the smooth term shows how the coefficient is expected to evolve
    -plot_mvgam_smooth(mod, smooth = 1, newdata = data)
    -abline(v = 180, lty = 'dashed', lwd = 2)
    -points(beta_temp, pch = 16)
    -
    -
    -
    -# Example showing how to incorporate an offset; simulate some count data
    -# with different means per series
    -set.seed(100)
    -dat <- sim_mvgam(prop_trend = 0, mu = c(0, 2, 2),
    -                 seasonality = 'hierarchical')
    -
    -# Add offset terms to the training and testing data
    -dat$data_train$offset <- 0.5 * as.numeric(dat$data_train$series)
    -dat$data_test$offset <- 0.5 * as.numeric(dat$data_test$series)
    -
    -# Fit a model that includes the offset in the linear predictor as well as
    -# hierarchical seasonal smooths
    -mod <- mvgam(formula = y ~ offset(offset) +
    -              s(series, bs = 're') +
    -              s(season, bs = 'cc') +
    -              s(season, by = series, m = 1, k = 5),
    -             data = dat$data_train,
    -             chains = 2)
    -#> Compiling Stan program using cmdstanr
    -#> 
    -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
    -#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math.hpp:19,
    -#>                  from stan/src/stan/model/model_header.hpp:4,
    -#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc5800a31.hpp:2:
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
    -#>   194 |       if (cdf_n < 0.0)
    -#>       | 
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
    -#> Start sampling
    -#> Running MCMC with 2 parallel chains...
    -#> 
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    -#> Chain 2 finished in 7.0 seconds.
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    -#> Chain 1 finished in 7.4 seconds.
    -#> 
    -#> Both chains finished successfully.
    -#> Mean chain execution time: 7.2 seconds.
    -#> Total execution time: 7.6 seconds.
    -#> 
    -
    -# Inspect the model file to see the modification to the linear predictor
    -# (eta)
    -code(mod)
    -#> // Stan model code generated by package mvgam
    -#> data {
    -#>   int<lower=0> total_obs; // total number of observations
    -#>   int<lower=0> n; // number of timepoints per series
    -#>   int<lower=0> n_sp; // number of smoothing parameters
    -#>   int<lower=0> n_series; // number of series
    -#>   int<lower=0> num_basis; // total number of basis coefficients
    -#>   vector[num_basis] zero; // prior locations for basis coefficients
    -#>   vector[total_obs] off_set; // offset vector
    -#>   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
    -#>   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
    -#>   matrix[8, 8] S1; // mgcv smooth penalty matrix S1
    -#>   matrix[4, 4] S2; // mgcv smooth penalty matrix S2
    -#>   matrix[4, 4] S3; // mgcv smooth penalty matrix S3
    -#>   matrix[4, 4] S4; // mgcv smooth penalty matrix S4
    -#>   int<lower=0> n_nonmissing; // number of nonmissing observations
    -#>   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
    -#>   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
    -#>   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
    -#> }
    -#> parameters {
    -#>   // raw basis coefficients
    -#>   vector[num_basis] b_raw;
    -#>   
    -#>   // random effect variances
    -#>   vector<lower=0>[1] sigma_raw;
    -#>   
    -#>   // random effect means
    -#>   vector[1] mu_raw;
    -#>   
    -#>   // smoothing parameters
    -#>   vector<lower=0>[n_sp] lambda;
    -#> }
    -#> transformed parameters {
    -#>   // basis coefficients
    -#>   vector[num_basis] b;
    -#>   b[1 : 21] = b_raw[1 : 21];
    -#>   b[22 : 24] = mu_raw[1] + b_raw[22 : 24] * sigma_raw[1];
    -#> }
    -#> model {
    -#>   // prior for random effect population variances
    -#>   sigma_raw ~ student_t(3, 0, 2.5);
    -#>   
    -#>   // prior for random effect population means
    -#>   mu_raw ~ std_normal();
    -#>   
    -#>   // prior for (Intercept)...
    -#>   b_raw[1] ~ student_t(3, 1.4, 2.5);
    -#>   
    -#>   // prior for s(season)...
    -#>   b_raw[2 : 9] ~ multi_normal_prec(zero[2 : 9], S1[1 : 8, 1 : 8] * lambda[1]);
    -#>   
    -#>   // prior for s(season):seriesseries_1...
    -#>   b_raw[10 : 13] ~ multi_normal_prec(zero[10 : 13],
    -#>                                      S2[1 : 4, 1 : 4] * lambda[2]);
    -#>   
    -#>   // prior for s(season):seriesseries_2...
    -#>   b_raw[14 : 17] ~ multi_normal_prec(zero[14 : 17],
    -#>                                      S3[1 : 4, 1 : 4] * lambda[3]);
    -#>   
    -#>   // prior for s(season):seriesseries_3...
    -#>   b_raw[18 : 21] ~ multi_normal_prec(zero[18 : 21],
    -#>                                      S4[1 : 4, 1 : 4] * lambda[4]);
    -#>   
    -#>   // prior (non-centred) for s(series)...
    -#>   b_raw[22 : 24] ~ std_normal();
    -#>   
    -#>   // priors for smoothing parameters
    -#>   lambda ~ normal(5, 30);
    -#>   {
    -#>     // likelihood functions
    -#>     flat_ys ~ poisson_log_glm(flat_xs, off_set[obs_ind], b);
    -#>   }
    -#> }
    -#> generated quantities {
    -#>   vector[total_obs] eta;
    -#>   matrix[n, n_series] mus;
    -#>   vector[n_sp] rho;
    -#>   array[n, n_series] int ypred;
    -#>   rho = log(lambda);
    -#>   
    -#>   // posterior predictions
    -#>   eta = X * b + off_set;
    -#>   for (s in 1 : n_series) {
    -#>     mus[1 : n, s] = eta[ytimes[1 : n, s]];
    -#>     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
    -#>   }
    -#> }
    -#> 
    -#> 
    -
    -# Forecasts for the first two series will differ in magnitude
    -fc <- forecast(mod, newdata = dat$data_test)
    -layout(matrix(1:2, ncol = 2))
    -plot(fc, series = 1, ylim = c(0, 75))
    -#> Out of sample DRPS:
    -#> 22.781273
    -plot(fc, series = 2, ylim = c(0, 75))
    -#> Out of sample DRPS:
    -#> 77.61833
    -
    -layout(1)
    -
    -# Changing the offset for the testing data should lead to changes in
    -# the forecast
    -dat$data_test$offset <- dat$data_test$offset - 2
    -fc <- forecast(mod, newdata = dat$data_test)
    -plot(fc)
    -#> Out of sample DRPS:
    -#> 38.523539
    -
    -
    -# Relative Risks can be computed by fixing the offset to the same value
    -# for each series
    -dat$data_test$offset <- rep(1, NROW(dat$data_test))
    -preds_rr <- predict(mod, type = 'link', newdata = dat$data_test,
    -                    summary = FALSE)
    -series1_inds <- which(dat$data_test$series == 'series_1')
    -series2_inds <- which(dat$data_test$series == 'series_2')
    -
    -# Relative Risks are now more comparable among series
    -layout(matrix(1:2, ncol = 2))
    -plot(preds_rr[1, series1_inds], type = 'l', col = 'grey75',
    -     ylim = range(preds_rr),
    -     ylab = 'Series1 Relative Risk', xlab = 'Time')
    -for(i in 2:50){
    - lines(preds_rr[i, series1_inds], col = 'grey75')
    -}
    -
    -plot(preds_rr[1, series2_inds], type = 'l', col = 'darkred',
    -     ylim = range(preds_rr),
    -     ylab = 'Series2 Relative Risk', xlab = 'Time')
    -for(i in 2:50){
    - lines(preds_rr[i, series2_inds], col = 'darkred')
    - }
    -
    -layout(1)
    -
    -
    -# Example showcasing how cbind() is needed for Binomial observations
    -# Simulate two time series of Binomial trials
    -trials <- sample(c(20:25), 50, replace = TRUE)
    -x <- rnorm(50)
    -detprob1 <- plogis(-0.5 + 0.9*x)
    -detprob2 <- plogis(-0.1 -0.7*x)
    -dat <- rbind(data.frame(y = rbinom(n = 50, size = trials, prob = detprob1),
    -                        time = 1:50,
    -                        series = 'series1',
    -                        x = x,
    -                        ntrials = trials),
    -             data.frame(y = rbinom(n = 50, size = trials, prob = detprob2),
    -                        time = 1:50,
    -                        series = 'series2',
    -                        x = x,
    -                        ntrials = trials))
    -dat <- dplyr::mutate(dat, series = as.factor(series))
    -dat <- dplyr::arrange(dat, time, series)
    -plot_mvgam_series(data = dat, series = 'all')
    -
    -
    -# Fit a model using the binomial() family; must specify observations
    -# and number of trials in the cbind() wrapper
    -mod <- mvgam(cbind(y, ntrials) ~ series + s(x, by = series),
    -             family = binomial(),
    -             data = dat,
    -             chains = 2)
    -#> Warning: Binomial and Beta-binomial families require cbind(n_successes, n_trials)
    -#> in the formula left-hand side. Do not use cbind(n_successes, n_failures)!
    -#> This warning is displayed once per session.
    -#> Compiling Stan program using cmdstanr
    -#> 
    -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4,
    -#>                  from stan/lib/stan_math/stan/math/prim/prob.hpp:359,
    -#>                  from stan/lib/stan_math/stan/math/prim.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math/rev.hpp:16,
    -#>                  from stan/lib/stan_math/stan/math.hpp:19,
    -#>                  from stan/src/stan/model/model_header.hpp:4,
    -#>                  from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc3d7b3d28.hpp:2:
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)':
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers
    -#>   194 |       if (cdf_n < 0.0)
    -#>       | 
    -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory
    -#> Start sampling
    -#> Running MCMC with 2 parallel chains...
    -#> 
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    -#> Chain 1 finished in 2.2 seconds.
    -#> 
    -#> Both chains finished successfully.
    -#> Mean chain execution time: 2.1 seconds.
    -#> Total execution time: 2.3 seconds.
    -#> 
    -summary(mod)
    -#> GAM formula:
    -#> cbind(y, ntrials) ~ series + s(x, by = series)
    -#> <environment: 0x0000016202170900>
    -#> 
    -#> Family:
    -#> binomial
    -#> 
    -#> Link function:
    -#> logit
    -#> 
    -#> Trend model:
    -#> None
    -#> 
    -#> N series:
    -#> 2 
    -#> 
    -#> N timepoints:
    -#> 50 
    -#> 
    -#> Status:
    -#> Fitted using Stan 
    -#> 2 chains, each with iter = 1000; warmup = 500; thin = 1 
    -#> Total post-warmup draws = 1000
    -#> 
    -#> 
    -#> GAM coefficient (beta) estimates:
    -#>                        2.5%      50%  97.5% Rhat n_eff
    -#> (Intercept)          -0.280 -0.17000 -0.036 1.00   592
    -#> seriesseries2        -0.320 -0.15000  0.028 1.00   577
    -#> s(x):seriesseries1.1 -0.120  0.02100  0.380 1.01   176
    -#> s(x):seriesseries1.2 -0.190  0.00420  0.260 1.00   222
    -#> s(x):seriesseries1.3 -0.088 -0.00440  0.063 1.00   307
    -#> s(x):seriesseries1.4 -0.150 -0.00084  0.150 1.00   250
    -#> s(x):seriesseries1.5 -0.064  0.00330  0.092 1.00   232
    -#> s(x):seriesseries1.6 -0.120 -0.00120  0.130 1.00   253
    -#> s(x):seriesseries1.7 -0.036 -0.00051  0.028 1.00   364
    -#> s(x):seriesseries1.8 -0.440  0.00740  0.500 1.00   223
    -#> s(x):seriesseries1.9  0.280  0.70000  0.920 1.01   171
    -#> s(x):seriesseries2.1 -0.650 -0.07300  0.070 1.02    76
    -#> s(x):seriesseries2.2 -0.270  0.02900  0.520 1.03   138
    -#> s(x):seriesseries2.3 -0.068  0.01300  0.170 1.02   191
    -#> s(x):seriesseries2.4 -0.160  0.02600  0.340 1.03   142
    -#> s(x):seriesseries2.5 -0.180 -0.01700  0.055 1.03   127
    -#> s(x):seriesseries2.6 -0.120  0.02400  0.310 1.03   130
    -#> s(x):seriesseries2.7 -0.031  0.00420  0.079 1.00   374
    -#> s(x):seriesseries2.8 -0.430  0.12000  1.200 1.03   117
    -#> s(x):seriesseries2.9 -0.800 -0.58000  0.013 1.02    89
    -#> 
    -#> Approximate significance of GAM smooths:
    -#>                     edf Ref.df Chi.sq p-value    
    -#> s(x):seriesseries1 2.12      9   27.4 < 2e-16 ***
    -#> s(x):seriesseries2 1.77      9   38.8 0.00017 ***
    -#> ---
    -#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    -#> 
    -#> Stan MCMC diagnostics:
    -#> n_eff / iter looks reasonable for all parameters
    -#> Rhat looks reasonable for all parameters
    -#> 0 of 1000 iterations ended with a divergence (0%)
    -#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%)
    -#> E-FMI indicated no pathological behavior
    -#> 
    -#> Samples were drawn using NUTS(diag_e) at Sat Nov 02 9:41:17 PM 2024.
    -#> For each parameter, n_eff is a crude measure of effective sample size,
    -#> and Rhat is the potential scale reduction factor on split MCMC chains
    -#> (at convergence, Rhat = 1)
    -pp_check(mod, type = "bars_grouped",
    -         group = "series", ndraws = 50)
    -
    -pp_check(mod, type = "ecdf_overlay_grouped",
    -         group = "series", ndraws = 50)
    -
    -conditional_effects(mod, type = 'link')
    -
    -
    -# }
    -
    -
    -
    - - -
    - - - - - - - + +Fit a Bayesian dynamic GAM to a univariate or multivariate set of time series — mvgam • mvgam + Skip to contents + + +
    +
    +
    + +
    +

    This function estimates the posterior distribution for Generalised Additive Models (GAMs) that can include +smooth spline functions, specified in the GAM formula, as well as latent temporal processes, +specified by trend_model. Further modelling options include State-Space representations to allow covariates +and dynamic processes to occur on the latent 'State' level while also capturing observation-level effects. +Prior specifications are flexible and explicitly encourage users to apply +prior distributions that actually reflect their beliefs. In addition, model fits can easily be assessed and +compared with posterior predictive checks, forecast comparisons and leave-one-out / leave-future-out cross-validation.

