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+#' Plot parameter variability of multistart objects
+#'
+#' Produces a boxplot with all parameters from the multiple runs, scaled
+#' either by the parameters of the run with the highest likelihood,
+#' or by their medians as proposed in the paper by Duchesne et al. (2021).
+#'
+#' @param object The [multistart] object
+#' @param llmin The minimum likelihood of objects to be shown
+#' @param scale By default, scale parameters using the best available fit.
+#' If 'median', parameters are scaled using the median parameters from all fits.
+#' @param main Title of the plot
+#' @param lpos Positioning of the legend.
+#' @param \dots Passed to [boxplot]
+#' @references Duchesne R, Guillemin A, Gandrillon O, Crauste F. Practical
+#' identifiability in the frame of nonlinear mixed effects models: the example
+#' of the in vitro erythropoiesis. BMC Bioinformatics. 2021 Oct 4;22(1):478.
+#' doi: 10.1186/s12859-021-04373-4.
+#' @seealso [multistart]
+#' @importFrom stats median
+#' @export
+parplot <- function(object, ...) {
+ UseMethod("parplot")
+}
+
+#' @rdname parplot
+#' @export
+parplot.multistart.saem.mmkin <- function(object, llmin = -Inf, scale = c("best", "median"),
+ lpos = "bottomleft", main = "", ...)
+{
+ oldpar <- par(no.readonly = TRUE)
+ on.exit(par(oldpar, no.readonly = TRUE))
+
+ orig <- attr(object, "orig")
+ orig_parms <- parms(orig)
+ start_parms <- orig$mean_dp_start
+ all_parms <- parms(object)
+
+ if (inherits(object, "multistart.saem.mmkin")) {
+ llfunc <- function(object) {
+ if (inherits(object$so, "try-error")) return(NA)
+ else return(logLik(object$so))
+ }
+ } else {
+ stop("parplot is only implemented for multistart.saem.mmkin objects")
+ }
+ ll <- sapply(object, llfunc)
+ selected <- which(ll > llmin)
+ selected_parms <- all_parms[selected, ]
+
+ par(las = 1)
+ if (orig$transformations == "mkin") {
+ degparm_names_transformed <- names(start_parms)
+ degparm_index <- which(names(orig_parms) %in% degparm_names_transformed)
+ orig_parms[degparm_names_transformed] <- backtransform_odeparms(
+ orig_parms[degparm_names_transformed],
+ orig$mmkin[[1]]$mkinmod,
+ transform_rates = orig$mmkin[[1]]$transform_rates,
+ transform_fractions = orig$mmkin[[1]]$transform_fractions)
+ start_parms <- backtransform_odeparms(start_parms,
+ orig$mmkin[[1]]$mkinmod,
+ transform_rates = orig$mmkin[[1]]$transform_rates,
+ transform_fractions = orig$mmkin[[1]]$transform_fractions)
+ degparm_names <- names(start_parms)
+
+ names(orig_parms) <- c(degparm_names, names(orig_parms[-degparm_index]))
+
+ selected_parms[, degparm_names_transformed] <-
+ t(apply(selected_parms[, degparm_names_transformed], 1, backtransform_odeparms,
+ orig$mmkin[[1]]$mkinmod,
+ transform_rates = orig$mmkin[[1]]$transform_rates,
+ transform_fractions = orig$mmkin[[1]]$transform_fractions))
+ colnames(selected_parms)[1:length(degparm_names)] <- degparm_names
+ }
+
+ scale <- match.arg(scale)
+ parm_scale <- switch(scale,
+ best = selected_parms[which.best(object[selected]), ],
+ median = apply(selected_parms, 2, median)
+ )
+
+ # Boxplots of all scaled parameters
+ selected_scaled_parms <- t(apply(selected_parms, 1, function(x) x / parm_scale))
+ boxplot(selected_scaled_parms, log = "y", main = main, ,
+ ylab = "Normalised parameters", ...)
+
+ # Show starting parameters
+ start_scaled_parms <- rep(NA_real_, length(orig_parms))
+ names(start_scaled_parms) <- names(orig_parms)
+ start_scaled_parms[names(start_parms)] <-
+ start_parms / parm_scale[names(start_parms)]
+ points(start_scaled_parms, col = 3, cex = 3)
+
+ # Show parameters of original run
+ orig_scaled_parms <- orig_parms / parm_scale
+ points(orig_scaled_parms, col = 2, cex = 2)
+
+ abline(h = 1, lty = 2)
+
+ legend(lpos, inset = c(0.05, 0.05), bty = "n",
+ pch = 1, col = 3:1, lty = c(NA, NA, 1),
+ legend = c(
+ "Starting parameters",
+ "Original run",
+ "Multistart runs"))
+}

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