From 9822ed74f832962a4dabec267d1520b4e45bfc6b Mon Sep 17 00:00:00 2001 From: Nicholas Clark Date: Tue, 29 Oct 2024 19:07:56 +1000 Subject: [PATCH 1/5] first steps toward a jsdgam function --- NEWS.md | 5 +- R/add_MACor.R | 4 +- R/marginaleffects.mvgam.R | 39 ++++- R/model.frame.mvgam.R | 69 +++++++- R/predict.mvgam.R | 80 +++++++-- R/stan_utils.R | 17 +- R/summary.mvgam.R | 2 +- R/validations.R | 60 ++++--- docs/news/index.html | 8 +- jsdgam_function.R | 337 ++++++++++++++++++++++++++++++++++++++ src/RcppExports.o | Bin 126880 -> 118706 bytes src/trend_funs.o | Bin 99568 -> 98386 bytes 12 files changed, 561 insertions(+), 60 deletions(-) create mode 100644 jsdgam_function.R diff --git a/NEWS.md b/NEWS.md index ceafd6cb..1d4dabec 100644 --- a/NEWS.md +++ b/NEWS.md @@ -1,10 +1,9 @@ # mvgam 1.1.4 (development version; not yet on CRAN) ## New functionalities -* Added a `stability.mvgam` method to compute stability metrics from models fit with Vector Autoregressive dynamics (#21) +* 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 -======= -* Added a `fevd.mvgam` method to compute forecast error variance decompositions from models fit with Vector Autoregressive dynamics +* Added a `fevd.mvgam` method to compute forecast error variance decompositions from models fit with Vector Autoregressive dynamics (#21 and #76) ## Bug fixes * Fixed a minor bug in the way `trend_map` recognises levels of the `series` factor diff --git a/R/add_MACor.R b/R/add_MACor.R index 824d8186..1c94505f 100644 --- a/R/add_MACor.R +++ b/R/add_MACor.R @@ -1893,7 +1893,7 @@ add_MaCor = function(model_file, model_file[grep("// posterior predictions", model_file, fixed = TRUE)] <- paste0('// computed (full) error covariance matrix\n', - 'matrix[n_lv, n_lv] Sigma;\n', + 'matrix[n_lv, n_lv] Sigma;\n', 'Sigma = rep_matrix(0, n_lv, n_lv);\n', 'for (g in 1 : n_groups){\n', 'Sigma[group_inds[g], group_inds[g]] = multiply_lower_tri_self_transpose(L_Sigma_group[g]);\n', @@ -1904,7 +1904,7 @@ add_MaCor = function(model_file, model_file[grep("// posterior predictions", model_file, fixed = TRUE)] <- paste0('// computed (full) error covariance matrix\n', - 'matrix[n_series, n_series] Sigma;\n', + 'matrix[n_series, n_series] Sigma;\n', 'Sigma = rep_matrix(0, n_series, n_series);\n', 'for (g in 1 : n_groups){\n', 'Sigma[group_inds[g], group_inds[g]] = multiply_lower_tri_self_transpose(L_Sigma_group[g]);\n', diff --git a/R/marginaleffects.mvgam.R b/R/marginaleffects.mvgam.R index 68059f5a..b149110d 100644 --- a/R/marginaleffects.mvgam.R +++ b/R/marginaleffects.mvgam.R @@ -171,11 +171,10 @@ get_data.mvgam = function (x, source = "environment", verbose = TRUE, ...) { unique(x$trend_map$trend))) # Trend-level data, before any slicing that took place - trend_level_data <- data.frame(trend_series = trend_indicators, - series = orig_dat$series, - time = orig_dat$time, - y = orig_dat$y, - row_num = 1:length(x$obs_data$index..time..index)) + orig_dat %>% + dplyr::bind_cols(data.frame(trend_series = trend_indicators, + row_num = 1:length(x$obs_data$index..time..index))) -> + trend_level_data # # We only kept one time observation per trend trend_level_data %>% @@ -373,6 +372,36 @@ find_predictors.mvgam = function(x, effects = c('fixed', } } + # Any other required variables, needed for grouped models + if(!inherits(attr(x$model_data, 'trend_model'), 'mvgam_trend')){ + trend_model <- list(trend_model = trend_model, + unit = 'time', + gr = 'NA', + subgr = 'series') + } else { + trend_model <- attr(x$model_data, 'trend_model') + } + other_vars <- c(trend_model$unit, + trend_model$gr, + trend_model$subgr) + if(!is.null(attr(x$model_data, 'prepped_trend_model'))){ + prepped_model <- attr(x$model_data, 'prepped_trend_model') + other_vars <- c(other_vars, + c(prepped_model$unit, + prepped_model$gr, + prepped_model$subgr)) + } + + if(flatten){ + other_vars <- setdiff(unique(other_vars), + c('NA', preds)) + preds <- c(preds, other_vars) + } else { + other_vars <- setdiff(unique(other_vars), + c('NA', preds$conditional)) + preds$conditional <- c(preds$conditional, other_vars) + } + return(preds) } diff --git a/R/model.frame.mvgam.R b/R/model.frame.mvgam.R index 22ec6659..6bcaae96 100644 --- a/R/model.frame.mvgam.R +++ b/R/model.frame.mvgam.R @@ -39,7 +39,38 @@ model.frame.mvgam = function(formula, trend_effects = FALSE, ...){ if(formula$family == 'nmix'){ out$cap <- formula$obs_data$cap } + + # Any other required variables, needed for grouped models + if(!inherits(attr(formula$model_data, 'trend_model'), 'mvgam_trend')){ + trend_model <- list(trend_model = trend_model, + unit = 'time', + gr = 'NA', + subgr = 'series') + } else { + trend_model <- attr(formula$model_data, 'trend_model') + } + other_vars <- c(trend_model$unit, + trend_model$gr, + trend_model$subgr) + if(!is.null(attr(formula$model_data, 'prepped_trend_model'))){ + prepped_model <- attr(formula$model_data, 'prepped_trend_model') + other_vars <- c(other_vars, + c(prepped_model$unit, + prepped_model$gr, + prepped_model$subgr)) + } + other_vars <- setdiff(unique(other_vars), + c('NA', colnames(out))) + + if(length(other_vars)){ + orig_names <- colnames(out) + for(i in 1:length(other_vars)){ + out <- cbind(out, formula$obs_data[[other_vars[i]]]) + } + colnames(out) <- c(orig_names, other_vars) + } } + return(out) } @@ -71,11 +102,41 @@ model.frame.mvgam_prefit = function(formula, trend_effects = FALSE, ...){ # Now add the observed response, in case there are any # NAs there that need to be updated out[,resp] <- formula$obs_data$y - } - # Ensure 'cap' is included if this is an N-mixture model - if(formula$family == 'nmix'){ - out$cap <- formula$obs_data$cap + # Ensure 'cap' is included if this is an N-mixture model + if(formula$family == 'nmix'){ + out$cap <- formula$obs_data$cap + } + + # Any other required variables, needed for grouped models + if(!inherits(attr(formula$model_data, 'trend_model'), 'mvgam_trend')){ + trend_model <- list(trend_model = trend_model, + unit = 'time', + gr = 'NA', + subgr = 'series') + } else { + trend_model <- attr(formula$model_data, 'trend_model') + } + other_vars <- c(trend_model$unit, + trend_model$gr, + trend_model$subgr) + if(!is.null(attr(formula$model_data, 'prepped_trend_model'))){ + prepped_model <- attr(formula$model_data, 'prepped_trend_model') + other_vars <- c(other_vars, + c(prepped_model$unit, + prepped_model$gr, + prepped_model$subgr)) + } + other_vars <- setdiff(unique(other_vars), + c('NA', colnames(out))) + + if(length(other_vars)){ + orig_names <- colnames(out) + for(i in 1:length(other_vars)){ + out <- cbind(out, formula$obs_data[[other_vars[i]]]) + } + colnames(out) <- c(orig_names, other_vars) + } } return(out) diff --git a/R/predict.mvgam.R b/R/predict.mvgam.R index 0261a75d..1696e781 100644 --- a/R/predict.mvgam.R +++ b/R/predict.mvgam.R @@ -106,10 +106,16 @@ predict.mvgam = function(object, # newdata needs to have a 'series' indicator in it for integrating # over the trend uncertainties - if(!'series' %in% names(newdata)){ - newdata$series <- factor(rep(levels(object$obs_data$series)[1], - length(newdata[[1]])), - levels = levels(object$obs_data$series)) + if(inherits(object, 'jsdgam')){ + newdata <- mvgam:::validate_series_time(data = newdata, + trend_model = attr(object$model_data, 'prepped_trend_model'), + check_levels = FALSE, + check_times = FALSE) + } else { + newdata <- validate_series_time(data = newdata, + trend_model = attr(object$model_data, 'trend_model'), + check_levels = FALSE, + check_times = FALSE) } type <- match.arg(arg = type, choices = c("link", @@ -151,8 +157,8 @@ predict.mvgam = function(object, # If a linear predictor was supplied for the latent process models, calculate - # predictions by assuming the trend is stationary (this is basically what