    +
    + +
    +

    Usage

    +
    mvgam(
    +  formula,
    +  trend_formula,
    +  knots,
    +  trend_knots,
    +  data,
    +  data_train,
    +  newdata,
    +  data_test,
    +  run_model = TRUE,
    +  prior_simulation = FALSE,
    +  return_model_data = FALSE,
    +  family = "poisson",
    +  share_obs_params = FALSE,
    +  use_lv = FALSE,
    +  n_lv,
    +  trend_map,
    +  trend_model = "None",
    +  drift = FALSE,
    +  noncentred = FALSE,
    +  chains = 4,
    +  burnin = 500,
    +  samples = 500,
    +  thin = 1,
    +  parallel = TRUE,
    +  threads = 1,
    +  priors,
    +  refit = FALSE,
    +  lfo = FALSE,
    +  residuals = TRUE,
    +  use_stan = TRUE,
    +  backend = getOption("brms.backend", "cmdstanr"),
    +  algorithm = getOption("brms.algorithm", "sampling"),
    +  autoformat = TRUE,
    +  save_all_pars = FALSE,
    +  max_treedepth = 12,
    +  adapt_delta = 0.85,
    +  silent = 1,
    +  jags_path,
    +  ...
    +)
    +
    + +
    +

    Arguments

    +
    formula
    +

    A character string specifying the GAM observation model formula. These are exactly like the formula +for a GLM except that smooth terms, s(), te(), ti(), t2(), as well as time-varying +dynamic() terms and nonparametric gp() terms, can be added to the right hand side +to specify that the linear predictor depends on smooth functions of predictors +(or linear functionals of these). In nmix() family models, the formula is used to +set up a linear predictor for the detection probability. Details of the formula syntax used by mvgam +can be found in mvgam_formulae

    + + +
    trend_formula
    +

    An optional character string specifying the GAM process model formula. If +supplied, a linear predictor will be modelled for the latent trends to capture process model evolution +separately from the observation model. Should not have a response variable specified on the left-hand side +of the formula (i.e. a valid option would be ~ season + s(year)). Also note that you should not use +the identifier series in this formula to specify effects that vary across time series. Instead you should use +trend. This will ensure that models in which a trend_map is supplied will still work consistently +(i.e. by allowing effects to vary across process models, even when some time series share the same underlying +process model). This feature is only currently available for RW(), AR() and VAR() trend models. +In nmix() family models, the trend_formula is used to set up a linear predictor for the underlying +latent abundance. Be aware that it can be very challenging to simultaneously estimate intercept parameters +for both the observation mode (captured by formula) and the process model (captured by trend_formula). +Users are recommended to drop one of these using the - 1 convention in the formula right hand side.

    + + +
    knots
    +

    An optional list containing user specified knot values to be used for basis construction. +For most bases the user simply supplies the knots to be used, which must match up with the k value supplied +(note that the number of knots is not always just k). Different terms can use different numbers of knots, +unless they share a covariate

    + + +
    trend_knots
    +

    As for knots above, this is an optional list of knot values for smooth +functions within the trend_formula

    + + +
    data
    +

    A dataframe or list containing the model response variable and covariates +required by the GAM formula and optional trend_formula. Most models should include columns:

    • series (a factor index of the series IDs; the number of levels should be identical +to the number of unique series labels (i.e. n_series = length(levels(data$series))))

    • +
    • time (numeric or integer index of the time point for each observation). +For most dynamic trend types available in mvgam (see argument trend_model), time should be +measured in discrete, regularly spaced intervals (i.e. c(1, 2, 3, ...)). However you can +use irregularly spaced intervals if using trend_model = CAR(1), though note that any +temporal intervals that are exactly 0 will be adjusted to a very small number +(1e-12) to prevent sampling errors. See an example of CAR() trends in CAR

    • +

    Note however that there are special cases where these identifiers are not needed. For +example, models with hierarchical temporal correlation processes (e.g. AR(gr = region, subgr = species)) +should NOT include a series identifier, as this will be constructed internally (see +mvgam_trends and AR for details). mvgam can also fit models that do not +include a time variable if there are no temporal dynamic structures included (i.e. trend_model = 'None' or +trend_model = ZMVN()). data should also include any other variables to be included in +the linear predictor of formula

    + + +
    data_train
    +

    Deprecated. Still works in place of data but users are recommended to use +data instead for more seamless integration into R workflows

    + + +
    newdata
    +

    Optional dataframe or list of test data containing the same variables +as in data. If included, the +observations in variable y will be set to NA when fitting the model so that posterior +simulations can be obtained

    + + +
    data_test
    +

    Deprecated. Still works in place of newdata but users are recommended to use +newdata instead for more seamless integration into R workflows

    + + +
    run_model
    +

    logical. If FALSE, the model is not fitted but instead the function will +return the model file and the data / initial values that are needed to fit the model outside of mvgam

    + + +
    prior_simulation
    +

    logical. If TRUE, no observations are fed to the model, and instead +simulations from prior distributions are returned

    + + +
    return_model_data
    +

    logical. If TRUE, the list of data that is needed to fit the +model is returned, along with the initial values for smooth and AR parameters, once the model is fitted. +This will be helpful if users wish to modify the model file to add +other stochastic elements that are not currently available in mvgam. +Default is FALSE to reduce +the size of the returned object, unless run_model == FALSE

    + + +
    family
    +

    family specifying the exponential observation family for the series. Currently supported +families are:

    • gaussian() for real-valued data

    • +
    • betar() for proportional data on (0,1)

    • +
    • lognormal() for non-negative real-valued data

    • +
    • student_t() for real-valued data

    • +
    • Gamma() for non-negative real-valued data

    • +
    • bernoulli() for binary data

    • +
    • poisson() for count data

    • +
    • nb() for overdispersed count data

    • +
    • binomial() for count data with imperfect detection when the number of trials is known; +note that the cbind() function must be used to bind the discrete observations and the discrete number +of trials

    • +
    • beta_binomial() as for binomial() but allows for overdispersion

    • +
    • nmix() for count data with imperfect detection when the number of trials +is unknown and should be modeled via a State-Space N-Mixture model. +The latent states are Poisson, capturing the 'true' latent +abundance, while the observation process is Binomial to account for +imperfect detection. +See mvgam_families for an example of how to use this family

    • +

    Note that only nb() and poisson() are available if using JAGS as the backend. +Default is poisson(). +See mvgam_families for more details

    + + +
    share_obs_params
    +

    logical. If TRUE and the family +has additional family-specific observation parameters (e.g. variance components in +student_t() or gaussian(), or dispersion parameters in nb() or betar()), +these parameters will be shared across all outcome variables. This is handy if you have multiple +outcomes (time series in most mvgam models) that you believe share some properties, +such as being from the same species over different spatial units. Default is FALSE.

    + + +
    use_lv
    +

    logical. If TRUE, use dynamic factors to estimate series' +latent trends in a reduced dimension format. Only available for +RW(), AR() and GP() trend models. Defaults to FALSE

    + + +
    n_lv
    +

    integer the number of latent dynamic factors to use if use_lv == TRUE. +Cannot be > n_series. Defaults arbitrarily to min(2, floor(n_series / 2))

    + + +
    trend_map
    +

    Optional data.frame specifying which series should depend on which latent +trends. Useful for allowing multiple series to depend on the same latent trend process, but with +different observation processes. If supplied, a latent factor model is set up by setting +use_lv = TRUE and using the mapping to set up the shared trends. Needs to have column names +series and trend, with integer values in the trend column to state which trend each series +should depend on. The series column should have a single unique entry for each series in the +data (names should perfectly match factor levels of the series variable in data). Note that +if this is supplied, the intercept parameter in the process model will NOT be automatically suppressed. +See examples for details

    + + +
    trend_model
    +

    character or function specifying the time series dynamics for the latent trend. Options are:

    • None (no latent trend component; i.e. the GAM component is all that contributes to the linear predictor, +and the observation process is the only source of error; similarly to what is estimated by gam)

    • +
    • ZMVN or ZMVN() (Zero-Mean Multivariate Normal; only available in Stan)

    • +
    • 'RW' or RW()

    • +
    • 'AR1' or AR(p = 1)

    • +
    • 'AR2' or AR(p = 2)

    • +
    • 'AR3' or AR(p = 3)

    • +
    • 'CAR1' or CAR(p = 1)

    • +
    • 'VAR1' or VAR()(only available in Stan)

    • +
    • 'PWlogistic, 'PWlinear' or PW() (only available in Stan)

    • +
    • 'GP' or GP() (Gaussian Process with squared exponential kernel; +only available in Stan)

    • +

    For all trend types apart from ZMVN(), GP(), CAR() and PW(), moving average and/or correlated +process error terms can also be estimated (for example, RW(cor = TRUE) will set up a +multivariate Random Walk if n_series > 1). It is also possible for many multivariate trends +to estimate hierarchical correlations if the data are structured among levels of +a relevant grouping factor. See mvgam_trends for more details and see ZMVN for an example.

    + + +
    drift
    +

    Deprecated. If you wish to estimate drift parameters, include parametric fixed effects +of 'time' in your formulae instead.

    + + +
    noncentred
    +

    logical Use the non-centred parameterisation for autoregressive +trend models? Setting to TRUE will reparameterise the model to avoid possible +degeneracies that can show up when estimating the latent dynamic random effects. For some +models, this can produce big gains in efficiency, meaning that fewer burnin and sampling +iterations are required for posterior exploration. But for other models, where the data +are highly informative about the latent dynamic processes, this can actually lead to worse +performance. Only available for certain trend models +(i.e. RW(), AR(), or CAR(), or for +trend = 'None' when using a trend_formula). Not yet available for moving average or +correlated error models

    + + +
    chains
    +

    integer specifying the number of parallel chains for the model. Ignored +if algorithm %in% c('meanfield', 'fullrank', 'pathfinder', 'laplace')

    + + +
    burnin
    +

    integer specifying the number of warmup iterations of the Markov chain to run +to tune sampling algorithms. Ignored +if algorithm %in% c('meanfield', 'fullrank', 'pathfinder', 'laplace')

    + + +
    samples
    +

    integer specifying the number of post-warmup iterations of the Markov chain to run for +sampling the posterior distribution

    + + +
    thin
    +

    Thinning interval for monitors. Ignored +if algorithm %in% c('meanfield', 'fullrank', 'pathfinder', 'laplace')

    + + +
    parallel
    +

    logical specifying whether multiple cores should be used for +generating MCMC simulations in parallel. If TRUE, the number of cores to use will be +min(c(chains, parallel::detectCores() - 1))

    + + +
    threads
    +

    integer Experimental option to use multithreading for within-chain +parallelisation in Stan. We recommend its use only if you are experienced with +Stan's reduce_sum function and have a slow running model that cannot be sped +up by any other means. Currently works for all families apart from nmix() and +when using Cmdstan as the backend

    + + +
    priors
    +

    An optional data.frame with prior +definitions (in JAGS or Stan syntax) or, preferentially, If using Stan, a vector containing +objects of class brmsprior (see. prior for details). +See get_mvgam_priors and Details' for more information on changing default prior distributions

    + + +
    refit
    +

    Logical indicating whether this is a refit, called using update.mvgam. Users should leave +as FALSE

    + + +
    lfo
    +

    Logical indicating whether this is part of a call to lfo_cv.mvgam. Returns a +lighter version of the model with no residuals and fewer monitored parameters to speed up +post-processing. But other downstream functions will not work properly, so users should always +leave this set as FALSE

    + + +
    residuals
    +

    Logical indicating whether to compute series-level randomized quantile residuals and include +them as part of the returned object. Defaults to TRUE, but you can set to FALSE to save +computational time and reduce the size of the returned object (users can always add residuals to +an object of class mvgam using add_residuals)

    + + +
    use_stan
    +

    Logical. If TRUE, the model will be compiled and sampled using +Hamiltonian Monte Carlo with a call to cmdstan_model or +a call to stan. Note that +there are many more options when using Stan vs JAGS

    + + +
    backend
    +

    Character string naming the package to use as the backend for fitting +the Stan model (if use_stan = TRUE). Options are "cmdstanr" (the default) or "rstan". Can be set globally +for the current R session via the "brms.backend" option (see options). Details on +the rstan and cmdstanr packages are available at https://mc-stan.org/rstan/ and +https://mc-stan.org/cmdstanr/, respectively

    + + +
    algorithm
    +

    Character string naming the estimation approach to use. +Options are "sampling" for MCMC (the default), "meanfield" for +variational inference with factorized normal distributions, +"fullrank" for variational inference with a multivariate normal +distribution, "laplace" for a Laplace approximation (only available +when using cmdstanr as the backend) or "pathfinder" for the pathfinder +algorithm (only currently available when using cmdstanr as the backend). +Can be set globally for the current R session via the +"brms.algorithm" option (see options). Limited testing +suggests that "meanfield" performs best out of the non-MCMC approximations for +dynamic GAMs, possibly because of the difficulties estimating covariances among the +many spline parameters and latent trend parameters. But rigorous testing has not +been carried out

    + + +
    autoformat
    +

    Logical. Use the stanc parser to automatically format the +Stan code and check for deprecations. Only for development purposes, so leave to TRUE

    + + +
    save_all_pars
    +

    Logical flag to indicate if draws from all +variables defined in Stan's parameters block should be saved +(default is FALSE).

    + + +
    max_treedepth
    +

    positive integer placing a cap on the number of simulation steps evaluated during each iteration when +use_stan == TRUE. Default is 12. Increasing this value can sometimes help with exploration of complex +posterior geometries, but it is rarely fruitful to go above a max_treedepth of 14

    + + +
    adapt_delta
    +

    positive numeric between 0 and 1 defining the target average proposal acceptance probability +during Stan's adaptation period, if use_stan == TRUE. Default is 0.8. In general you should not need to change adapt_delta +unless you see a warning message about divergent transitions, in which case you can increase adapt_delta from the default +to a value closer to 1 (e.g. from 0.95 to 0.99, or from 0.99 to 0.999, etc). +The step size used by the numerical integrator is a function of adapt_delta in that increasing +adapt_delta will result in a smaller step size and fewer divergences. Increasing adapt_delta will +typically result in a slower sampler, but it will always lead to a more robust sampler

    + + +
    silent
    +

    Verbosity level between 0 and 2. If 1 (the default), most of the informational +messages of compiler and sampler are suppressed. If 2, even more messages are suppressed. The +actual sampling progress is still printed. Set refresh = 0 to turn this off as well. If using +backend = "rstan" you can also set open_progress = FALSE to prevent opening additional +progress bars.

    + + +
    jags_path
    +

    Optional character vector specifying the path to the location of the JAGS executable (.exe) to use +for modelling if use_stan == FALSE. If missing, the path will be recovered from a call to findjags

    + + +
    ...
    +

    Further arguments passed to Stan. +For backend = "rstan" the arguments are passed to +sampling or vb. +For backend = "cmdstanr" the arguments are passed to the +cmdstanr::sample, cmdstanr::variational, +cmdstanr::laplace or +cmdstanr::pathfinder method

    + +
    +
    +

    Value

    + + +

    A list object of class mvgam containing model output, the text representation of the model file, +the mgcv model output (for easily generating simulations at +unsampled covariate values), Dunn-Smyth residuals for each series and key information needed +for other functions in the package. See mvgam-class for details. +Use methods(class = "mvgam") for an overview on available methods.

