From 31bac649623fad995a396d945ebce0d37c7cb5a4 Mon Sep 17 00:00:00 2001 From: Nicholas Clark Date: Fri, 6 Sep 2024 10:43:02 +1000 Subject: [PATCH] update stability examples --- R/stability.R | 100 +++++++++++++++++++++++++---------- man/mvgam_marginaleffects.Rd | 2 + man/stability.mvgam.Rd | 93 ++++++++++++++++++++++---------- src/RcppExports.o | Bin 115605 -> 118706 bytes src/mvgam.dll | Bin 1091584 -> 1068032 bytes src/trend_funs.o | Bin 100099 -> 98386 bytes 6 files changed, 140 insertions(+), 55 deletions(-) diff --git a/R/stability.R b/R/stability.R index f8f863a3..84cba1c0 100644 --- a/R/stability.R +++ b/R/stability.R @@ -42,13 +42,20 @@ #' \deqn{ #' [2~det(A) (A^{-1})^T] \quad #' } -#' \item `prop_cov`: Sensitivity of \eqn{\Sigma_{\infty}} to intra-series error correlations +#' \item `prop_cov_offdiag`: Sensitivity of \eqn{\Sigma_{\infty}} to inter-series error correlations #' (i.e. how important are off-diagonal covariances in \eqn{\Sigma} for shaping #' \eqn{\Sigma_{\infty}}?), calculated as the relative magnitude of the *off-diagonals* in #' the partial derivative matrix: #' \deqn{ #' [2~det(\Sigma_{\infty}) (\Sigma_{\infty}^{-1})^T] \quad #' } +#' \item `prop_cov_diag`: Sensitivity of \eqn{\Sigma_{\infty}} to intra-series error variances +#' (i.e. how important are diagonal variances in \eqn{\Sigma} for shaping +#' \eqn{\Sigma_{\infty}}?), calculated as the relative magnitude of the *diagonals* in +#' the partial derivative matrix: +#' \deqn{ +#' [2~det(\Sigma_{\infty}) (\Sigma_{\infty}^{-1})^T] \quad +#' } #' \item `reactivity`: A measure of the degree to which the system moves #' away from a stable equilibrium following a perturbation #' values `> 0` suggest the system is reactive, whereby a @@ -70,12 +77,12 @@ #' } #' Again, lower values suggest greater stability #' } -#'@return An \code{data.frame} containing posterior draws for each of the above stability metrics. +#'@return A \code{data.frame} containing posterior draws for each of the above stability metrics. #'@references AR Ives, B Dennis, KL Cottingham & SR Carpenter (2003). #'Estimating community stability and ecological interactions from time-series data. #'Ecological Monographs. 73, 301-330. #'@author Nicholas J Clark -#'@seealso \code{\link{VAR}} +#'@seealso \code{\link{VAR}},\code{\link{irf}} #' @examples #' \donttest{ #' # Simulate some time series that follow a latent VAR(1) process @@ -85,13 +92,14 @@ #' prop_trend = 1) #' plot_mvgam_series(data = simdat$data_train, series = 'all') #' -#' # Fit a model that uses a latent VAR(1) -#' mod <- mvgam(y ~ -1, -#' trend_formula = ~ 1, +#' # Fit a State-Space VAR(1) +#' mod <- mvgam(y ~ series, +#' trend_formula = ~ -1, #' trend_model = VAR(cor = TRUE), #' family = gaussian(), +#' share_obs_params = TRUE, #' data = simdat$data_train, -#' silent = 2) +#' silent = 1) #' #' # Calulate stability metrics for this system #' metrics <- stability(mod) @@ -99,30 +107,61 @@ #' # Proportion of stationary forecast distribution #' # attributable to lagged interactions #' hist(metrics$prop_int, -#' xlim = c(0, 1), -#' xlab = 'Prop_int', -#' main = '', -#' col = '#B97C7C', -#' border = 'white') +#' xlim = c(0, 1), +#' xlab = 'Prop_int', +#' main = '', +#' col = '#B97C7C', +#' border = 'white') #' -#' # Proportion of stationary forecast distribution -#' # attributable to correlated process errors -#' hist(metrics$prop_env, -#' xlim = c(0, 1), -#' xlab = 'Prop_env', -#' main = '', -#' col = '#B97C7C', -#' border = 'white') +#' # Within this contribution of interactions, how important +#' # are inter-series interactions (offdiagonals of the A matrix) vs +#' # intra-series density dependence (diagonals of the A matrix)? +#' layout(matrix(1:2, nrow = 2)) +#' hist(metrics$prop_int_offdiag, +#' xlim = c(0, 1), +#' xlab = '', +#' main = 'Inter-series interactions', +#' col = '#B97C7C', +#' border = 'white') +#' +#' hist(metrics$prop_int_diag, +#' xlim = c(0, 1), +#' xlab = 'Contribution to interaction effect', +#' main = 'Intra-series interactions (density dependence)', +#' col = 'darkblue', +#' border = 'white') +#' layout(1) +#' +#' # How important are inter-series error covariances +#' # (offdiagonals of the Sigma matrix) vs +#' # intra-series variances (diagonals of the Sigma matrix) for explaining +#' # the variance of the stationary forecast distribution? +#' layout(matrix(1:2, nrow = 2)) +#' hist(metrics$prop_cov_offdiag, +#' xlim = c(0, 1), +#' xlab = '', +#' main = 'Inter-series covariances', +#' col = '#B97C7C', +#' border = 'white') +#' +#' hist(metrics$prop_cov_diag, +#' xlim = c(0, 1), +#' xlab = 'Contribution to forecast variance', +#' main = 'Intra-series variances', +#' col = 'darkblue', +#' border = 'white') +#' layout(1) #' #' # Reactivity, i.e. degree to which the system moves #' # away from a stable equilibrium following a perturbation +#' # (values > 1 suggest a more reactive, less stable system) #' hist(metrics$reactivity, -#' main = '', -#' xlab = 'Reactivity', -#' col = '#B97C7C', -#' border = 'white', -#' xlim = c(-1*max(abs(metrics$reactivity)), -#' max(abs(metrics$reactivity)))) +#' main = '', +#' xlab = 'Reactivity', +#' col = '#B97C7C', +#' border = 'white', +#' xlim = c(-1*max(abs(metrics$reactivity)), +#' max(abs(metrics$reactivity)))) #' abline(v = 0, lwd = 2.5) #' } #'@export @@ -133,7 +172,7 @@ stability <- function(object, ...){ #'@rdname stability.mvgam #'@method stability mvgam #'@export -stability.mvgam = function(object){ +stability.mvgam = function(object, ...){ # Check trend_model trend_model <- attr(object$model_data, 'trend_model') @@ -172,15 +211,20 @@ stability.mvgam = function(object){ # We can take partial derivatives to determine which elements of # Sigma_inf contribute most to rates of change in the # proportion of Sigma_inf that is due to process error + # Thanks to Mark Scheuerell for providing inspirational code + # https://github.com/mdscheuerell/safs-quant-sem-2022/blob/main/lwa_analysis.R int_env <- det(Sigma_inf) * t(solve(Sigma_inf)) # Proportion of inter-series covariance to # to overall environmental variation contribution (i.e. how important are # correlated errors for controlling the shape of the stationary forecast # distribution?) - dat <- data.frame(prop_cov = mean(abs(int_env[lower.tri(int_env)])) / + dat <- data.frame(prop_cov_offdiag = mean(abs(int_env[lower.tri(int_env)])) / (mean(abs(diag(int_env))) + mean(abs(int_env[lower.tri(int_env)])))) + # Proportion of error variances to stationary forecast distribution + dat$prop_cov_diag <- 1 - dat$prop_cov_offdiag + # Proportion of volume of Sigma_inf attributable to series interactions, # measuring the degree to which interactions increase # the variance of the stationary distribution (Sigma_inf) relative 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/stability.mvgam.Rd b/man/stability.mvgam.Rd index 9f25f533..dd0e9ec6 100644 --- a/man/stability.mvgam.Rd +++ b/man/stability.mvgam.Rd @@ -7,7 +7,7 @@ \usage{ stability(object, ...) -\method{stability}{mvgam}(object) +\method{stability}{mvgam}(object, ...) } \arguments{ \item{object}{\code{list} object of class \code{mvgam} resulting from a call to \code{\link[=mvgam]{mvgam()}} @@ -17,7 +17,7 @@ that used a Vector Autoregressive latent process model (either as \code{VAR(cor \item{...