brms) - # does when predicting for autocor() models + # predictions by assuming the trend is stationary (this is basically what brms + # does when predicting for autocor() models) if(!is.null(object$trend_call)){ # Linear predictor matrix for the latent process models @@ -215,21 +221,61 @@ predict.mvgam = function(object, }) names(family_extracts) <- names(family_pars) - # Pre-multiply the linear predictors - all_linpreds <- as.matrix(as.vector(t(apply(as.matrix(betas), 1, - function(row) Xp %*% row + - attr(Xp, 'model.offset'))))) - attr(all_linpreds, 'model.offset') <- 0 - # Trend stationary predictions if(!process_error){ family_extracts <- list(sigma_obs = .Machine$double.eps) } - trend_predictions <- mvgam_predict(family = 'gaussian', - Xp = all_linpreds, - type = 'response', - betas = 1, - family_pars = family_extracts) + if(inherits(object, 'jsdgam')){ + # JSDMs should generate one set of predictions per latent variable and then + # create a weighted set of predictions based on the loading estimates + lv_coefs <- mcmc_chains(object$model_output, 'lv_coefs') + n_draws <- dim(mcmc_chains(object$model_output, 'b'))[1] + series_ind <- as.numeric(newdata$series) + all_linpreds <- as.matrix(as.vector(t(apply(as.matrix(betas), 1, + function(row) Xp %*% row + + attr(Xp, 'model.offset'))))) + attr(all_linpreds, 'model.offset') <- 0 + trend_predictions_raw <- lapply(1:object$n_lv, function(x){ + pred_vec <- mvgam_predict(family = 'gaussian', + Xp = all_linpreds, + type = 'response', + betas = 1, + family_pars = family_extracts) + matrix(pred_vec, nrow = NROW(betas)) + }) + + # Create weighted set of predictions using the loadings + weighted_mat = function(pred_matrices, + weights, + index = 1){ + as.vector(unlist(lapply(pred_matrices, '[', index)) %*% weights) + } + + trend_predictions <- matrix(NA, nrow = n_draws, + ncol = length(newdata[[1]])) + for(i in 1:n_draws){ + for(x in 1:length(newdata[[1]])){ + trend_predictions[i, x] <- weighted_mat(trend_predictions_raw, + matrix(lv_coefs[i,], + nrow = object$n_lv)[,series_ind[x]], + i) + } + } + trend_predictions <- as.vector(trend_predictions) + + } else { + # Pre-multiply the linear predictors + all_linpreds <- as.matrix(as.vector(t(apply(as.matrix(betas), 1, + function(row) Xp %*% row + + attr(Xp, 'model.offset'))))) + attr(all_linpreds, 'model.offset') <- 0 + trend_predictions <- mvgam_predict(family = 'gaussian', + Xp = all_linpreds, + type = 'response', + betas = 1, + family_pars = family_extracts) + } + } else if(attr(object$model_data, 'trend_model') != 'None' & process_error){ # If no linear predictor for the trends but a dynamic trend model was used, diff --git a/R/stan_utils.R b/R/stan_utils.R index db411492..5de5f88c 100644 --- a/R/stan_utils.R +++ b/R/stan_utils.R @@ -24,7 +24,7 @@ #' str(sdata) #' code = function(object){ - if(!class(object) %in% c('mvgam', 'mvgam_prefit')){ + if(!inherits(object, c('mvgam', 'mvgam_prefit'))){ stop('argument "object" must be of class "mvgam" or "mvgam_prefit"') } @@ -3388,6 +3388,13 @@ check_n_eff <- function(fit, quiet=FALSE, fit_summary) { if(any(grep('LV', rownames(fit_summary)))){ fit_summary <- fit_summary[-grep('LV', rownames(fit_summary)), ] fit_summary <- fit_summary[-grep('lv_coefs', rownames(fit_summary)), ] + + if(any(grepl('L[', rownames(fit_summary), fixed = TRUE))){ + fit_summary <- fit_summary[-grep('L[', rownames(fit_summary), fixed = TRUE), ] + } + if(any(grepl('LV_raw[', rownames(fit_summary), fixed = TRUE))){ + fit_summary <- fit_summary[-grep('LV_raw[', rownames(fit_summary), fixed = TRUE), ] + } } N <- dim(fit_summary)[[1]] @@ -3423,7 +3430,15 @@ check_rhat <- function(fit, quiet=FALSE, fit_summary) { if(any(grep('LV', rownames(fit_summary)))){ fit_summary <- fit_summary[-grep('LV', rownames(fit_summary)), ] fit_summary <- fit_summary[-grep('lv_coefs', rownames(fit_summary)), ] + + if(any(grepl('L[', rownames(fit_summary), fixed = TRUE))){ + fit_summary <- fit_summary[-grep('L[', rownames(fit_summary), fixed = TRUE), ] + } + if(any(grepl('LV_raw[', rownames(fit_summary), fixed = TRUE))){ + fit_summary <- fit_summary[-grep('LV_raw[', rownames(fit_summary), fixed = TRUE), ] + } } + N <- dim(fit_summary)[[1]] no_warning <- TRUE diff --git a/R/summary.mvgam.R b/R/summary.mvgam.R index 3460b395..62375393 100644 --- a/R/summary.mvgam.R +++ b/R/summary.mvgam.R @@ -348,7 +348,7 @@ if(object$use_lv){ } else { trend_model <- object$trend_model } - if(trend_model == 'None' & object$family == 'nmix'){ + if(trend_model == 'None' & object$family == 'nmix' | inherits(object, 'jsdgam')){ } else { cat("\nProcess error parameter estimates:\n") diff --git a/R/validations.R b/R/validations.R index 36c9a919..a36c8e1d 100644 --- a/R/validations.R +++ b/R/validations.R @@ -3,7 +3,9 @@ #'@noRd validate_series_time = function(data, name = 'data', - trend_model){ + trend_model, + check_levels = TRUE, + check_times = TRUE){ # First validation requires the full trend_model object if(!inherits(trend_model, 'mvgam_trend')){ @@ -104,34 +106,39 @@ validate_series_time = function(data, data$index..time..index <- times } - # Series factor must have all unique levels present - if(!all(levels(data$series) %in% unique(data$series))){ - stop(paste0('Mismatch between factor levels of "series" and unique values of "series"', - '\n', - 'Use\n `setdiff(levels(data$series), unique(data$series))` \nand', - '\n', - ' `intersect(levels(data$series), unique(data$series))`\nfor guidance'), - call. = FALSE) + # Series factor must have all unique levels present if this is a + # forecast check + if(check_levels){ + if(!all(levels(data$series) %in% unique(data$series))){ + stop(paste0('Mismatch between factor levels of "series" and unique values of "series"', + '\n', + 'Use\n `setdiff(levels(data$series), unique(data$series))` \nand', + '\n', + ' `intersect(levels(data$series), unique(data$series))`\nfor guidance'), + call. = FALSE) + } } # Ensure each series has an observation, even if NA, for each # unique timepoint (only for trend models that require discrete time with # regularly spaced sampling intervals) - all_times_avail = function(time, min_time, max_time){ - identical(as.numeric(sort(time)), - as.numeric(seq.int(from = min_time, to = max_time))) - } - min_time <- as.numeric(min(data$index..time..index)) - max_time <- as.numeric(max(data$index..time..index)) - data.frame(series = data$series, - time = data$index..time..index) %>% - dplyr::group_by(series) %>% - dplyr::summarise(all_there = all_times_avail(time, - min_time, - max_time)) -> checked_times - if(any(checked_times$all_there == FALSE)){ - stop("One or more series in ", name, " is missing observations for one or more timepoints", - call. = FALSE) + if(check_times){ + all_times_avail = function(time, min_time, max_time){ + identical(as.numeric(sort(time)), + as.numeric(seq.int(from = min_time, to = max_time))) + } + min_time <- as.numeric(min(data$index..time..index)) + max_time <- as.numeric(max(data$index..time..index)) + data.frame(series = data$series, + time = data$index..time..index) %>% + dplyr::group_by(series) %>% + dplyr::summarise(all_there = all_times_avail(time, + min_time, + max_time)) -> checked_times + if(any(checked_times$all_there == FALSE)){ + stop("One or more series in ", name, " is missing observations for one or more timepoints", + call. = FALSE) + } } return(data) @@ -259,6 +266,11 @@ validate_var_exists = function(data, } } +#'@noRd +deparse_variable = function(...){ + deparse0(substitute(...)) +} + #'@noRd as_one_logical = function (x, allow_na = FALSE) { s <- substitute(x) diff --git a/docs/news/index.html b/docs/news/index.html index 6dcb4a88..b7a3ec5d 100644 --- a/docs/news/index.html +++ b/docs/news/index.html @@ -10,7 +10,7 @@ mvgam - 1.1.3 + 1.1.4 + + + + + +
+
+
+ +
+