    +
    +
    +

    Details

    +

    Dynamic GAMs are useful when we wish to predict future values from time series that show temporal dependence +but we do not want to rely on extrapolating from a smooth term (which can sometimes lead to unpredictable and unrealistic behaviours). +In addition, smooths can often try to wiggle excessively to capture any autocorrelation that is present in a time series, +which exacerbates the problem of forecasting ahead. As GAMs are very naturally viewed through a Bayesian lens, and we often +must model time series that show complex distributional features and missing data, parameters for mvgam models are estimated +in a Bayesian framework using Markov Chain Monte Carlo by default. A general overview is provided +in the primary vignettes: vignette("mvgam_overview") and vignette("data_in_mvgam"). +For a full list of available vignettes see vignette(package = "mvgam") +

    Formula syntax: Details of the formula syntax used by mvgam can be found in +mvgam_formulae. Note that it is possible to supply an empty formula where +there are no predictors or intercepts in the observation model (i.e. y ~ 0 or y ~ -1). +In this case, an intercept-only observation model will be set up but the intercept coefficient +will be fixed at zero. This can be handy if you wish to fit pure State-Space models where +the variation in the dynamic trend controls the average expectation, and/or where intercepts +are non-identifiable (as in piecewise trends, see examples below) +

    Families and link functions: Details of families supported by mvgam can be found in +mvgam_families. +

    Trend models: Details of latent error process models supported by mvgam can be found in +mvgam_trends. +

    Priors: Default priors for intercepts and any scale parameters are generated +using the same practice as brms. Prior distributions for most important model parameters can be +altered by the user to inspect model +sensitivities to given priors (see get_mvgam_priors for details). +Note that latent trends are estimated on the link scale so choose priors +accordingly. However more control over the model specification can be accomplished by first using mvgam as a +baseline, then editing the returned model accordingly. The model file can be edited and run outside +of mvgam by setting run_model = FALSE and this is encouraged for complex +modelling tasks. Note, no priors are +formally checked to ensure they are in the right syntax for the respective +probabilistic modelling framework, so it is +up to the user to ensure these are correct (i.e. use dnorm for normal +densities in JAGS, with the mean and precision +parameterisation; but use normal for normal densities in Stan, with the mean +and standard deviation parameterisation) +

    Random effects: For any smooth terms using the random effect basis (smooth.construct.re.smooth.spec), +a non-centred parameterisation is automatically employed to avoid degeneracies that are common in hierarchical models. +Note however that centred versions may perform better for series that are particularly informative, so as with any +foray into Bayesian modelling, it is worth building an understanding of the model's assumptions and limitations by following a +principled workflow. Also note that models are parameterised using drop.unused.levels = FALSE in jagam +to ensure predictions can be made for all levels of the supplied factor variable +

    Observation level parameters: When more than one series is included in data and an +observation family that contains more than one parameter is used, additional observation family parameters +(i.e. phi for nb() or sigma for gaussian()) are +by default estimated independently for each series. But if you wish for the series to share +the same observation parameters, set share_obs_params = TRUE +

    Factor regularisation: When using a dynamic factor model for the trends with JAGS factor precisions are given +regularized penalty priors to theoretically allow some factors to be dropped from the model by squeezing increasing +factors' variances to zero. This is done to help protect against selecting too many latent factors than are needed to +capture dependencies in the data, so it can often be advantageous to set n_lv to a slightly larger number. However +larger numbers of factors do come with additional computational costs so these should be balanced as well. When using +Stan, all factors are parameterised with fixed variance parameters +

    Residuals: For each series, randomized quantile (i.e. Dunn-Smyth) residuals are calculated for inspecting model diagnostics +If the fitted model is appropriate then Dunn-Smyth residuals will be standard normal in distribution and no +autocorrelation will be evident. When a particular observation is missing, the residual is calculated by comparing independent +draws from the model's posterior distribution +

    Using Stan: mvgam is primarily designed to use Hamiltonian Monte Carlo for parameter estimation +via the software Stan (using either the cmdstanr or rstan interface). +There are great advantages when using Stan over Gibbs / Metropolis Hastings samplers, which includes the option +to estimate nonlinear effects via Hilbert space approximate Gaussian Processes, +the availability of a variety of inference algorithms (i.e. variational inference, laplacian inference etc...) and +capabilities to enforce stationarity for complex Vector Autoregressions. +Because of the many advantages of Stan over JAGS, +further development of the package will only be applied to Stan. This includes the planned addition +of more response distributions, plans to handle zero-inflation, and plans to incorporate a greater +variety of trend models. Users are strongly encouraged to opt for Stan over JAGS in any proceeding workflows +

    How to start?: The mvgam cheatsheet is a +good starting place if you are just learning to use the package. It gives an overview of the package's key functions and objects, +as well as providing a reasonable workflow that new users can follow. In general it is recommended to

    +
    +

    References

    +

    Nicholas J Clark & Konstans Wells (2020). Dynamic generalised additive models (DGAMs) for forecasting discrete ecological time series. +Methods in Ecology and Evolution. 14:3, 771-784.

