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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"))
+}