Set up latent correlated multivariate Gaussian residual processes +in mvgam. This function does not evaluate it's arguments – +it exists purely to help set up a model with particular error processes.

+
+ +
+

Usage

+
ZMVN(unit = time, gr = NA, subgr = series)
+
+ +
+

Arguments

+
unit
+

The unquoted name of the variable that represents the unit of analysis in data over +which latent residuals should be correlated. This variable should be either a +numeric or integer variable in the supplied data. +Defaults to time to be consistent with other functionalities +in mvgam, though note that the data need not be time series in this case. See examples below +for further details and explanations

+ + +
gr
+

An optional grouping variable, which must be a factor in the supplied data, +for setting up hierarchical residual correlation structures. If specified, +this will automatically set up a model where the +residual correlations for a specific level of gr are modelled hierarchically: +\(\Omega_{group} = p\Omega_{global} + (1 - p)\Omega_{group, local}\), +where \(\Omega_{global}\) is a global correlation +matrix, \(\Omega_{group, local}\) is a local deviation correlation matrix +and \(p\) is a weighting parameter +controlling how strongly the local correlation matrix \(\Omega_{group}\) is shrunk towards the global +correlation matrix \(\Omega_{global}\). If gr is supplied then subgr must also be supplied

+ + +
subgr
+

A subgrouping factor variable specifying which element in data represents the +different observational units. Defaults to series to be consistent with other functionalities +in mvgam, though note that the data need not be time series in this case. +But note that models that use the hierarchical correlations (by supplying a value for gr) +should not include a series element in data. Rather, this element will be created internally based +on the supplied variables for gr and subgr. For example, if you are modelling +counts for a group of species (labelled as species in the data) across sampling sites +(labelled as site in the data) in three +different geographical regions (labelled as region), and you would like the residuals to be correlated +within regions, then you should specify +unit = site, gr = region, and subgr = species. Internally, mvgam() will appropriately order +the data by unit (in this case, by site) and create +the series element for the data using something like: series = as.factor(paste0(group, '_', subgroup))