    +
    + +
    +

    Author

    +

    Nicholas J Clark

    +
    + +
    +

    Examples

    +
    # \donttest{
    +# Simulate a collection of three time series that have shared seasonal dynamics
    +# and independent AR1 trends, with a Poisson observation process
    +set.seed(0)
    +dat <- sim_mvgam(T = 80,
    +                n_series = 3,
    +                mu = 2,
    +                trend_model = AR(p = 1),
    +                prop_missing = 0.1,
    +                prop_trend = 0.6)
    +
    +# Plot key summary statistics for a single series
    +plot_mvgam_series(data = dat$data_train, series = 1)
    +
    +
    +# Plot all series together
    +plot_mvgam_series(data = dat$data_train, series = 'all')
    +
    +
    +# Formulate a model using Stan where series share a cyclic smooth for
    +# seasonality and each series has an independent AR1 temporal process.
    +# Note that 'noncentred = TRUE' will likely give performance gains.
    +# Set run_model = FALSE to inspect the returned objects
    +mod1 <- mvgam(formula = y ~ s(season, bs = 'cc', k = 6),
    +             data = dat$data_train,
    +             trend_model = AR(),
    +             family = poisson(),
    +             noncentred = TRUE,
    +             use_stan = TRUE,
    +             run_model = FALSE)
    +
    +# View the model code in Stan language
    +stancode(mod1)
    +#> // Stan model code generated by package mvgam
    +#> data {
    +#>   int<lower=0> total_obs; // total number of observations
    +#>   int<lower=0> n; // number of timepoints per series
    +#>   int<lower=0> n_sp; // number of smoothing parameters
    +#>   int<lower=0> n_series; // number of series
    +#>   int<lower=0> num_basis; // total number of basis coefficients
    +#>   vector[num_basis] zero; // prior locations for basis coefficients
    +#>   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
    +#>   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
    +#>   matrix[4, 4] S1; // mgcv smooth penalty matrix S1
    +#>   int<lower=0> n_nonmissing; // number of nonmissing observations
    +#>   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
    +#>   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
    +#>   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
    +#> }
    +#> parameters {
    +#>   // raw basis coefficients
    +#>   vector[num_basis] b_raw;
    +#>   
    +#>   // latent trend AR1 terms
    +#>   vector<lower=-1, upper=1>[n_series] ar1;
    +#>   
    +#>   // latent trend variance parameters
    +#>   vector<lower=0>[n_series] sigma;
    +#>   
    +#>   // raw latent trends
    +#>   matrix[n, n_series] trend_raw;
    +#>   
    +#>   // smoothing parameters
    +#>   vector<lower=0>[n_sp] lambda;
    +#> }
    +#> transformed parameters {
    +#>   // basis coefficients
    +#>   vector[num_basis] b;
    +#>   
    +#>   // latent trends
    +#>   matrix[n, n_series] trend;
    +#>   trend = trend_raw .* rep_matrix(sigma', rows(trend_raw));
    +#>   for (s in 1 : n_series) {
    +#>     trend[2 : n, s] += ar1[s] * trend[1 : (n - 1), s];
    +#>   }
    +#>   b[1 : num_basis] = b_raw[1 : num_basis];
    +#> }
    +#> model {
    +#>   // prior for (Intercept)...
    +#>   b_raw[1] ~ student_t(3, 1.9, 2.5);
    +#>   
    +#>   // prior for s(season)...
    +#>   b_raw[2 : 5] ~ multi_normal_prec(zero[2 : 5], S1[1 : 4, 1 : 4] * lambda[1]);
    +#>   
    +#>   // priors for AR parameters
    +#>   ar1 ~ std_normal();
    +#>   
    +#>   // priors for smoothing parameters
    +#>   lambda ~ normal(5, 30);
    +#>   
    +#>   // priors for latent trend variance parameters
    +#>   sigma ~ student_t(3, 0, 2.5);
    +#>   to_vector(trend_raw) ~ std_normal();
    +#>   {
    +#>     // likelihood functions
    +#>     vector[n_nonmissing] flat_trends;
    +#>     flat_trends = to_vector(trend)[obs_ind];
    +#>     flat_ys ~ poisson_log_glm(append_col(flat_xs, flat_trends), 0.0,
    +#>                               append_row(b, 1.0));
    +#>   }
    +#> }
    +#> generated quantities {
    +#>   vector[total_obs] eta;
    +#>   matrix[n, n_series] mus;
    +#>   vector[n_sp] rho;
    +#>   vector[n_series] tau;
    +#>   array[n, n_series] int ypred;
    +#>   rho = log(lambda);
    +#>   for (s in 1 : n_series) {
    +#>     tau[s] = pow(sigma[s], -2.0);
    +#>   }
    +#>   
    +#>   // posterior predictions
    +#>   eta = X * b;
    +#>   for (s in 1 : n_series) {
    +#>     mus[1 : n, s] = eta[ytimes[1 : n, s]] + trend[1 : n, s];
    +#>     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
    +#>   }
    +#> }
    +#> 
    +#> 
    +
    +# View the data objects needed to fit the model in Stan
    +sdata1 <- standata(mod1)
    +str(sdata1)
    +#> List of 18
    +#>  $ y           : num [1:60, 1:3] 12 17 12 31 30 8 0 1 3 5 ...
    +#>  $ n           : int 60
    +#>  $ X           : num [1:180, 1:5] 1 1 1 1 1 1 1 1 1 1 ...
    +#>   ..- attr(*, "dimnames")=List of 2
    +#>   .. ..$ : NULL
    +#>   .. ..$ : chr [1:5] "X.Intercept." "V2" "V3" "V4" ...
    +#>  $ S1          : num [1:4, 1:4] 1.244 -0.397 0.384 0.619 -0.397 ...
    +#>  $ zero        : num [1:5] 0 0 0 0 0
    +#>  $ p_coefs     : Named num 0
    +#>   ..- attr(*, "names")= chr "(Intercept)"
    +#>  $ p_taus      : num 1.09
    +#>  $ ytimes      : int [1:60, 1:3] 1 4 7 10 13 16 19 22 25 28 ...
    +#>  $ n_series    : int 3
    +#>  $ sp          : Named num 0.368
    +#>   ..- attr(*, "names")= chr "s(season)"
    +#>  $ y_observed  : num [1:60, 1:3] 1 1 1 1 1 1 1 1 1 1 ...
    +#>  $ total_obs   : int 180
    +#>  $ num_basis   : int 5
    +#>  $ n_sp        : num 1
    +#>  $ n_nonmissing: int 161
    +#>  $ obs_ind     : int [1:161] 1 2 3 4 5 6 7 8 9 10 ...
    +#>  $ flat_ys     : num [1:161] 12 17 12 31 30 8 0 1 3 5 ...
    +#>  $ flat_xs     : num [1:161, 1:5] 1 1 1 1 1 1 1 1 1 1 ...
    +#>   ..- attr(*, "dimnames")=List of 2
    +#>   .. ..$ : NULL
    +#>   .. ..$ : chr [1:5] "X.Intercept." "V2" "V3" "V4" ...
    +#>  - attr(*, "trend_model")= chr "AR1"
    +
    +# Now fit the model
    +mod1 <- mvgam(formula = y ~ s(season, bs = 'cc', k = 6),
    +              data = dat$data_train,
    +              trend_model = AR(),
    +              family = poisson(),
    +              noncentred = TRUE,
    +              chains = 2)
    +#> Compiling Stan program using cmdstanr
    +#> 
    +#> Start sampling
    +#> Running MCMC with 2 parallel chains...
    +#> 
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    +#> Chain 1 finished in 1.9 seconds.
    +#> Chain 2 finished in 1.8 seconds.
    +#> 
    +#> Both chains finished successfully.
    +#> Mean chain execution time: 1.8 seconds.
    +#> Total execution time: 2.2 seconds.
    +#> 
    +
    +# Extract the model summary
    +summary(mod1)
    +#> GAM formula:
    +#> y ~ s(season, bs = "cc", k = 6)
    +#> <environment: 0x0000022e983e9af0>
    +#> 
    +#> Family:
    +#> poisson
    +#> 
    +#> Link function:
    +#> log
    +#> 
    +#> Trend model:
    +#> AR()
    +#> 
    +#> N series:
    +#> 3 
    +#> 
    +#> N timepoints:
    +#> 60 
    +#> 
    +#> Status:
    +#> Fitted using Stan 
    +#> 2 chains, each with iter = 1000; warmup = 500; thin = 1 
    +#> Total post-warmup draws = 1000
    +#> 
    +#> 
    +#> GAM coefficient (beta) estimates:
    +#>              2.5%    50% 97.5% Rhat n_eff
    +#> (Intercept)  1.80  1.900  2.10    1   475
    +#> s(season).1  0.14  0.370  0.60    1   514
    +#> s(season).2 -0.34 -0.097  0.15    1   566
    +#> s(season).3 -1.00 -0.720 -0.46    1   470
    +#> s(season).4 -0.50 -0.270 -0.03    1   799
    +#> 
    +#> Approximate significance of GAM smooths:
    +#>            edf Ref.df Chi.sq p-value    
    +#> s(season) 3.88      4     26  <2e-16 ***
    +#> ---
    +#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    +#> 
    +#> Latent trend parameter AR estimates:
    +#>            2.5%   50% 97.5% Rhat n_eff
    +#> ar1[1]    0.300  0.74  0.99 1.00   384
    +#> ar1[2]   -0.930 -0.34  0.23 1.00   127
    +#> ar1[3]    0.011  0.41  0.96 1.00   167
    +#> sigma[1]  0.380  0.52  0.73 1.00   446
    +#> sigma[2]  0.390  0.55  0.79 1.00   198
    +#> sigma[3]  0.410  0.58  0.78 1.01   313
    +#> 
    +#> Stan MCMC diagnostics:
    +#> n_eff / iter looks reasonable for all parameters
    +#> Rhat looks reasonable for all parameters
    +#> 0 of 1000 iterations ended with a divergence (0%)
    +#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%)
    +#> E-FMI indicated no pathological behavior
    +#> 
    +#> Samples were drawn using NUTS(diag_e) at Mon Nov 04 10:39:14 AM 2024.
    +#> For each parameter, n_eff is a crude measure of effective sample size,
    +#> and Rhat is the potential scale reduction factor on split MCMC chains
    +#> (at convergence, Rhat = 1)
    +
    +# Plot the estimated historical trend and forecast for one series
    +plot(mod1, type = 'trend', series = 1)
    +
    +plot(mod1, type = 'forecast', series = 1)
    +
    +
    +# Residual diagnostics
    +plot(mod1, type = 'residuals', series = 1)
    +
    +resids <- residuals(mod1)
    +str(resids)
    +#>  num [1:180, 1:4] 0.0253 -0.0822 0.1508 0.5405 -0.0836 ...
    +#>  - attr(*, "dimnames")=List of 2
    +#>   ..$ : NULL
    +#>   ..$ : chr [1:4] "Estimate" "Est.Error" "Q2.5" "Q97.5"
    +
    +# Compute the forecast using covariate information in data_test
    +fc <- forecast(mod1, newdata = dat$data_test)
    +str(fc)
    +#> List of 16
    +#>  $ call              :Class 'formula'  language y ~ s(season, bs = "cc", k = 6)
    +#>   .. ..- attr(*, ".Environment")=<environment: 0x0000022e983e9af0> 
    +#>  $ trend_call        : NULL
    +#>  $ family            : chr "poisson"
    +#>  $ family_pars       : NULL
    +#>  $ trend_model       :List of 7
    +#>   ..$ trend_model: chr "AR1"
    +#>   ..$ ma         : logi FALSE
    +#>   ..$ cor        : logi FALSE
    +#>   ..$ unit       : chr "time"
    +#>   ..$ gr         : chr "NA"
    +#>   ..$ subgr      : chr "series"
    +#>   ..$ label      : language AR()
    +#>   ..- attr(*, "class")= chr "mvgam_trend"
    +#>  $ drift             : logi FALSE
    +#>  $ use_lv            : logi FALSE
    +#>  $ fit_engine        : chr "stan"
    +#>  $ type              : chr "response"
    +#>  $ series_names      : Factor w/ 3 levels "series_1","series_2",..: 1 2 3
    +#>  $ train_observations:List of 3
    +#>   ..$ series_1: int [1:60] 12 17 12 31 30 8 0 1 3 5 ...
    +#>   ..$ series_2: int [1:60] 8 8 21 7 6 NA 1 8 9 3 ...
    +#>   ..$ series_3: int [1:60] 10 NA 7 2 1 11 4 NA 5 4 ...
    +#>  $ train_times       : int [1:60] 1 2 3 4 5 6 7 8 9 10 ...
    +#>  $ test_observations :List of 3
    +#>   ..$ series_1: int [1:20] 4 9 5 6 4 11 NA 3 8 11 ...
    +#>   ..$ series_2: int [1:20] 19 51 19 10 3 6 7 1 6 4 ...
    +#>   ..$ series_3: int [1:20] 10 NA 8 5 16 13 0 0 3 2 ...
    +#>  $ test_times        : int [1:20] 61 62 63 64 65 66 67 68 69 70 ...
    +#>  $ hindcasts         :List of 3
    +#>   ..$ series_1: num [1:1000, 1:60] 16 13 8 13 6 17 12 9 11 8 ...
    +#>   .. ..- attr(*, "dimnames")=List of 2
    +#>   .. .. ..$ : NULL
    +#>   .. .. ..$ : chr [1:60] "ypred[1,1]" "ypred[2,1]" "ypred[3,1]" "ypred[4,1]" ...
    +#>   ..$ series_2: num [1:1000, 1:60] 7 10 2 5 11 12 8 7 8 12 ...
    +#>   .. ..- attr(*, "dimnames")=List of 2
    +#>   .. .. ..$ : NULL
    +#>   .. .. ..$ : chr [1:60] "ypred[1,2]" "ypred[2,2]" "ypred[3,2]" "ypred[4,2]" ...
    +#>   ..$ series_3: num [1:1000, 1:60] 8 14 7 15 7 13 8 6 10 5 ...
    +#>   .. ..- attr(*, "dimnames")=List of 2
    +#>   .. .. ..$ : NULL
    +#>   .. .. ..$ : chr [1:60] "ypred[1,3]" "ypred[2,3]" "ypred[3,3]" "ypred[4,3]" ...
    +#>  $ forecasts         :List of 3
    +#>   ..$ series_1: int [1:1000, 1:20] 5 9 6 7 9 4 3 11 1 9 ...
    +#>   ..$ series_2: int [1:1000, 1:20] 5 22 10 9 8 14 28 5 9 12 ...
    +#>   ..$ series_3: int [1:1000, 1:20] 20 26 4 18 16 10 13 23 3 31 ...
    +#>  - attr(*, "class")= chr "mvgam_forecast"
    +plot(fc)
    +#> Out of sample DRPS:
    +#> 55.025328
    +
    +
    +# Plot the estimated seasonal smooth function
    +plot(mod1, type = 'smooths')
    +
    +
    +# Plot estimated first derivatives of the smooth
    +plot(mod1, type = 'smooths', derivatives = TRUE)
    +
    +
    +# Plot partial residuals of the smooth
    +plot(mod1, type = 'smooths', residuals = TRUE)
    +
    +
    +# Plot posterior realisations for the smooth
    +plot(mod1, type = 'smooths', realisations = TRUE)
    +
    +
    +# Plot conditional response predictions using marginaleffects
    +library(marginaleffects)
    +conditional_effects(mod1)
    +#> Warning: Removed 19 rows containing missing values or values outside the scale range
    +#> (`geom_point()`).
    +
    +plot_predictions(mod1, condition = 'season', points = 0.5)
    +#> Warning: Removed 19 rows containing missing values or values outside the scale range
    +#> (`geom_point()`).
    +
    +
    +# Generate posterior predictive checks using bayesplot
    +pp_check(mod1)
    +#> Using 10 posterior draws for ppc type 'dens_overlay' by default.
    +#> Warning: NA responses are not shown in 'pp_check'.
    +
    +
    +# Extract observation model beta coefficient draws as a data.frame
    +beta_draws_df <- as.data.frame(mod1, variable = 'betas')
    +head(beta_draws_df)
    +#>   (Intercept) s(season).1 s(season).2 s(season).3 s(season).4
    +#> 1     1.87065    0.473169 -0.03894510   -0.488944   -0.335604
    +#> 2     1.99174    0.186258 -0.00918666   -0.841499   -0.193604
    +#> 3     1.90925    0.670423 -0.17225100   -0.755631   -0.429818
    +#> 4     1.94451    0.534511 -0.04538430   -0.691632   -0.516703
    +#> 5     2.08142    0.221111  0.10645400   -0.559959   -0.221205
    +#> 6     2.02562    0.354744 -0.01871940   -0.662982   -0.435189
    +str(beta_draws_df)
    +#> 'data.frame':	1000 obs. of  5 variables:
    +#>  $ (Intercept): num  1.87 1.99 1.91 1.94 2.08 ...
    +#>  $ s(season).1: num  0.473 0.186 0.67 0.535 0.221 ...
    +#>  $ s(season).2: num  -0.03895 -0.00919 -0.17225 -0.04538 0.10645 ...
    +#>  $ s(season).3: num  -0.489 -0.841 -0.756 -0.692 -0.56 ...
    +#>  $ s(season).4: num  -0.336 -0.194 -0.43 -0.517 -0.221 ...
    +
    +# Investigate model fit
    +mc.cores.def <- getOption('mc.cores')
    +options(mc.cores = 1)
    +loo(mod1)
    +#> Warning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.
    +#> 
    +#> Computed from 1000 by 161 log-likelihood matrix
    +#> 
    +#>          Estimate   SE
    +#> elpd_loo   -449.6  7.9
    +#> p_loo        88.7  4.3
    +#> looic       899.2 15.9
    +#> ------
    +#> Monte Carlo SE of elpd_loo is NA.
    +#> 
    +#> Pareto k diagnostic values:
    +#>                          Count Pct.    Min. n_eff
    +#> (-Inf, 0.5]   (good)     19    11.8%   151       
    +#>  (0.5, 0.7]   (ok)       67    41.6%   59        
    +#>    (0.7, 1]   (bad)      67    41.6%   17        
    +#>    (1, Inf)   (very bad)  8     5.0%   8         
    +#> See help('pareto-k-diagnostic') for details.
    +options(mc.cores = mc.cores.def)
    +
    +
    +# Example of supplying a trend_map so that some series can share
    +# latent trend processes
    +sim <- sim_mvgam(n_series = 3)
    +mod_data <- sim$data_train
    +
    +# Here, we specify only two latent trends; series 1 and 2 share a trend,
    +# while series 3 has it's own unique latent trend
    +trend_map <- data.frame(series = unique(mod_data$series),
    +                       trend = c(1, 1, 2))
    +
    +# Fit the model using AR1 trends
    +mod <- mvgam(y ~ s(season, bs = 'cc', k = 6),
    +             trend_map = trend_map,
    +             trend_model = AR(),
    +             data = mod_data,
    +             return_model_data = TRUE,
    +             chains = 2)
    +#> Compiling Stan program using cmdstanr
    +#> 
    +#> Start sampling
    +#> Running MCMC with 2 parallel chains...
    +#> 
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    +#> Chain 1 finished in 3.3 seconds.
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    +#> Chain 2 finished in 3.5 seconds.
    +#> 
    +#> Both chains finished successfully.
    +#> Mean chain execution time: 3.4 seconds.
    +#> Total execution time: 3.8 seconds.
    +#> 
    +
    +# The mapping matrix is now supplied as data to the model in the 'Z' element
    +mod$model_data$Z
    +#>      [,1] [,2]
    +#> [1,]    1    0
    +#> [2,]    1    0
    +#> [3,]    0    1
    +code(mod)
    +#> // Stan model code generated by package mvgam
    +#> data {
    +#>   int<lower=0> total_obs; // total number of observations
    +#>   int<lower=0> n; // number of timepoints per series
    +#>   int<lower=0> n_lv; // number of dynamic factors
    +#>   int<lower=0> n_sp; // number of smoothing parameters
    +#>   int<lower=0> n_series; // number of series
    +#>   matrix[n_series, n_lv] Z; // matrix mapping series to latent trends
    +#>   int<lower=0> num_basis; // total number of basis coefficients
    +#>   vector[num_basis] zero; // prior locations for basis coefficients
    +#>   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
    +#>   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
    +#>   matrix[4, 4] S1; // mgcv smooth penalty matrix S1
    +#>   int<lower=0> n_nonmissing; // number of nonmissing observations
    +#>   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
    +#>   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
    +#>   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
    +#> }
    +#> transformed data {
    +#>   
    +#> }
    +#> parameters {
    +#>   // raw basis coefficients
    +#>   vector[num_basis] b_raw;
    +#>   
    +#>   // latent factor SD terms
    +#>   vector<lower=0>[n_lv] sigma;
    +#>   
    +#>   // latent factor AR1 terms
    +#>   vector<lower=-1, upper=1>[n_lv] ar1;
    +#>   
    +#>   // dynamic factors
    +#>   matrix[n, n_lv] LV;
    +#>   
    +#>   // smoothing parameters
    +#>   vector<lower=0>[n_sp] lambda;
    +#> }
    +#> transformed parameters {
    +#>   // trends and dynamic factor loading matrix
    +#>   matrix[n, n_series] trend;
    +#>   
    +#>   // basis coefficients
    +#>   vector[num_basis] b;
    +#>   b[1 : num_basis] = b_raw[1 : num_basis];
    +#>   
    +#>   // derived latent trends
    +#>   for (i in 1 : n) {
    +#>     for (s in 1 : n_series) {
    +#>       trend[i, s] = dot_product(Z[s,  : ], LV[i,  : ]);
    +#>     }
    +#>   }
    +#> }
    +#> model {
    +#>   // prior for (Intercept)...
    +#>   b_raw[1] ~ student_t(3, 0, 2.5);
    +#>   
    +#>   // prior for s(season)...
    +#>   b_raw[2 : 5] ~ multi_normal_prec(zero[2 : 5], S1[1 : 4, 1 : 4] * lambda[1]);
    +#>   
    +#>   // priors for AR parameters
    +#>   ar1 ~ std_normal();
    +#>   
    +#>   // priors for smoothing parameters
    +#>   lambda ~ normal(5, 30);
    +#>   
    +#>   // priors for factor SD parameters
    +#>   sigma ~ student_t(3, 0, 2.5);
    +#>   
    +#>   // dynamic factor estimates
    +#>   LV[1, 1 : n_lv] ~ normal(0, sigma);
    +#>   for (j in 1 : n_lv) {
    +#>     LV[2 : n, j] ~ normal(ar1[j] * LV[1 : (n - 1), j], sigma[j]);
    +#>   }
    +#>   {
    +#>     // likelihood functions
    +#>     vector[n_nonmissing] flat_trends;
    +#>     flat_trends = to_vector(trend)[obs_ind];
    +#>     flat_ys ~ poisson_log_glm(append_col(flat_xs, flat_trends), 0.0,
    +#>                               append_row(b, 1.0));
    +#>   }
    +#> }
    +#> generated quantities {
    +#>   vector[total_obs] eta;
    +#>   matrix[n, n_series] mus;
    +#>   vector[n_sp] rho;
    +#>   vector[n_lv] penalty;
    +#>   array[n, n_series] int ypred;
    +#>   rho = log(lambda);
    +#>   penalty = 1.0 / (sigma .* sigma);
    +#>   
    +#>   matrix[n_series, n_lv] lv_coefs = Z;
    +#>   // posterior predictions
    +#>   eta = X * b;
    +#>   for (s in 1 : n_series) {
    +#>     mus[1 : n, s] = eta[ytimes[1 : n, s]] + trend[1 : n, s];
    +#>     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
    +#>   }
    +#> }
    +#> 
    +#> 
    +
    +# The first two series share an identical latent trend; the third is different
    +plot(mod, type = 'trend', series = 1)
    +
    +plot(mod, type = 'trend', series = 2)
    +
    +plot(mod, type = 'trend', series = 3)
    +
    +
    +
    +# Example of how to use dynamic coefficients
    +# Simulate a time-varying coefficient for the effect of temperature
    +set.seed(123)
    +N <- 200
    +beta_temp <- vector(length = N)
    +beta_temp[1] <- 0.4
    +for(i in 2:N){
    + beta_temp[i] <- rnorm(1, mean = beta_temp[i - 1] - 0.0025, sd = 0.05)
    +}
    +plot(beta_temp)
    +
    +
    +# Simulate a covariate called 'temp'
    +temp <- rnorm(N, sd = 1)
    +
    +# Simulate the Gaussian observation process
    +out <- rnorm(N, mean = 4 + beta_temp * temp,
    +             sd = 0.5)
    +
    +# Gather necessary data into a data.frame; split into training / testing
    +data = data.frame(out, temp, time = seq_along(temp))
    +data_train <- data[1:180,]
    +data_test <- data[181:200,]
    +
    +# Fit the model using the dynamic() formula helper
    +mod <- mvgam(out ~
    +              dynamic(temp,
    +                      scale = FALSE,
    +                      k = 40),
    +             family = gaussian(),
    +             data = data_train,
    +             newdata = data_test,
    +             chains = 2)
    +#> Compiling Stan program using cmdstanr
    +#> 
    +#> Error in c("process_initialize(self, private, command, args, stdin, stdout, ",  : 
    +#>   ! Native call to `processx_exec` failed
    +#> Caused by error in `chain_call(c_processx_exec, command, c(command, args), pty, pty_options, …`:
    +#> ! create process 'C:/Users/Nick/AppData/Local/Temp/RtmpE9ivV8/model_379ab8b82a7e2251b0ef651b7de6cfc5.exe' (system error 193, %1 is not a valid Win32 application.
    
    +#> ) @win/processx.c:1040 (processx_exec)
    +#> Error in c("process_initialize(self, private, command, args, stdin, stdout, ", "    stderr, pty, pty_options, connections, poll_connection, env, "): ! Native call to `processx_exec` failed
    +#> Caused by error in `chain_call(c_processx_exec, command, c(command, args), pty, pty_options, …`:
    +#> ! create process 'C:/Users/Nick/AppData/Local/Temp/RtmpE9ivV8/model_379ab8b82a7e2251b0ef651b7de6cfc5.exe' (system error 193, %1 is not a valid Win32 application.
    
