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-#' Estimation of parameter distributions from mmkin row objects
-#'
-#' This function sets up and attempts to fit a mixed effects model to
-#' an mmkin row object which is essentially a list of mkinfit objects
-#' that have been obtained by fitting the same model to a list of
-#' datasets.
-#'
-#' @param object An mmkin row object containing several fits of the same model to different datasets
-#' @param random_spec Either "auto" or a specification of random effects for \code{\link{nlme}}
-#'   given as a character vector
-#' @param ... Additional arguments passed to \code{\link{nlme}}
-#' @import nlme
-#' @importFrom purrr map_dfr
-#' @return An nlme object
-#' @examples
-#' sampling_times = c(0, 1, 3, 7, 14, 28, 60, 90, 120)
-#' m_SFO <- mkinmod(parent = mkinsub("SFO"))
-#' d_SFO_1 <- mkinpredict(m_SFO,
-#'   c(k_parent_sink = 0.1),
-#'   c(parent = 98), sampling_times)
-#' d_SFO_1_long <- mkin_wide_to_long(d_SFO_1, time = "time")
-#' d_SFO_2 <- mkinpredict(m_SFO,
-#'   c(k_parent_sink = 0.05),
-#'   c(parent = 102), sampling_times)
-#' d_SFO_2_long <- mkin_wide_to_long(d_SFO_2, time = "time")
-#' d_SFO_3 <- mkinpredict(m_SFO,
-#'   c(k_parent_sink = 0.02),
-#'   c(parent = 103), sampling_times)
-#' d_SFO_3_long <- mkin_wide_to_long(d_SFO_3, time = "time")
-#'
-#' d1 <- add_err(d_SFO_1, function(value) 3, n = 1)
-#' d2 <- add_err(d_SFO_2, function(value) 2, n = 1)
-#' d3 <- add_err(d_SFO_3, function(value) 4, n = 1)
-#' ds <- c(d1 = d1, d2 = d2, d3 = d3)
-#'
-#' f <- mmkin("SFO", ds)
-#' x <- memkin(f)
-#' summary(x)
-#'
-#' ds_2 <- lapply(experimental_data_for_UBA_2019[6:10],
-#'  function(x) x$data[c("name", "time", "value")])
-#' m_sfo_sfo <- mkinmod(parent = mkinsub("SFO", "A1"),
-#'   A1 = mkinsub("SFO"), use_of_ff = "min")
-#' m_sfo_sfo_ff <- mkinmod(parent = mkinsub("SFO", "A1"),
-#'   A1 = mkinsub("SFO"), use_of_ff = "max")
-#' m_fomc_sfo <- mkinmod(parent = mkinsub("FOMC", "A1"),
-#'   A1 = mkinsub("SFO"))
-#' m_dfop_sfo <- mkinmod(parent = mkinsub("DFOP", "A1"),
-#'   A1 = mkinsub("SFO"))
-#' m_sforb_sfo <- mkinmod(parent = mkinsub("SFORB", "A1"),
-#'   A1 = mkinsub("SFO"))
-#'
-#' f_2 <- mmkin(list("SFO-SFO" = m_sfo_sfo,
-#'  "SFO-SFO-ff" = m_sfo_sfo_ff,
-#'  "FOMC-SFO" = m_fomc_sfo,
-#'  "DFOP-SFO" = m_dfop_sfo,
-#'  "SFORB-SFO" = m_sforb_sfo),
-#'   ds_2)
-#'
-#' f_nlme_sfo_sfo <- memkin(f_2[1, ])
-#' f_nlme_sfo_sfo_2 <- memkin(f_2[1, ], "pdDiag(parent_0 + log_k_parent_sink + log_k_parent_A1 + log_k_A1_sink ~ 1)") # explicit
-#' f_nlme_sfo_sfo_3 <- memkin(f_2[1, ], "pdDiag(parent_0 + log_k_parent_sink + log_k_parent_A1 ~ 1)") # reduced
-#' f_nlme_sfo_sfo_4 <- memkin(f_2[1, ], "pdDiag(parent_0 + log_k_parent_sink ~ 1)") # further reduced
-#' \dontrun{
-#'   f_nlme_sfo_sfo_ff <- memkin(f_2[2, ]) # does not converge with maxIter = 50
-#' }
-#' f_nlme_fomc_sfo <- memkin(f_2[3, ])
-#' \dontrun{
-#'   f_nlme_dfop_sfo <- memkin(f_2[4, ])  # apparently underdetermined
-#'   f_nlme_sforb_sfo <- memkin(f_2[5, ]) # also does not converge
-#' }
-#' anova(f_nlme_fomc_sfo, f_nlme_sfo_sfo, f_nlme_sfo_sfo_4)
-#' @export
-memkin <- function(object, random_spec = "auto", ...) {
-  if (nrow(object) > 1) stop("Only row objects allowed")
-  ds_names <- colnames(object)
-
-  p_mat_start_trans <- sapply(object, parms, transformed = TRUE)
-  colnames(p_mat_start_trans) <- ds_names
-
-  p_names_mean_function <- setdiff(rownames(p_mat_start_trans), names(object[[1]]$errparms))
-  p_start_mean_function <- apply(p_mat_start_trans[p_names_mean_function, ], 1, mean)
-