+ +
+
+

Value

+ + +

An object of class mvgam_trend, which contains a list of +arguments to be interpreted by the parsing functions in mvgam

+ + +
+ +
+

Examples

+
if (FALSE) {
+# Simulate counts of four species over ten sampling locations
+site_dat <- data.frame(site = rep(1:10, 4),
+                      species = as.factor(sort(rep(letters[1:4], 10))),
+                      y = c(NA, rpois(39, 3)))
+head(site_dat)
+
+# Set up a correlated residual (i.e. Joint Species Distribution) model,
+# where 'site' represents the unit of analysis
+trend_model <- ZMVN(unit = site, subgr = species)
+mod <- mvgam(y ~ species,
+            trend_model = ZMVN(unit = site,
+                               subgr = species),
+            data = site_dat,
+            chains = 2,
+            silent = 2)
+
+# Inspect the estimated species-species residual covariances
+mcmc_plot(mod, variable = 'Sigma', regex = TRUE, type = 'hist')
+
+# A hierarchical correlation example; set up correlated counts
+# for three species across two sampling locations
+Sigma <- matrix(c(1, -0.4, 0.5,
+                 -0.4, 1, 0.3,
+                 0.5, 0.3, 1),
+               byrow = TRUE,
+               nrow = 3)
+               Sigma
+
+make_site_dat = function(...){
+ errors <- mgcv::rmvn(n = 30,
+                      mu = c(0.6, 0.8, 1.8),
+                      V = Sigma)
+ site_dat <- do.call(rbind, lapply(1:3, function(spec){
+   data.frame(y = rpois(30,
+                        lambda = exp(errors[, spec])),
+              species = paste0('species',
+                               spec),
+              site = 1:30)
+}))
+site_dat
+}
+
+site_dat <- rbind(make_site_dat() %>%
+                   dplyr::mutate(group = 'group1'),
+                 make_site_dat() %>%
+                   dplyr::mutate(group = 'group2')) %>%
+   dplyr::mutate(species = as.factor(species),
+                 group = as.factor(group))
+
+# Fit the hierarchical correlated residual model
+mod <- mvgam(y ~ species,
+            trend_model = ZMVN(unit = site,
+                               gr = group,
+                               subgr = species),
+            data = site_dat)
+
+# Inspect the estimated species-species residual covariances
+mcmc_plot(mod, variable = 'Sigma', regex = TRUE, type = 'hist')
+}
+
+
+
+
+ + +
+ + + + + + + diff --git a/docs/reference/fevd.mvgam.html b/docs/reference/fevd.mvgam.html index 9cecddfb..0f04f72e 100644 --- a/docs/reference/fevd.mvgam.html +++ b/docs/reference/fevd.mvgam.html @@ -12,7 +12,7 @@ mvgam - 1.1.3 + 1.1.4 + + + + + +
+
+
+ +
+

This function sets up a Joint Species Distribution Model whereby the residual associations among +species can be modelled in a reduced-rank format using a set of latent factors. The factor +specification is extremely flexible, allowing users to include spatial, temporal or any other type +of predictor effects to more efficiently capture unmodelled residual associations, while the +observation model can also be highly flexible (including all smooth, GP and other effects that +mvgam can handle)

+
+ +
+

Usage

+
jsdgam(
+  formula,
+  factor_formula = ~-1,
+  knots,
+  factor_knots,
+  data,
+  newdata,
+  family = poisson(),
+  unit = time,
+  subgr = series,
+  share_obs_params = FALSE,
+  priors,
+  n_lv = 2,
+  chains = 4,
+  burnin = 500,
+  samples = 500,
+  thin = 1,
+  parallel = TRUE,
+  threads = 1,
+  silent = 1,
+  max_treedepth = 12,
+  adapt_delta = 0.85,
+  backend = getOption("brms.backend", "cmdstanr"),
+  algorithm = getOption("brms.algorithm", "sampling"),
+  run_model = TRUE,
+  return_model_data = FALSE,
+  ...
+)
+
+ +
+