    +#> ) @win/processx.c:1040 (processx_exec)
    +
    +# Inspect the model summary, forecast and time-varying coefficient distribution
    +summary(mod)
    +#> GAM formula:
    +#> y ~ s(season, bs = "cc", k = 6)
    +#> <environment: 0x0000022e983e9af0>
    +#> 
    +#> Family:
    +#> poisson
    +#> 
    +#> Link function:
    +#> log
    +#> 
    +#> Trend model:
    +#> AR()
    +#> 
    +#> N latent factors:
    +#> 2 
    +#> 
    +#> N series:
    +#> 3 
    +#> 
    +#> N timepoints:
    +#> 75 
    +#> 
    +#> Status:
    +#> Fitted using Stan 
    +#> 2 chains, each with iter = 1000; warmup = 500; thin = 1 
    +#> Total post-warmup draws = 1000
    +#> 
    +#> 
    +#> GAM coefficient (beta) estimates:
    +#>              2.5%   50% 97.5% Rhat n_eff
    +#> (Intercept) -0.75 -0.36  0.10 1.01    55
    +#> s(season).1 -1.10 -0.66 -0.34 1.01   519
    +#> s(season).2 -0.46 -0.12  0.21 1.00   943
    +#> s(season).3  0.39  0.67  0.93 1.00   769
    +#> s(season).4  0.47  0.73  1.10 1.01   675
    +#> 
    +#> Approximate significance of GAM smooths:
    +#>            edf Ref.df Chi.sq p-value    
    +#> s(season) 2.25      4     66  <2e-16 ***
    +#> ---
    +#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    +#> 
    +#> Latent trend AR parameter estimates:
    +#>         2.5%   50% 97.5% Rhat n_eff
    +#> ar1[1]  0.54  0.92  1.00 1.01    39
    +#> ar1[2] -0.83 -0.15  0.91 1.13    26
    +#> 
    +#> Stan MCMC diagnostics:
    +#> n_eff / iter looks reasonable for all parameters
    +#> Rhats above 1.05 found for 5 parameters
    +#>  *Diagnose further to investigate why the chains have not mixed
    +#> 0 of 1000 iterations ended with a divergence (0%)
    +#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%)
    +#> Chain 1: E-FMI = 0.1002
    +#> Chain 2: E-FMI = 0.0936
    +#>  *E-FMI below 0.2 indicates you may need to reparameterize your model
    +#> 
    +#> Samples were drawn using NUTS(diag_e) at Mon Nov 04 10:40:17 AM 2024.
    +#> For each parameter, n_eff is a crude measure of effective sample size,
    +#> and Rhat is the potential scale reduction factor on split MCMC chains
    +#> (at convergence, Rhat = 1)
    +plot(mod, type = 'smooths')
    +
    +fc <- forecast(mod, newdata = data_test)
    +#> Error in `$<-.data.frame`(`*tmp*`, "index..orig..order", value = 1:0): replacement has 2 rows, data has 0
    +plot(fc)
    +#> Out of sample DRPS:
    +#> 55.025328
    +
    +# Propagating the smooth term shows how the coefficient is expected to evolve
    +plot_mvgam_smooth(mod, smooth = 1, newdata = data)
    +#> Error: not all required variables have been supplied in newdata!
    +abline(v = 180, lty = 'dashed', lwd = 2)
    +points(beta_temp, pch = 16)
    +
    +
    +
    +# Example showing how to incorporate an offset; simulate some count data
    +# with different means per series
    +set.seed(100)
    +dat <- sim_mvgam(prop_trend = 0, mu = c(0, 2, 2),
    +                 seasonality = 'hierarchical')
    +
    +# Add offset terms to the training and testing data
    +dat$data_train$offset <- 0.5 * as.numeric(dat$data_train$series)
    +dat$data_test$offset <- 0.5 * as.numeric(dat$data_test$series)
    +
    +# Fit a model that includes the offset in the linear predictor as well as
    +# hierarchical seasonal smooths
    +mod <- mvgam(formula = y ~ offset(offset) +
    +              s(series, bs = 're') +
    +              s(season, bs = 'cc') +
    +              s(season, by = series, m = 1, k = 5),
    +             data = dat$data_train,
    +             chains = 2)
    +#> Compiling Stan program using cmdstanr
    +#> 
    +#> Start sampling
    +#> Running MCMC with 2 parallel chains...
    +#> 
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    +#> Chain 2 finished in 13.6 seconds.
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    +#> Chain 1 finished in 14.6 seconds.
    +#> 
    +#> Both chains finished successfully.
    +#> Mean chain execution time: 14.1 seconds.
    +#> Total execution time: 14.9 seconds.
    +#> 
    +
    +# Inspect the model file to see the modification to the linear predictor
    +# (eta)
    +code(mod)
    +#> // Stan model code generated by package mvgam
    +#> data {
    +#>   int<lower=0> total_obs; // total number of observations
    +#>   int<lower=0> n; // number of timepoints per series
    +#>   int<lower=0> n_sp; // number of smoothing parameters
    +#>   int<lower=0> n_series; // number of series
    +#>   int<lower=0> num_basis; // total number of basis coefficients
    +#>   vector[num_basis] zero; // prior locations for basis coefficients
    +#>   vector[total_obs] off_set; // offset vector
    +#>   matrix[total_obs, num_basis] X; // mgcv GAM design matrix
    +#>   array[n, n_series] int<lower=0> ytimes; // time-ordered matrix (which col in X belongs to each [time, series] observation?)
    +#>   matrix[8, 8] S1; // mgcv smooth penalty matrix S1
    +#>   matrix[4, 4] S2; // mgcv smooth penalty matrix S2
    +#>   matrix[4, 4] S3; // mgcv smooth penalty matrix S3
    +#>   matrix[4, 4] S4; // mgcv smooth penalty matrix S4
    +#>   int<lower=0> n_nonmissing; // number of nonmissing observations
    +#>   array[n_nonmissing] int<lower=0> flat_ys; // flattened nonmissing observations
    +#>   matrix[n_nonmissing, num_basis] flat_xs; // X values for nonmissing observations
    +#>   array[n_nonmissing] int<lower=0> obs_ind; // indices of nonmissing observations
    +#> }
    +#> parameters {
    +#>   // raw basis coefficients
    +#>   vector[num_basis] b_raw;
    +#>   
    +#>   // random effect variances
    +#>   vector<lower=0>[1] sigma_raw;
    +#>   
    +#>   // random effect means
    +#>   vector[1] mu_raw;
    +#>   
    +#>   // smoothing parameters
    +#>   vector<lower=0>[n_sp] lambda;
    +#> }
    +#> transformed parameters {
    +#>   // basis coefficients
    +#>   vector[num_basis] b;
    +#>   b[1 : 21] = b_raw[1 : 21];
    +#>   b[22 : 24] = mu_raw[1] + b_raw[22 : 24] * sigma_raw[1];
    +#> }
    +#> model {
    +#>   // prior for random effect population variances
    +#>   sigma_raw ~ student_t(3, 0, 2.5);
    +#>   
    +#>   // prior for random effect population means
    +#>   mu_raw ~ std_normal();
    +#>   
    +#>   // prior for (Intercept)...
    +#>   b_raw[1] ~ student_t(3, 1.4, 2.5);
    +#>   
    +#>   // prior for s(season)...
    +#>   b_raw[2 : 9] ~ multi_normal_prec(zero[2 : 9], S1[1 : 8, 1 : 8] * lambda[1]);
    +#>   
    +#>   // prior for s(season):seriesseries_1...
    +#>   b_raw[10 : 13] ~ multi_normal_prec(zero[10 : 13],
    +#>                                      S2[1 : 4, 1 : 4] * lambda[2]);
    +#>   
    +#>   // prior for s(season):seriesseries_2...
    +#>   b_raw[14 : 17] ~ multi_normal_prec(zero[14 : 17],
    +#>                                      S3[1 : 4, 1 : 4] * lambda[3]);
    +#>   
    +#>   // prior for s(season):seriesseries_3...
    +#>   b_raw[18 : 21] ~ multi_normal_prec(zero[18 : 21],
    +#>                                      S4[1 : 4, 1 : 4] * lambda[4]);
    +#>   
    +#>   // prior (non-centred) for s(series)...
    +#>   b_raw[22 : 24] ~ std_normal();
    +#>   
    +#>   // priors for smoothing parameters
    +#>   lambda ~ normal(5, 30);
    +#>   {
    +#>     // likelihood functions
    +#>     flat_ys ~ poisson_log_glm(flat_xs, off_set[obs_ind], b);
    +#>   }
    +#> }
    +#> generated quantities {
    +#>   vector[total_obs] eta;
    +#>   matrix[n, n_series] mus;
    +#>   vector[n_sp] rho;
    +#>   array[n, n_series] int ypred;
    +#>   rho = log(lambda);
    +#>   
    +#>   // posterior predictions
    +#>   eta = X * b + off_set;
    +#>   for (s in 1 : n_series) {
    +#>     mus[1 : n, s] = eta[ytimes[1 : n, s]];
    +#>     ypred[1 : n, s] = poisson_log_rng(mus[1 : n, s]);
    +#>   }
    +#> }
    +#> 
    +#> 
    +
    +# Forecasts for the first two series will differ in magnitude
    +fc <- forecast(mod, newdata = dat$data_test)
    +layout(matrix(1:2, ncol = 2))
    +plot(fc, series = 1, ylim = c(0, 75))
    +#> Out of sample DRPS:
    +#> 22.754399
    +plot(fc, series = 2, ylim = c(0, 75))
    +#> Out of sample DRPS:
    +#> 77.633266
    +
    +layout(1)
    +
    +# Changing the offset for the testing data should lead to changes in
    +# the forecast
    +dat$data_test$offset <- dat$data_test$offset - 2
    +fc <- forecast(mod, newdata = dat$data_test)
    +plot(fc)
    +#> Out of sample DRPS:
    +#> 38.550576
    +
    +
    +# Relative Risks can be computed by fixing the offset to the same value
    +# for each series
    +dat$data_test$offset <- rep(1, NROW(dat$data_test))
    +preds_rr <- predict(mod, type = 'link', newdata = dat$data_test,
    +                    summary = FALSE)
    +series1_inds <- which(dat$data_test$series == 'series_1')
    +series2_inds <- which(dat$data_test$series == 'series_2')
    +
    +# Relative Risks are now more comparable among series
    +layout(matrix(1:2, ncol = 2))
    +plot(preds_rr[1, series1_inds], type = 'l', col = 'grey75',
    +     ylim = range(preds_rr),
    +     ylab = 'Series1 Relative Risk', xlab = 'Time')
    +for(i in 2:50){
    + lines(preds_rr[i, series1_inds], col = 'grey75')
    +}
    +
    +plot(preds_rr[1, series2_inds], type = 'l', col = 'darkred',
    +     ylim = range(preds_rr),
    +     ylab = 'Series2 Relative Risk', xlab = 'Time')
    +for(i in 2:50){
    + lines(preds_rr[i, series2_inds], col = 'darkred')
    + }
    +
    +layout(1)
    +
    +
    +# Example showcasing how cbind() is needed for Binomial observations
    +# Simulate two time series of Binomial trials
    +trials <- sample(c(20:25), 50, replace = TRUE)
    +x <- rnorm(50)
    +detprob1 <- plogis(-0.5 + 0.9*x)
    +detprob2 <- plogis(-0.1 -0.7*x)
    +dat <- rbind(data.frame(y = rbinom(n = 50, size = trials, prob = detprob1),
    +                        time = 1:50,
    +                        series = 'series1',
    +                        x = x,
    +                        ntrials = trials),
    +             data.frame(y = rbinom(n = 50, size = trials, prob = detprob2),
    +                        time = 1:50,
    +                        series = 'series2',
    +                        x = x,
    +                        ntrials = trials))
    +dat <- dplyr::mutate(dat, series = as.factor(series))
    +dat <- dplyr::arrange(dat, time, series)
    +plot_mvgam_series(data = dat, series = 'all')
    +
    +
    +# Fit a model using the binomial() family; must specify observations
    +# and number of trials in the cbind() wrapper
    +mod <- mvgam(cbind(y, ntrials) ~ series + s(x, by = series),
    +             family = binomial(),
    +             data = dat,
    +             chains = 2)
    +#> Warning: Binomial and Beta-binomial families require cbind(n_successes, n_trials)
    +#> in the formula left-hand side. Do not use cbind(n_successes, n_failures)!
    +#> This warning is displayed once per session.
    +#> Compiling Stan program using cmdstanr
    +#> 
    +#> Start sampling
    +#> Running MCMC with 2 parallel chains...
    +#> 
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    +#> Chain 1 finished in 3.0 seconds.
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    +#> Chain 2 finished in 3.0 seconds.
    +#> 
    +#> Both chains finished successfully.
    +#> Mean chain execution time: 3.0 seconds.
    +#> Total execution time: 3.4 seconds.
    +#> 
    +summary(mod)
    +#> GAM formula:
    +#> cbind(y, ntrials) ~ series + s(x, by = series)
    +#> <environment: 0x0000022e983e9af0>
    +#> 
    +#> Family:
    +#> binomial
    +#> 
    +#> Link function:
    +#> logit
    +#> 
    +#> Trend model:
    +#> None
    +#> 
    +#> N series:
    +#> 2 
    +#> 
    +#> N timepoints:
    +#> 50 
    +#> 
    +#> Status:
    +#> Fitted using Stan 
    +#> 2 chains, each with iter = 1000; warmup = 500; thin = 1 
    +#> Total post-warmup draws = 1000
    +#> 
    +#> 
    +#> GAM coefficient (beta) estimates:
    +#>                        2.5%      50%  97.5% Rhat n_eff
    +#> (Intercept)          -0.690 -0.55000 -0.410 1.00   816
    +#> seriesseries2         0.300  0.50000  0.680 1.00   898
    +#> s(x):seriesseries1.1 -0.110  0.06900  0.500 1.02   198
    +#> s(x):seriesseries1.2 -0.170  0.01700  0.290 1.01   428
    +#> s(x):seriesseries1.3 -0.098 -0.00420  0.061 1.00   552
    +#> s(x):seriesseries1.4 -0.110  0.00380  0.150 1.00   433
    +#> s(x):seriesseries1.5 -0.056 -0.00098  0.046 1.00   715
    +#> s(x):seriesseries1.6 -0.130 -0.00410  0.100 1.00   430
    +#> s(x):seriesseries1.7 -0.045  0.00130  0.053 1.00   422
    +#> s(x):seriesseries1.8 -0.680  0.03200  0.880 1.00   410
    +#> s(x):seriesseries1.9  0.360  0.96000  1.300 1.01   197
    +#> s(x):seriesseries2.1 -0.350 -0.03300  0.160 1.01   244
    +#> s(x):seriesseries2.2 -0.260 -0.01600  0.180 1.00   289
    +#> s(x):seriesseries2.3 -0.048  0.00810  0.110 1.01   307
    +#> s(x):seriesseries2.4 -0.140 -0.00520  0.120 1.00   312
    +#> s(x):seriesseries2.5 -0.047  0.00230  0.052 1.00   935
    +#> s(x):seriesseries2.6 -0.110  0.00380  0.120 1.00   314
    +#> s(x):seriesseries2.7 -0.043  0.00015  0.043 1.00   346
    +#> s(x):seriesseries2.8 -0.790 -0.02200  0.700 1.00   293
    +#> s(x):seriesseries2.9 -0.950 -0.69000 -0.220 1.01   259
    +#> 
    +#> Approximate significance of GAM smooths:
    +#>                     edf Ref.df Chi.sq p-value    
    +#> s(x):seriesseries1 1.93      9   53.8  <2e-16 ***
    +#> s(x):seriesseries2 1.08      9   27.6    0.42    
    +#> ---
    +#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
    +#> 
    +#> Stan MCMC diagnostics:
    +#> n_eff / iter looks reasonable for all parameters
    +#> Rhat looks reasonable for all parameters
    +#> 0 of 1000 iterations ended with a divergence (0%)
    +#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%)
    +#> E-FMI indicated no pathological behavior
    +#> 
    +#> Samples were drawn using NUTS(diag_e) at Mon Nov 04 10:42:59 AM 2024.
    +#> For each parameter, n_eff is a crude measure of effective sample size,
    +#> and Rhat is the potential scale reduction factor on split MCMC chains
    +#> (at convergence, Rhat = 1)
    +pp_check(mod, type = "bars_grouped",
    +         group = "series", ndraws = 50)
    +
    +pp_check(mod, type = "ecdf_overlay_grouped",
    +         group = "series", ndraws = 50)
    +
    +conditional_effects(mod, type = 'link')
    +
    +
    +# }
    +
    +
    +
    + + +
    + + + + + + + diff --git a/docs/reference/mvgam_marginaleffects.html b/docs/reference/mvgam_marginaleffects.html index 4e897e07..9a53c822 100644 --- a/docs/reference/mvgam_marginaleffects.html +++ b/docs/reference/mvgam_marginaleffects.html @@ -156,6 +156,8 @@

    Argumentsdatagrid() call to specify a custom grid of regressors. For example:

    • newdata = datagrid(cyl = c(4, 6)): cyl variable equal to 4 and 6 and other regressors fixed at their means or modes.

