fix stability MAN page

R/stability.R

@@ -43,13 +43,20 @@
 #'     \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 intra-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 inter-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
@@ -102,30 +109,61 @@
 #' # 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