}{ignored} } \value{ -An \code{data.frame} containing posterior draws for each of the above stability metrics. +A \code{data.frame} containing posterior draws for each of the above stability metrics. } \description{ Compute reactivity, return rates and contributions of interactions to @@ -58,10 +58,17 @@ matrix: \deqn{ [2~det(A) (A^{-1})^T] \quad } -\item \code{prop_cov}: Sensitivity of \eqn{\Sigma_{\infty}} to intra-series error correlations +\item \code{prop_cov_offdiag}: Sensitivity of \eqn{\Sigma_{\infty}} to inter-series error correlations (i.e. how important are off-diagonal covariances in \eqn{\Sigma} for shaping \eqn{\Sigma_{\infty}}?), calculated as the relative magnitude of the \emph{off-diagonals} in the partial derivative matrix: +\deqn{ + [2~det(\Sigma_{\infty}) (\Sigma_{\infty}^{-1})^T] \quad + } +\item \code{prop_cov_diag}: Sensitivity of \eqn{\Sigma_{\infty}} to intra-series error variances +(i.e. how important are diagonal variances in \eqn{\Sigma} for shaping +\eqn{\Sigma_{\infty}}?), calculated as the relative magnitude of the \emph{diagonals} in +the partial derivative matrix: \deqn{ [2~det(\Sigma_{\infty}) (\Sigma_{\infty}^{-1})^T] \quad } @@ -96,13 +103,14 @@ simdat <- sim_mvgam(family = gaussian(), prop_trend = 1) plot_mvgam_series(data = simdat$data_train, series = 'all') -# Fit a model that uses a latent VAR(1) -mod <- mvgam(y ~ -1, - trend_formula = ~ 1, +# Fit a State-Space VAR(1) +mod <- mvgam(y ~ series, + trend_formula = ~ -1, trend_model = VAR(cor = TRUE), family = gaussian(), + share_obs_params = TRUE, data = simdat$data_train, - silent = 2) + silent = 1) # Calulate stability metrics for this system metrics <- stability(mod) @@ -110,30 +118,61 @@ metrics <- stability(mod) # Proportion of stationary forecast distribution # attributable to lagged interactions hist(metrics$prop_int, - xlim = c(0, 1), - xlab = 'Prop_int', - main = '', - col = '#B97C7C', - border = 'white') + xlim = c(0, 1), + xlab = 'Prop_int', + main = '', + col = '#B97C7C', + border = 'white') -# Proportion of stationary forecast distribution -# attributable to correlated process errors -hist(metrics$prop_env, - xlim = c(0, 1), - xlab = 'Prop_env', - main = '', - col = '#B97C7C', - border = 'white') +# Within this contribution of interactions, how important +# are inter-series interactions (offdiagonals of the A matrix) vs +# intra-series density dependence (diagonals of the A matrix)? +layout(matrix(1:2, nrow = 2)) +hist(metrics$prop_int_offdiag, + xlim = c(0, 1), + xlab = '', + main = 'Inter-series interactions', + col = '#B97C7C', + border = 'white') + +hist(metrics$prop_int_diag, + xlim = c(0, 1), + xlab = 'Contribution to interaction effect', + main = 'Intra-series interactions (density dependence)', + col = 'darkblue', + border = 'white') +layout(1) + +# How important are inter-series error covariances +# (offdiagonals of the Sigma matrix) vs +# intra-series variances (diagonals of the Sigma matrix) for explaining +# the variance of the stationary forecast distribution? +layout(matrix(1:2, nrow = 2)) +hist(metrics$prop_cov_offdiag, + xlim = c(0, 1), + xlab = '', + main = 'Inter-series covariances', + col = '#B97C7C', + border = 'white') + +hist(metrics$prop_cov_diag, + xlim = c(0, 1), + xlab = 'Contribution to forecast variance', + main = 'Intra-series variances', + col = 'darkblue', + border = 'white') +layout(1) # Reactivity, i.e. degree to which the system moves # away from a stable equilibrium following a perturbation +# (values > 1 suggest a more reactive, less stable system) hist(metrics$reactivity, - main = '', - xlab = 'Reactivity', - col = '#B97C7C', - border = 'white', - xlim = c(-1*max(abs(metrics$reactivity)), - max(abs(metrics$reactivity)))) + main = '', + xlab = 'Reactivity', + col = '#B97C7C', + border = 'white', + xlim = c(-1*max(abs(metrics$reactivity)), + max(abs(metrics$reactivity)))) abline(v = 0, lwd = 2.5) } } @@ -143,7 +182,7 @@ Estimating community stability and ecological interactions from time-series data Ecological Monographs. 73, 301-330. } \seealso{ -\code{\link{VAR}} +\code{\link{VAR}},\code{\link{irf}} } \author{ Nicholas J Clark diff --git a/src/RcppExports.o b/src/RcppExports.o index e8dd19f02d5a6828265717bb42d99b3dd1139877..03b011192531eff382f7b4b3aad3c852fa2b68e4 100644 GIT binary patch literal 118706 zcmeEv3wRVo)^<%YorK&b2q>(#Q3efOaB@!scPA3GqZ7>{uI$Q6FocWCCBj6}MGYn> 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