    • See the Examples section and the datagrid() documentation.

    +
  • subset() call with a single argument to select a subset of the dataset used to fit the model, ex: newdata = subset(treatment == 1)

  • +
  • dplyr::filter() call with a single argument to select a subset of the dataset used to fit the model, ex: newdata = filter(treatment == 1)

  • string:

    • "mean": Marginal Effects at the Mean. Slopes when each predictor is held at its mean or mode.

    • "median": Marginal Effects at the Median. Slopes when each predictor is held at its median or mode.

    • "marginalmeans": Marginal Effects at Marginal Means. See Details section below.

    • diff --git a/docs/reference/residual_cor.jsdgam.html b/docs/reference/residual_cor.jsdgam.html new file mode 100644 index 00000000..fc7dbda1 --- /dev/null +++ b/docs/reference/residual_cor.jsdgam.html @@ -0,0 +1,199 @@ + +Extract residual correlations based on latent factors from a fitted jsdgam — residual_cor.jsdgam • mvgam + Skip to contents + + +
      +
      +
      + +
      +

      Compute residual correlation estimates from Joint Species Distribution +jsdgam models using latent factor loadings

      +
      + +
      +

      Usage

      +
      residual_cor(object, ...)
      +
      +# S3 method for jsdgam
      +residual_cor(
      +  object,
      +  summary = TRUE,
      +  robust = FALSE,
      +  probs = c(0.025, 0.975),
      +  ...
      +)
      +
      + +
      +

      Arguments

      +
      object
      +

      list object of class mvgam resulting from a call to jsdgam()

      + + +
      ...
      +

      ignored

      + + +
      summary
      +

      Should summary statistics be returned +instead of the raw values? Default is TRUE..

      + + +
      robust
      +

      If FALSE (the default) the mean is used as a measure of central tendency. +If TRUE, the median is used instead. Only used if summary is TRUE

      + + +
      probs
      +

      The percentiles to be computed by the quantile +function. Only used if summary is TRUE.

      + +
      +
      +

      Value

      + + +

      If summary = TRUE, a list with the following components:

      • cor, cor_lower, cor_upper: A set of \(p \times p\) correlation matrices, +containing either the posterior median or mean estimate, plus lower and upper limits +of the corresponding credible intervals supplied to probs

      • +
      • sig_cor: A \(p \times p\) correlation matrix containing only those correlations whose credible +interval does not contain zero. All other correlations are set to zero

      • +
      • prec, prec_lower, prec_upper: A set of \(p \times p\) precision matrices, +containing either the posterior median or mean estimate, plus lower and upper limits +of the corresponding credible intervals supplied to probs

      • +
      • sig_prec: A \(p \times p\) precision matrix containing only those precisions whose credible +interval does not contain zero. All other precisions are set to zero

      • +
      • cov: A \(p \times p\) posterior median or mean covariance matrix

      • +
      • trace: The median/mean point estimator of the trace (sum of the diagonal elements) +of the residual covariance matrix cov

      • +

      If summary = FALSE, this function returns a list containing the following components:

      • all_cormat: A \(n_{draws} \times p \times p\) array of posterior +residual correlation matrix draws

      • +
      • all_covmat: A \(n_{draws} \times p \times p\) array of posterior +residual covariance matrix draws

      • +
      • all_presmat: A \(n_{draws} \times p \times p\) array of posterior +residual precision matrix draws

      • +
      • all_trace: A \(n_{draws}\) vector of posterior covariance trace draws

      • +
      +
      +

      Details

      +

      Hui (2016) provides an excellent description of the quantities that this function calculates, so this passage +is heavily paraphrased from his associated boral package.

      +

      In Joint Species Distribution Models, the residual covariance matrix is calculated +based on the matrix of latent factor loading matrix \(\Theta\), where the residual covariance +matrix \(\Sigma = \Theta\Theta'\). A strong residual covariance/correlation matrix +between two species can be interpreted as evidence of species interaction (e.g., +facilitation or competition), +missing covariates, as well as any additional species correlation not accounted for by shared +environmental captured in formula.

      +

      The residual precision matrix (also known as partial correlation matrix, Ovaskainen et al., 2016) +is defined as the inverse of the residual correlation matrix. The precision matrix is often used to +identify direct or causal relationships between two species e.g., two species can have a zero +precision but still be correlated, which can be interpreted as saying that two species are not +directly associated, but they are still correlated through other species. In other words, they +are conditionally independent given the other species. It is important that the precision matrix +does not exhibit the exact same properties of the correlation e.g., the diagonal elements are +not equal to 1. Nevertheless, relatively larger values of precision imply a stronger +direct relationships between two species.

      +

      In addition to the residual correlation and precision matrices, the median or mean point estimator +of trace of the residual covariance matrix is returned, +\(\sum\limits_{j=1}^p [\Theta\Theta']_{jj}\). Often used in other areas of multivariate +statistics, the trace may be interpreted as the amount of covariation explained by the latent factors. +One situation where the trace may be useful is when comparing a pure latent factor model +(where no terms are suppled to formula) versus a model with latent +factors and some additional predictors in formula -- the proportional difference in trace +between these two models may be interpreted as the proportion of covariation between species explained +by the predictors in formula. Of course, the trace itself is random due to the MCMC sampling, and so it +is not always guaranteed to produce sensible answers.

      +
      +
      +

      References

      +

      Francis KC Hui (2016). BORAL - Bayesian ordination and regression analysis of +multivariate abundance data in R. Methods in Ecology and Evolution. 7, 744-750. +

      +Otso Ovaskainen et al. (2016). Using latent variable models to identify large networks of +species-to-species associations at different spatial scales. Methods in Ecology and Evolution, +7, 549-555.

      +
      +
      +

      See also

      + +
      +
      +

      Author

      +

      Nicholas J Clark

      +
      + +
      + + +
      + + + + + + + diff --git a/docs/reference/residuals.mvgam.html b/docs/reference/residuals.mvgam.html index 19af2050..1e68e383 100644 --- a/docs/reference/residuals.mvgam.html +++ b/docs/reference/residuals.mvgam.html @@ -3,7 +3,7 @@ residuals in the order in which the data were supplied to the model. It included additional arguments for obtaining summaries of the computed residuals">Posterior draws of mvgam residuals — residuals.mvgam • mvgam @@ -14,7 +14,7 @@ mvgam - 1.1.3 + 1.1.4
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    @@ -149,37 +148,37 @@

    Examples#> Chain 1 Iteration: 100 / 1000 [ 10%] (Warmup) #> Chain 1 Iteration: 200 / 1000 [ 20%] (Warmup) #> Chain 1 Iteration: 300 / 1000 [ 30%] (Warmup) +#> Chain 1 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 2 Iteration: 100 / 1000 [ 10%] (Warmup) #> Chain 2 Iteration: 200 / 1000 [ 20%] (Warmup) -#> Chain 1 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 2 Iteration: 300 / 1000 [ 30%] (Warmup) -#> Chain 2 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 1 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 1 Iteration: 501 / 1000 [ 50%] (Sampling) +#> Chain 2 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 2 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 2 Iteration: 501 / 1000 [ 50%] (Sampling) #> Chain 1 Iteration: 600 / 1000 [ 60%] (Sampling) -#> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) #> Chain 1 Iteration: 700 / 1000 [ 70%] (Sampling) -#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) +#> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) #> Chain 1 Iteration: 800 / 1000 [ 80%] (Sampling) +#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 2 Iteration: 800 / 1000 [ 80%] (Sampling) #> Chain 1 Iteration: 900 / 1000 [ 90%] (Sampling) -#> Chain 2 Iteration: 900 / 1000 [ 90%] (Sampling) #> Chain 1 Iteration: 1000 / 1000 [100%] (Sampling) -#> Chain 2 Iteration: 1000 / 1000 [100%] (Sampling) +#> Chain 2 Iteration: 900 / 1000 [ 90%] (Sampling) #> Chain 1 finished in 0.9 seconds. -#> Chain 2 finished in 1.0 seconds. +#> Chain 2 Iteration: 1000 / 1000 [100%] (Sampling) +#> Chain 2 finished in 0.8 seconds. #> #> Both chains finished successfully. -#> Mean chain execution time: 1.0 seconds. -#> Total execution time: 1.1 seconds. +#> Mean chain execution time: 0.8 seconds. +#> Total execution time: 1.2 seconds. #> # Extract posterior residuals resids <- residuals(mod) str(resids) -#> num [1:75, 1:4] 0.63 -1.122 1.121 0.931 -0.898 ... +#> num [1:75, 1:4] 1.312 0.902 0.354 0.402 0.395 ... #> - attr(*, "dimnames")=List of 2 #> ..$ : NULL #> ..$ : chr [1:4] 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z2cSscw9>hFxN=(&KCr_sE@+;)w)xIAI(&nwvZ1SpQ-m3ELn<4f0-*j-h^s=ZBEWTQ zVm%XiKwPLySMY=;s}=qs2~Qgae6xqw4WrMkD`(|Tnw#bf(8R4}&gexTyJnnVf!#}fx`Ta);7(=A0arhGfUBn9@Hc4)DLyxwey0kp8} zJB&sx*7ks|pw4;g%82_y;#ydHV?bLgpj_5Yel;q}d&g;4$*y#oW+LA*F(HBKBaH6aslHgO{pY8-*CE&gBES2RW;_g1BtigFHs1b*U*$g zb~_-iU&B`COXZ38LTrKe|y=4Lgow$v+jM;v7H2Y=^p zLi5t_f?U}ac-^g;Q$^pexOIW=O+P=vp4kP2+vp*Sbpiqcj?x~WKu_qOe1`|V18i6Y z)<~oRh)60mOa#$rE@sG|(DWQo$x=B zrTK`OGQ+vNifD&L^4l^|SuhxSfUl;gg6>6j$?n@3h^G@X0rrnt8Fr{LyAbxs8Usage object, formula, trend_formula, + knots, + trend_knots, data, newdata, trend_model, @@ -84,6 +86,28 @@

    Usage algorithm, lfo = FALSE, ... +) + +# S3 method for jsdgam +update( + object, + formula, + factor_formula, + knots, + factor_knots, + data, + newdata, + n_lv, + family, + share_obs_params, + priors, + chains, + burnin, + samples, + threads, + algorithm, + lfo = FALSE, + ... )

    @@ -114,6 +138,18 @@

    ArgumentsArgumentsmvgam

    +

    Other arguments to be passed to mvgam or jsdgam

    + + +
    factor_formula
    +

    Optional new formula object for the factor linear predictors

    + + +
    factor_knots
    +

    An optional list containing user specified knot values to +be used for basis construction of any smooth terms in factor_formula. +For most bases the user simply supplies the knots to be used, which must match up with the k value supplied +(note that the number of knots is not always just k). Different terms can use different numbers of knots, +unless they share a covariate

    Value

    +

    A list object of class mvgam containing model output, the text representation of the model file, +the mgcv model output (for easily generating simulations at +unsampled covariate values), Dunn-Smyth residuals for each outcome variable and key information needed +for other functions in the package. See mvgam-class for details. +Use methods(class = "mvgam") for an overview on available methods.

    + +

    A list object of class mvgam containing model output, the text representation of the model file, the mgcv model output (for easily generating simulations at unsampled covariate values), Dunn-Smyth residuals for each series and key information needed for other functions in the package. See mvgam-class for details. Use methods(class = "mvgam") for an overview on available methods.