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

+ + +
factor_formula
+

A character string specifying the linear predictor +effects for the latent factors. 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). Details of the formula syntax used by mvgam +can be found in mvgam_formulae

+ + +
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

+ + +
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

+ + +
data
+

A dataframe or list containing the model response variable and covariates +required by the GAM formula and factor_formula objects

+ + +
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

+ + +
family
+

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

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 series. This is handy if you have multiple +time series that you believe share some properties, such as being from the same +species over different spatial units. Default is FALSE.

+ + +
priors
+

An optional data.frame with prior +definitions (in JAGS or Stan syntax). if using Stan, this can also be an object of +class brmsprior (see. prior for details). See get_mvgam_priors and +'Details' for more information on changing default prior distributions

+ + +
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))

+ + +
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. Only available for some families(poisson(), nb(), gaussian()) and +when using Cmdstan as the backend

+ + +
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.

+ + +
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

+ + +
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

+ + +
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

+ + +
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

+ + +
...
+

Other arguments to pass to mvgam()

+ +
+
+

Value

+ + +

A list object of classes jsdgam and 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") and methods(class = "jsdgam") for an overview on available methods

+
+
+

Details

+

Joint Species Distribution Models allow for responses of multiple species to be +learned hierarchically, whereby responses to environmental variables in formula can be partially +pooled and any latent, unmodelled residual associations can also be learned. In mvgam, both of +these effects can be modelled with the full power of latent factor Hierarchical GAMs, providing unmatched +flexibility to model full communities of species