    +
    +

    Author

    +

    Nicholas J Clark

    +

    Examples

    @@ -298,32 +357,19 @@

    Examples chains = 2) #> Compiling Stan program using cmdstanr #> -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5, -#> from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4, -#> from stan/lib/stan_math/stan/math/prim/prob.hpp:359, -#> from stan/lib/stan_math/stan/math/prim.hpp:16, -#> from stan/lib/stan_math/stan/math/rev.hpp:16, -#> from stan/lib/stan_math/stan/math.hpp:19, -#> from stan/src/stan/model/model_header.hpp:4, -#> from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bcd4b472f.hpp:2: -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)': -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers -#> 194 | if (cdf_n < 0.0) -#> | -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory #> Start sampling #> Running MCMC with 2 parallel chains... #> #> Chain 1 Iteration: 1 / 1000 [ 0%] (Warmup) -#> Chain 2 Iteration: 1 / 1000 [ 0%] (Warmup) #> Chain 1 Iteration: 100 / 1000 [ 10%] (Warmup) +#> Chain 2 Iteration: 1 / 1000 [ 0%] (Warmup) #> Chain 1 Iteration: 200 / 1000 [ 20%] (Warmup) #> Chain 1 Iteration: 300 / 1000 [ 30%] (Warmup) #> Chain 1 Iteration: 400 / 1000 [ 40%] (Warmup) +#> Chain 1 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 2 Iteration: 100 / 1000 [ 10%] (Warmup) #> Chain 2 Iteration: 200 / 1000 [ 20%] (Warmup) #> Chain 2 Iteration: 300 / 1000 [ 30%] (Warmup) -#> Chain 1 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 1 Iteration: 501 / 1000 [ 50%] (Sampling) #> Chain 1 Iteration: 600 / 1000 [ 60%] (Sampling) #> Chain 2 Iteration: 400 / 1000 [ 40%] (Warmup) @@ -331,24 +377,24 @@

    Examples#> Chain 2 Iteration: 501 / 1000 [ 50%] (Sampling) #> Chain 1 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) -#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 1 Iteration: 800 / 1000 [ 80%] (Sampling) -#> Chain 1 Iteration: 900 / 1000 [ 90%] (Sampling) +#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 2 Iteration: 800 / 1000 [ 80%] (Sampling) -#> Chain 1 Iteration: 1000 / 1000 [100%] (Sampling) +#> Chain 1 Iteration: 900 / 1000 [ 90%] (Sampling) #> Chain 2 Iteration: 900 / 1000 [ 90%] (Sampling) +#> Chain 1 Iteration: 1000 / 1000 [100%] (Sampling) #> Chain 2 Iteration: 1000 / 1000 [100%] (Sampling) -#> Chain 1 finished in 0.7 seconds. -#> Chain 2 finished in 0.7 seconds. +#> Chain 1 finished in 0.9 seconds. +#> Chain 2 finished in 0.8 seconds. #> #> Both chains finished successfully. -#> Mean chain execution time: 0.7 seconds. -#> Total execution time: 0.9 seconds. +#> Mean chain execution time: 0.8 seconds. +#> Total execution time: 1.2 seconds. #> summary(mod) #> GAM formula: #> y ~ s(season, bs = "cc") -#> <environment: 0x00000162775c3b90> +#> <environment: 0x0000022e84a980e8> #> #> Family: #> poisson @@ -372,36 +418,37 @@

    Examples#> #> #> GAM coefficient (beta) estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> (Intercept) 0.550 0.75 0.930 1 859 -#> s(season).1 -0.890 -0.48 -0.094 1 860 -#> s(season).2 -0.730 -0.24 0.230 1 804 -#> s(season).3 0.002 0.41 0.820 1 908 -#> s(season).4 0.390 0.76 1.100 1 701 -#> s(season).5 0.370 0.72 1.100 1 776 -#> s(season).6 0.310 0.71 1.100 1 849 -#> s(season).7 0.190 0.61 1.000 1 787 -#> s(season).8 -0.530 -0.13 0.240 1 530 +#> 2.5% 50% 97.5% Rhat n_eff +#> (Intercept) -1.30 -0.86 -0.47 1 390 +#> s(season).1 -1.60 -0.85 -0.24 1 458 +#> s(season).2 -1.90 -1.10 -0.27 1 563 +#> s(season).3 -1.90 -0.91 -0.14 1 528 +#> s(season).4 -1.20 -0.36 0.40 1 672 +#> s(season).5 -0.17 0.48 1.10 1 685 +#> s(season).6 0.72 1.30 2.00 1 367 +#> s(season).7 0.63 1.30 1.90 1 494 +#> s(season).8 0.18 0.80 1.40 1 480 #> #> Approximate significance of GAM smooths: #> edf Ref.df Chi.sq p-value -#> s(season) 4.69 8 23.5 0.00064 *** +#> s(season) 3.16 8 54.4 0.00054 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Latent trend parameter AR estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> ar1[1] -0.99 -0.50 0.21 1.01 250 -#> sigma[1] 0.22 0.43 0.70 1.00 341 +#> 2.5% 50% 97.5% Rhat n_eff +#> ar1[1] -0.94 -0.043 0.89 1 441 +#> sigma[1] 0.01 0.290 0.81 1 278 #> #> Stan MCMC diagnostics: #> n_eff / iter looks reasonable for all parameters #> Rhat looks reasonable for all parameters -#> 0 of 1000 iterations ended with a divergence (0%) +#> 1 of 1000 iterations ended with a divergence (0.1%) +#> *Try running with larger adapt_delta to remove the divergences #> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Sat Nov 02 9:42:28 PM 2024. +#> Samples were drawn using NUTS(diag_e) at Mon Nov 04 10:44:47 AM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) @@ -413,57 +460,44 @@

    Examples noncentred = TRUE) #> Compiling Stan program using cmdstanr #> -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5, -#> from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4, -#> from stan/lib/stan_math/stan/math/prim/prob.hpp:359, -#> from stan/lib/stan_math/stan/math/prim.hpp:16, -#> from stan/lib/stan_math/stan/math/rev.hpp:16, -#> from stan/lib/stan_math/stan/math.hpp:19, -#> from stan/src/stan/model/model_header.hpp:4, -#> from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc27275bd0.hpp:2: -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)': -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers -#> 194 | if (cdf_n < 0.0) -#> | -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory #> Start sampling #> Running MCMC with 2 parallel chains... #> #> Chain 1 Iteration: 1 / 1000 [ 0%] (Warmup) -#> Chain 2 Iteration: 1 / 1000 [ 0%] (Warmup) #> Chain 1 Iteration: 100 / 1000 [ 10%] (Warmup) +#> Chain 2 Iteration: 1 / 1000 [ 0%] (Warmup) #> Chain 1 Iteration: 200 / 1000 [ 20%] (Warmup) #> Chain 1 Iteration: 300 / 1000 [ 30%] (Warmup) #> Chain 1 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 2 Iteration: 100 / 1000 [ 10%] (Warmup) #> Chain 2 Iteration: 200 / 1000 [ 20%] (Warmup) -#> Chain 2 Iteration: 300 / 1000 [ 30%] (Warmup) #> Chain 1 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 1 Iteration: 501 / 1000 [ 50%] (Sampling) #> Chain 1 Iteration: 600 / 1000 [ 60%] (Sampling) +#> Chain 2 Iteration: 300 / 1000 [ 30%] (Warmup) #> Chain 2 Iteration: 400 / 1000 [ 40%] (Warmup) +#> Chain 1 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 2 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 2 Iteration: 501 / 1000 [ 50%] (Sampling) -#> Chain 1 Iteration: 700 / 1000 [ 70%] (Sampling) -#> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) -#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 1 Iteration: 800 / 1000 [ 80%] (Sampling) +#> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) #> Chain 1 Iteration: 900 / 1000 [ 90%] (Sampling) -#> Chain 2 Iteration: 800 / 1000 [ 80%] (Sampling) +#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 1 Iteration: 1000 / 1000 [100%] (Sampling) +#> Chain 2 Iteration: 800 / 1000 [ 80%] (Sampling) +#> Chain 1 finished in 0.9 seconds. #> Chain 2 Iteration: 900 / 1000 [ 90%] (Sampling) #> Chain 2 Iteration: 1000 / 1000 [100%] (Sampling) -#> Chain 1 finished in 0.7 seconds. -#> Chain 2 finished in 0.7 seconds. +#> Chain 2 finished in 0.9 seconds. #> #> Both chains finished successfully. -#> Mean chain execution time: 0.7 seconds. -#> Total execution time: 0.9 seconds. +#> Mean chain execution time: 0.9 seconds. +#> Total execution time: 1.4 seconds. #> summary(updated_mod) #> GAM formula: #> y ~ s(season, bs = "cc") -#> <environment: 0x00000162775c3b90> +#> <environment: 0x0000022e84a980e8> #> #> Family: #> poisson @@ -487,37 +521,38 @@

    Examples#> #> #> GAM coefficient (beta) estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> (Intercept) 0.560 0.76 0.94 1 665 -#> s(season).1 -0.900 -0.48 -0.12 1 844 -#> s(season).2 -0.740 -0.23 0.23 1 699 -#> s(season).3 0.012 0.40 0.80 1 647 -#> s(season).4 0.390 0.76 1.20 1 458 -#> s(season).5 0.300 0.70 1.10 1 607 -#> s(season).6 0.290 0.71 1.10 1 623 -#> s(season).7 0.250 0.62 1.10 1 585 -#> s(season).8 -0.520 -0.12 0.25 1 758 +#> 2.5% 50% 97.5% Rhat n_eff +#> (Intercept) -1.40 -0.85 -0.470 1.01 141 +#> s(season).1 -1.50 -0.81 -0.210 1.00 421 +#> s(season).2 -1.90 -1.00 -0.260 1.00 459 +#> s(season).3 -2.00 -0.93 -0.055 1.00 258 +#> s(season).4 -1.30 -0.41 0.270 1.00 356 +#> s(season).5 -0.25 0.44 1.100 1.00 657 +#> s(season).6 0.65 1.30 1.900 1.01 472 +#> s(season).7 0.71 1.20 1.800 1.00 537 +#> s(season).8 0.26 0.79 1.300 1.00 460 #> #> Approximate significance of GAM smooths: -#> edf Ref.df Chi.sq p-value -#> s(season) 4.24 8 25.3 0.0082 ** +#> edf Ref.df Chi.sq p-value +#> s(season) 3.04 8 53.8 9e-04 *** #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Latent trend AR parameter estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> ar1[1] -0.96 -0.50 0.19 1.01 216 -#> ar2[1] -0.64 0.23 0.94 1.02 156 -#> sigma[1] 0.21 0.39 0.65 1.00 312 +#> 2.5% 50% 97.5% Rhat n_eff +#> ar1[1] -0.930 -0.063 0.90 1.00 597 +#> ar2[1] -0.930 0.041 0.94 1.00 449 +#> sigma[1] 0.013 0.280 0.79 1.01 165 #> #> Stan MCMC diagnostics: #> n_eff / iter looks reasonable for all parameters #> Rhat looks reasonable for all parameters -#> 0 of 1000 iterations ended with a divergence (0%) +#> 6 of 1000 iterations ended with a divergence (0.6%) +#> *Try running with larger adapt_delta to remove the divergences #> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Sat Nov 02 9:43:26 PM 2024. +#> Samples were drawn using NUTS(diag_e) at Mon Nov 04 10:45:35 AM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) @@ -534,57 +569,44 @@

    Examples family = binomial()) #> Compiling Stan program using cmdstanr #> -#> In file included from stan/lib/stan_math/stan/math/prim/prob/von_mises_lccdf.hpp:5, -#> from stan/lib/stan_math/stan/math/prim/prob/von_mises_ccdf_log.hpp:4, -#> from stan/lib/stan_math/stan/math/prim/prob.hpp:359, -#> from stan/lib/stan_math/stan/math/prim.hpp:16, -#> from stan/lib/stan_math/stan/math/rev.hpp:16, -#> from stan/lib/stan_math/stan/math.hpp:19, -#> from stan/src/stan/model/model_header.hpp:4, -#> from C:/Users/uqnclar2/AppData/Local/Temp/RtmpWM8hW3/model-f8bc5a4e3f02.hpp:2: -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp: In function 'stan::return_type_t<T_x, T_sigma, T_l> stan::math::von_mises_cdf(const T_x&, const T_mu&, const T_k&)': -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: '-Wmisleading-indentation' is disabled from this point onwards, since column-tracking was disabled due to the size of the code/headers -#> 194 | if (cdf_n < 0.0) -#> | -#> stan/lib/stan_math/stan/math/prim/prob/von_mises_cdf.hpp:194: note: adding '-flarge-source-files' will allow for more column-tracking support, at the expense of compilation time and memory #> Start sampling #> Running MCMC with 2 parallel chains... #> #> Chain 1 Iteration: 1 / 1000 [ 0%] (Warmup) -#> Chain 2 Iteration: 1 / 1000 [ 0%] (Warmup) #> Chain 1 Iteration: 100 / 1000 [ 10%] (Warmup) +#> Chain 2 Iteration: 1 / 1000 [ 0%] (Warmup) #> Chain 1 Iteration: 200 / 1000 [ 20%] (Warmup) #> Chain 1 Iteration: 300 / 1000 [ 30%] (Warmup) -#> Chain 1 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 2 Iteration: 100 / 1000 [ 10%] (Warmup) #> Chain 2 Iteration: 200 / 1000 [ 20%] (Warmup) +#> Chain 1 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 2 Iteration: 300 / 1000 [ 30%] (Warmup) -#> Chain 2 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 1 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 1 Iteration: 501 / 1000 [ 50%] (Sampling) +#> Chain 2 Iteration: 400 / 1000 [ 40%] (Warmup) #> Chain 1 Iteration: 600 / 1000 [ 60%] (Sampling) +#> Chain 1 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 2 Iteration: 500 / 1000 [ 50%] (Warmup) #> Chain 2 Iteration: 501 / 1000 [ 50%] (Sampling) -#> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) -#> Chain 1 Iteration: 700 / 1000 [ 70%] (Sampling) -#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 1 Iteration: 800 / 1000 [ 80%] (Sampling) +#> Chain 2 Iteration: 600 / 1000 [ 60%] (Sampling) #> Chain 1 Iteration: 900 / 1000 [ 90%] (Sampling) -#> Chain 2 Iteration: 800 / 1000 [ 80%] (Sampling) +#> Chain 2 Iteration: 700 / 1000 [ 70%] (Sampling) #> Chain 1 Iteration: 1000 / 1000 [100%] (Sampling) +#> Chain 1 finished in 1.0 seconds. +#> Chain 2 Iteration: 800 / 1000 [ 80%] (Sampling) #> Chain 2 Iteration: 900 / 1000 [ 90%] (Sampling) #> Chain 2 Iteration: 1000 / 1000 [100%] (Sampling) -#> Chain 1 finished in 0.7 seconds. -#> Chain 2 finished in 0.7 seconds. +#> Chain 2 finished in 1.2 seconds. #> #> Both chains finished successfully. -#> Mean chain execution time: 0.7 seconds. -#> Total execution time: 0.8 seconds. +#> Mean chain execution time: 1.1 seconds. +#> Total execution time: 2.0 seconds. #> summary(updated_mod) #> GAM formula: #> cbind(y, trials) ~ s(season, bs = "cc") -#> <environment: 0x00000162775c3b90> +#> <environment: 0x0000022e84a980e8> #> #> Family: #> binomial @@ -608,27 +630,27 @@

    Examples#> #> #> GAM coefficient (beta) estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> (Intercept) -2.800 -2.50 -2.400 1.00 447 -#> s(season).1 -0.930 -0.52 -0.099 1.00 632 -#> s(season).2 -0.740 -0.25 0.240 1.00 626 -#> s(season).3 -0.031 0.43 0.900 1.00 480 -#> s(season).4 0.430 0.85 1.300 1.01 341 -#> s(season).5 0.380 0.81 1.200 1.00 453 -#> s(season).6 0.360 0.79 1.200 1.00 749 -#> s(season).7 0.200 0.63 1.200 1.00 456 -#> s(season).8 -0.620 -0.14 0.230 1.01 441 +#> 2.5% 50% 97.5% Rhat n_eff +#> (Intercept) -4.30 -3.80 -3.40 1 561 +#> s(season).1 -1.70 -0.87 -0.27 1 509 +#> s(season).2 -2.00 -1.10 -0.29 1 576 +#> s(season).3 -1.80 -0.90 -0.17 1 591 +#> s(season).4 -1.30 -0.39 0.37 1 503 +#> s(season).5 -0.23 0.49 1.20 1 789 +#> s(season).6 0.72 1.30 2.00 1 756 +#> s(season).7 0.72 1.30 1.90 1 618 +#> s(season).8 0.23 0.81 1.40 1 442 #> #> Approximate significance of GAM smooths: -#> edf Ref.df Chi.sq p-value -#> s(season) 4.32 8 28.9 0.0045 ** +#> edf Ref.df Chi.sq p-value +#> s(season) 1.94 8 63 0.012 * #> --- #> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 #> #> Latent trend parameter AR estimates: -#> 2.5% 50% 97.5% Rhat n_eff -#> ar1[1] -0.95 -0.48 0.039 1.00 254 -#> sigma[1] 0.33 0.56 0.830 1.01 233 +#> 2.5% 50% 97.5% Rhat n_eff +#> ar1[1] -0.900 -0.10 0.88 1.00 503 +#> sigma[1] 0.015 0.31 0.86 1.02 251 #> #> Stan MCMC diagnostics: #> n_eff / iter looks reasonable for all parameters @@ -637,7 +659,7 @@