+
+
+

See also

+

mvgam

+
+
+

Author

+

Nicholas J Clark

+
+ +
+

Examples

+
if (FALSE) {
+# Simulate latent count data for 500 spatial locations and 10 species
+set.seed(0)
+N_points <- 500
+N_species <- 10
+
+# Species-level intercepts (on the log scale)
+alphas <- runif(N_species, 2, 2.25)
+
+# Simulate a covariate and species-level responses to it
+temperature <- rnorm(N_points)
+betas <- runif(N_species, -0.5, 0.5)
+
+# Simulate background spatial points uniformly over a space
+lon <- runif(N_points, min = 150, max = 155)
+lat <- runif(N_points, min = -20, max = -19)
+
+# Set up spatial basis functions as a tensor product of lat and lon;
+# keep this number small so there are noticeable spatiotemporal 'clusters'
+sm <- mgcv::smoothCon(mgcv::te(lon, lat, k = 5),
+                      data = data.frame(lon, lat),
+                      knots = NULL)[[1]]
+
+# The design matrix for this smooth is in the 'X' slot
+des_mat <- sm$X
+dim(des_mat)
+
+# Function to generate a random covariance matrix where all variables
+# have unit variance (i.e. diagonals are all 1)
+random_Sigma = function(N){
+  L_Omega <- matrix(0, N, N);
+  L_Omega[1, 1] <- 1;
+  for (i in 2 : N) {
+    bound <- 1;
+    for (j in 1 : (i - 1)) {
+      L_Omega[i, j] <- runif(1, -sqrt(bound), sqrt(bound));
+      bound <- bound - L_Omega[i, j] ^ 2;
+    }
+    L_Omega[i, i] <- sqrt(bound);
+  }
+  Sigma <- L_Omega %*% t(L_Omega);
+  return(Sigma)
+}
+
+# Simulate a variance-covariance matrix for the correlations among
+# basis coefficients
+Sigma <- random_Sigma(N = NCOL(des_mat))
+
+# Now simulate the species-level basis coefficients hierarchically, where
+# spatial basis function correlations are a convex sum of a base correlation
+# matrix and a species-level correlation matrix
+basis_coefs <- matrix(NA, nrow = N_species, ncol = NCOL(Sigma))
+base_field <- mgcv::rmvn(1, mu = rep(0, NCOL(Sigma)), V = Sigma)
+for(t in 1:N_species){
+  corOmega <- (cov2cor(Sigma) * 0.7) +
+                      (0.3 * cov2cor(random_Sigma(N = NCOL(des_mat))))
+  basis_coefs[t, ] <- mgcv::rmvn(1, mu = rep(0, NCOL(Sigma)), V = corOmega)
+}
+
+# Simulate the latent spatiotemporal processes
+st_process <- do.call(rbind, lapply(seq_len(N_species), function(t){
+  data.frame(lat = lat,
+             lon = lon,
+             species = paste0('species_', t),
+             temperature = temperature,
+             process = alphas[t] +
+               betas[t] * temperature +
+               des_mat %*% basis_coefs[t,])
+}))
+
+# Now take noisy observations at some of the points (60)
+obs_points <- sample(1:N_points, size = 60, replace = FALSE)
+obs_points <- data.frame(lat = lat[obs_points],
+                         lon = lon[obs_points],
+                         site = 1:60)
+
+# Keep only the process data at these points
+st_process %>%
+  dplyr::inner_join(obs_points, by = c('lat', 'lon')) %>%
+  # now take noisy Poisson observations of the process
+  dplyr::mutate(count = rpois(NROW(.), lambda = exp(process))) %>%
+  dplyr::mutate(species = factor(species,
+                                 levels = paste0('species_', 1:N_species))) %>%
+  dplyr::group_by(lat, lon) -> dat
+
+# View the count distributions for each species
+library(ggplot2)
+ggplot(dat, aes(x = count)) +
+  geom_histogram() +
+  facet_wrap(~ species, scales = 'free')
+
+ggplot(dat, aes(x = lat, y = lon, col = log(count + 1))) +
+  geom_point(size = 2.25) +
+  facet_wrap(~ species, scales = 'free') +
+  viridis::scale_color_viridis() +
+  theme_classic()
+
+# Fit a JSDM that estimates a hierarchical temperature responses
+# and that uses three latent spatial factors
+mod <- jsdgam(formula = count ~
+                # Environmental model includes species-level interecepts
+                # and random slopes for a linear effect of temperature
+                species +
+                s(species, bs = 're', by = temperature),
+
+              # Each factor estimates a different nonlinear spatial process, using
+              # 'by = trend' as in other mvgam State-Space models
+              factor_formula = ~ te(lat, lon, k = 5, by = trend) - 1,
+              n_lv = 3,
+
+              # The data and the grouping variables
+              data = dat,
+              unit = site,
+              subgr = species,
+
+              # Poisson observations
+              family = poisson())
+
+# Plot species-level intercept estimates
+plot_predictions(mod, condition = 'species',
+                 type = 'link')
+
+# Plot species' hierarchical responses to temperature
+plot_predictions(mod, condition = c('temperature', 'species', 'species'),
+                 type = 'link')
+
+# Plotting species' average geographical predictions against the observed
+# data gives some idea of whether more flexibility in the spatial process
+# may be needed
+plot_predictions(mod, condition = c('lat', 'species', 'species'),
+                 points = 0.5)
+plot_predictions(mod, condition = c('lon', 'species', 'species'),
+                 points = 0.5)
+
+# Calculate (median) residual spatial correlations
+med_loadings <- matrix(apply(as.matrix(mod$model_output, 'lv_coefs'),
+                             2, median),
+                       nrow = N_species, ncol = 3)
+cormat <- cov2cor(tcrossprod(med_loadings))
+rownames(cormat) <- colnames(cormat) <- levels(dat$species)
+
+# Plot it using corrplot (if installed)
+if(requireNamespace('corrplot', quietly = TRUE)){
+  corrplot::corrplot(cormat, type = 'lower', tl.col = 'black',
+                     tl.srt = 45)
+}
+
+# Posterior predictive checks and ELPD-LOO can ascertain model fit
+pp_check(mod, type = "ecdf_overlay_grouped",
+         group = "species", ndraws = 50)
+loo(mod)
+}
+
+
+
+ + +
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