    Examples#> 0 of 1000 iterations saturated the maximum tree depth of 12 (0%) #> E-FMI indicated no pathological behavior #> -#> Samples were drawn using NUTS(diag_e) at Sat Nov 02 9:44:25 PM 2024. +#> Samples were drawn using NUTS(diag_e) at Mon Nov 04 10:46:25 AM 2024. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split MCMC chains #> (at convergence, Rhat = 1) diff --git a/man/jsdgam.Rd b/man/jsdgam.Rd index 1bbe2936..066d71a3 100644 --- a/man/jsdgam.Rd +++ b/man/jsdgam.Rd @@ -101,9 +101,9 @@ outcomes (time series in most \code{mvgam} models) that you believe share some p such as being from the same species over different spatial units. Default is \code{FALSE}.} \item{priors}{An optional \code{data.frame} with prior -definitions (in JAGS or Stan syntax) or, preferentially, If using Stan, a vector containing +definitions (in Stan syntax) or, preferentially, a vector containing objects of class \code{brmsprior} (see. \code{\link[brms]{prior}} for details). -See \link{get_mvgam_priors} and Details' for more information on changing default prior distributions} +See \link{get_mvgam_priors} and for more information on changing default prior distributions} \item{n_lv}{\code{integer} the number of latent factors to use for modelling residual associations. @@ -221,8 +221,8 @@ where \eqn{g(.)} is a known link function, any of \code{mvgam}'s predictor effects, including random intercepts and slopes, multidimensional penalized smooths, GP effects etc... The factor loadings \eqn{\theta_j} are constrained for identifiability but can be used to reconstruct an estimate of the species' residual variance-covariance matrix -using \eqn{\theta \theta'} (see the example below -for an illustration of this). The latent factors are further modelled using: +using \eqn{\Theta \Theta'} (see the example below and \code{\link[=residual_cor]{residual_cor()}} for details). +The latent factors are further modelled using: \deqn{ u_i \sim \text{Normal}(Q_i\beta_{factor}, 1) \quad } @@ -387,15 +387,16 @@ if(requireNamespace('gratia', quietly = TRUE)){ gratia::draw(mod, trend_effects = TRUE) } -# Calculate (median) residual spatial correlations -med_loadings <- matrix(apply(as.matrix(mod$model_output, 'lv_coefs'), - 2, median), - nrow = N_species, ncol = 4) -cormat <- cov2cor(tcrossprod(med_loadings)) -rownames(cormat) <- colnames(cormat) <- levels(dat$species) - -# A quick and dirty correlation matrix plot -image(cormat) +# Calculate residual spatial correlations +post_cors <- residual_cor(mod) +names(post_cors) +# Look at lower and upper credible interval estimates for +# some of the estimated correlations +post_cors$cor[1:5, 1:5] +post_cors$cor_upper[1:5, 1:5] +post_cors$cor_lower[1:5, 1:5] +# A quick and dirty plot of the posterior median correlations +image(post_cors$cor) # Posterior predictive checks and ELPD-LOO can ascertain model fit pp_check(mod, type = "ecdf_overlay_grouped", @@ -426,13 +427,14 @@ ggplot(newdata, aes(x = lat, y = lon, col = log_count)) + \references{ Nicholas J Clark & Konstans Wells (2020). Dynamic generalised additive models (DGAMs) for forecasting discrete ecological time series. Methods in Ecology and Evolution. 14:3, 771-784. - +\cr +\cr David I Warton, F Guillaume Blanchet, Robert B O’Hara, Otso Ovaskainen, Sara Taskinen, Steven C Walker & Francis KC Hui (2015). So many variables: joint modeling in community ecology. Trends in Ecology & Evolution 30:12, 766-779. } \seealso{ -\link{mvgam} +\code{\link[=mvgam]{mvgam()}}, \code{\link[=residual_cor]{residual_cor()}} } \author{ Nicholas J Clark diff --git a/man/mvgam_marginaleffects.Rd b/man/mvgam_marginaleffects.Rd index 5564cfdb..16e6648e 100644 --- a/man/mvgam_marginaleffects.Rd +++ b/man/mvgam_marginaleffects.Rd @@ -86,6 +86,8 @@ arguments.} \item \code{newdata = datagrid(cyl = c(4, 6))}: \code{cyl} variable equal to 4 and 6 and other regressors fixed at their means or modes. \item See the Examples section and the \code{\link[marginaleffects:datagrid]{datagrid()}} documentation. } +\item \code{\link[=subset]{subset()}} call with a single argument to select a subset of the dataset used to fit the model, ex: \code{newdata = subset(treatment == 1)} +\item \code{\link[dplyr:filter]{dplyr::filter()}} call with a single argument to select a subset of the dataset used to fit the model, ex: \code{newdata = filter(treatment == 1)} \item string: \itemize{ \item "mean": Marginal Effects at the Mean. Slopes when each predictor is held at its mean or mode. diff --git a/man/residual_cor.jsdgam.Rd b/man/residual_cor.jsdgam.Rd new file mode 100644 index 00000000..4eae00bb --- /dev/null +++ b/man/residual_cor.jsdgam.Rd @@ -0,0 +1,111 @@ +% Generated by roxygen2: do not edit by hand +% Please edit documentation in R/residual_cor.R +\name{residual_cor.jsdgam} +\alias{residual_cor.jsdgam} +\alias{residual_cor} +\title{Extract residual correlations based on latent factors from a fitted jsdgam} +\usage{ +residual_cor(object, ...) + +\method{residual_cor}{jsdgam}( + object, + summary = TRUE, + robust = FALSE, + probs = c(0.025, 0.975), + ... +) +} +\arguments{ +\item{object}{\code{list} object of class \code{mvgam} resulting from a call to \code{\link[=jsdgam]{jsdgam()}}} + +\item{...}{ignored} + +\item{summary}{Should summary statistics be returned +instead of the raw values? Default is \code{TRUE}..} + +\item{robust}{If \code{FALSE} (the default) the mean is used as a measure of central tendency. +If \code{TRUE}, the median is used instead. Only used if \code{summary} is \code{TRUE}} + +\item{probs}{The percentiles to be computed by the \code{quantile} +function. Only used if \code{summary} is \code{TRUE}.} +} +\value{ +If \code{summary = TRUE}, a \code{list} with the following components: +\itemize{ +\item{cor, cor_lower, cor_upper}{: A set of \eqn{p \times p} correlation matrices, +containing either the posterior median or mean estimate, plus lower and upper limits +of the corresponding credible intervals supplied to \code{probs}} +\item{sig_cor}{: A \eqn{p \times p} correlation matrix containing only those correlations whose credible +interval does not contain zero. All other correlations are set to zero} +\item{prec, prec_lower, prec_upper}{: A set of \eqn{p \times p} precision matrices, +containing either the posterior median or mean estimate, plus lower and upper limits +of the corresponding credible intervals supplied to \code{probs}} +\item{sig_prec}{: A \eqn{p \times p} precision matrix containing only those precisions whose credible +interval does not contain zero. All other precisions are set to zero} +\item{cov}{: A \eqn{p \times p} posterior median or mean covariance matrix} +\item{trace}{: The median/mean point estimator of the trace (sum of the diagonal elements) +of the residual covariance matrix \code{cov}} +} +If \code{summary = FALSE}, this function returns a \code{list} containing the following components: +\itemize{ +\item{all_cormat}{: A \eqn{n_{draws} \times p \times p} \code{array} of posterior +residual correlation matrix draws} +\item{all_covmat}{: A \eqn{n_{draws} \times p \times p} \code{array} of posterior +residual covariance matrix draws} +\item{all_presmat}{: A \eqn{n_{draws} \times p \times p} \code{array} of posterior +residual precision matrix draws} +\item{all_trace}{: A \eqn{n_{draws}} \code{vector} of posterior covariance trace draws} +} +} +\description{ +Compute residual correlation estimates from Joint Species Distribution +\code{jsdgam} models using latent factor loadings +} +\details{ +Hui (2016) provides an excellent description of the quantities that this function calculates, so this passage +is heavily paraphrased from his associated \code{boral} package. + +In Joint Species Distribution Models, the residual covariance matrix is calculated +based on the matrix of latent factor loading matrix \eqn{\Theta}, where the residual covariance +matrix \eqn{\Sigma = \Theta\Theta'}. A strong residual covariance/correlation matrix +between two species can be interpreted as evidence of species interaction (e.g., +facilitation or competition), +missing covariates, as well as any additional species correlation not accounted for by shared +environmental captured in \code{formula}. + +The residual precision matrix (also known as partial correlation matrix, Ovaskainen et al., 2016) +is defined as the inverse of the residual correlation matrix. The precision matrix is often used to +identify direct or causal relationships between two species e.g., two species can have a zero +precision but still be correlated, which can be interpreted as saying that two species are not +directly associated, but they are still correlated \emph{through} other species. In other words, they +are conditionally independent given the other species. It is important that the precision matrix +does not exhibit the exact same properties of the correlation e.g., the diagonal elements are +not equal to 1. Nevertheless, relatively larger values of precision imply a stronger +direct relationships between two species. + +In addition to the residual correlation and precision matrices, the median or mean point estimator +of trace of the residual covariance matrix is returned, +\eqn{\sum\limits_{j=1}^p [\Theta\Theta']_{jj}}. Often used in other areas of multivariate +statistics, the trace may be interpreted as the amount of covariation explained by the latent factors. +One situation where the trace may be useful is when comparing a pure latent factor model +(where no terms are suppled to \code{formula}) versus a model with latent +factors and some additional predictors in \code{formula} -- the proportional difference in trace +between these two models may be interpreted as the proportion of covariation between species explained +by the predictors in \code{formula}. Of course, the trace itself is random due to the MCMC sampling, and so it +is not always guaranteed to produce sensible answers. +} +\references{ +Francis KC Hui (2016). BORAL - Bayesian ordination and regression analysis of +multivariate abundance data in R. Methods in Ecology and Evolution. 7, 744-750. +\cr +\cr +Otso Ovaskainen et al. (2016). Using latent variable models to identify large networks of +species-to-species associations at different spatial scales. Methods in Ecology and Evolution, +7, 549-555. +} +\seealso{ +\code{\link[=jsdgam]{jsdgam()}} +} +\author{ +Nicholas J Clark +} diff --git a/man/residuals.mvgam.Rd b/man/residuals.mvgam.Rd index 3ffd00ae..f82faee6 100644 --- a/man/residuals.mvgam.Rd +++ b/man/residuals.mvgam.Rd @@ -21,8 +21,7 @@ Only used if \code{summary} is \code{TRUE}.} \item{probs}{The percentiles to be computed by the \code{quantile} function. Only used if \code{summary} is \code{TRUE}.} -\item{...}{Further arguments passed to \code{\link[brms]{prepare_predictions}} -that control several aspects of data validation and prediction.} +\item{...}{ignored} } \value{ An \code{array} of randomized quantile residual values. diff --git a/man/update.mvgam.Rd b/man/update.mvgam.Rd index 5060203a..870e3c0f 100644 --- a/man/update.mvgam.Rd +++ b/man/update.mvgam.Rd @@ -2,12 +2,15 @@ % Please edit documentation in R/update.mvgam.R \name{update.mvgam} \alias{update.mvgam} +\alias{update.jsdgam} \title{Update an existing \code{mvgam} object} \usage{ \method{update}{mvgam}( object, formula, trend_formula, + knots, + trend_knots, data, newdata, trend_model, @@ -25,6 +28,27 @@ lfo = FALSE, ... ) + +\method{update}{jsdgam}( + object, + formula, + factor_formula, + knots, + factor_knots, + data, + newdata, + n_lv, + family, + share_obs_params, + priors, + chains, + burnin, + samples, + threads, + algorithm, + lfo = FALSE, + ... +) } \arguments{ \item{object}{\code{list} object returned from \code{mvgam}. See \code{\link[=mvgam]{mvgam()}}} @@ -46,6 +70,14 @@ latent abundance. Be aware that it can be very challenging to simultaneously est for both the observation mode (captured by \code{formula}) and the process model (captured by \code{trend_formula}). Users are recommended to drop one of these using the \code{- 1} convention in the formula right hand side.} +\item{knots}{An optional \code{list} containing user specified knot values to be used for basis construction. +For most bases the user simply supplies the knots to be used, which must match up with the \code{k} value supplied +(note that the number of knots is not always just \code{k}). Different terms can use different numbers of knots, +unless they share a covariate} + +\item{trend_knots}{As for \code{knots} above, this is an optional \code{list} of knot values for smooth +functions within the \code{trend_formula}} + \item{data}{A \code{dataframe} or \code{list} containing the model response variable and covariates required by the GAM \code{formula} and optional \code{trend_formula}. Most models should include columns: \itemize{ @@ -181,9 +213,23 @@ lighter version of the model with no residuals and fewer monitored parameters to post-processing. But other downstream functions will not work properly, so users should always leave this set as \code{FALSE}} -\item{...}{Other arguments to be passed to \code{\link{mvgam}}} +\item{...}{Other arguments to be passed to \code{\link{mvgam}} or \code{\link{jsdgam}}} + +\item{factor_formula}{Optional new \code{formula} object for the factor linear predictors} + +\item{factor_knots}{An optional \code{list} containing user specified knot values to +be used for basis construction of any smooth terms in \code{factor_formula}. +For most bases the user simply supplies the knots to be used, which must match up with the \code{k} value supplied +(note that the number of knots is not always just \code{k}). Different terms can use different numbers of knots, +unless they share a covariate} } \value{ +A \code{list} object of class \code{mvgam} containing model output, the text representation of the model file, +the mgcv model output (for easily generating simulations at +unsampled covariate values), Dunn-Smyth residuals for each outcome variable and key information needed +for other functions in the package. See \code{\link{mvgam-class}} for details. +Use \code{methods(class = "mvgam")} for an overview on available methods. + A \code{list} object of class \code{mvgam} containing model output, the text representation of the model file, the mgcv model output (for easily generating simulations at unsampled covariate values), Dunn-Smyth residuals for each series and key information needed @@ -223,3 +269,6 @@ summary(updated_mod) conditional_effects(updated_mod, type = 'link') } } +\author{ +Nicholas J Clark +} diff --git a/src/RcppExports.o b/src/RcppExports.o index 5cf5ae212a40f74725a9674bfa1be2b221d56b80..03b011192531eff382f7b4b3aad3c852fa2b68e4 100644 GIT binary patch literal 118706 zcmeEv3wRVo)^<%YorK&b2q>(#Q3efOaB@!scPA3GqZ7>{uI$Q6FocWCCBj6}MGYn> z;}D68E~|bkt9W-^R#^pa8!iGWs}WJr^%4b@aZo{7MZEC8r%rWE_spRAF8}xK|NLJ+ zPfx#Hb?Tg|Q&s0wRaf^+ye7*faGY_lOZ+6AkXsB3HO&bTR7dOKLW~(Ig#T#{7?CD~ zSJXEQn>Zmf!6L%di*w6qLM(WN1Kqd;M19w=3un*f5cMnNI6_3LXy`hr)EQQQ+dbfC zKfDF?4JVaU*n^N`Nmt}AvlEis{t5h~+@g|7 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