-  ds_list <- lapply(object, function(x) x$data[c("time", "variable", "observed")])
-  names(ds_list) <- ds_names
-  ds_nlme <- purrr::map_dfr(ds_list, function(x) x, .id = "ds")
-  ds_nlme$variable <- as.character(ds_nlme$variable)
-  ds_nlme_grouped <- groupedData(observed ~ time | ds, ds_nlme)
-
-  mkin_model <- object[[1]]$mkinmod
-
-  # Inspired by https://stackoverflow.com/a/12983961/3805440
-  # and https://stackoverflow.com/a/26280789/3805440
-  model_function_alist <- replicate(length(p_names_mean_function) + 2, substitute())
-  names(model_function_alist) <- c("name", "time", p_names_mean_function)
-
-  model_function_body <- quote({
-    arg_frame <- as.data.frame(as.list((environment())), stringsAsFactors = FALSE)
-    res_frame <- arg_frame[1:2]
-    parm_frame <- arg_frame[-(1:2)]
-    parms_unique <- unique(parm_frame)
-
-    n_unique <- nrow(parms_unique)
-
-    times_ds <- list()
-    names_ds <- list()
-    for (i in 1:n_unique) {
-      times_ds[[i]] <-
-        arg_frame[which(arg_frame[[3]] == parms_unique[i, 1]), "time"]
-      names_ds[[i]] <-
-        arg_frame[which(arg_frame[[3]] == parms_unique[i, 1]), "name"]
-    }
-
-    res_list <- lapply(1:n_unique, function(x) {
-      transparms_optim <- unlist(parms_unique[x, , drop = TRUE])
-      parms_fixed <- object[[1]]$bparms.fixed
-
-      odeini_optim_parm_names <- grep('_0$', names(transparms_optim), value = TRUE)
-      odeini_optim <- transparms_optim[odeini_optim_parm_names]
-      names(odeini_optim) <- gsub('_0$', '', odeini_optim_parm_names)
-      odeini_fixed_parm_names <- grep('_0$', names(parms_fixed), value = TRUE)
-      odeini_fixed <- parms_fixed[odeini_fixed_parm_names]
-      names(odeini_fixed) <- gsub('_0$', '', odeini_fixed_parm_names)
-      odeini <- c(odeini_optim, odeini_fixed)[names(mkin_model$diffs)]
-
-      ode_transparms_optim_names <- setdiff(names(transparms_optim), odeini_optim_parm_names)
-      odeparms_optim <- backtransform_odeparms(transparms_optim[ode_transparms_optim_names], mkin_model,
-        transform_rates = object[[1]]$transform_rates,
-        transform_fractions = object[[1]]$transform_fractions)
-      odeparms_fixed_names <- setdiff(names(parms_fixed), odeini_fixed_parm_names)
-      odeparms_fixed <- parms_fixed[odeparms_fixed_names]
-      odeparms <- c(odeparms_optim, odeparms_fixed)
-
-      out_wide <- mkinpredict(mkin_model,
-        odeparms = odeparms, odeini = odeini,
-        solution_type = object[[1]]$solution_type,
-        outtimes = sort(unique(times_ds[[x]])))
-      out_array <- out_wide[, -1, drop = FALSE]
-      rownames(out_array) <- as.character(unique(times_ds[[x]]))
-      out_times <- as.character(times_ds[[x]])
-      out_names <- as.character(names_ds[[x]])
-      out_values <- mapply(function(times, names) out_array[times, names],
-        out_times, out_names)
-      return(as.numeric(out_values))
-    })
-    res <- unlist(res_list)
-    return(res)
-  })
-  model_function <- as.function(c(model_function_alist, model_function_body))
-  # For some reason, using envir = parent.frame() here is not enough,
-  # we need to use assign
-  assign("model_function", model_function, envir = parent.frame())
-
-  random_spec <- if (random_spec[1] == "auto") {
-      paste0("pdDiag(", paste(p_names_mean_function, collapse = " + "), " ~ 1),\n")
-  } else {
-      paste0(random_spec, ",\n")
-  }
-  nlme_call_text <- paste0(
-    "nlme(observed ~ model_function(variable, time, ",
-      paste(p_names_mean_function, collapse = ", "), "),\n",
-    "  data = ds_nlme_grouped,\n",
-    "  fixed = ", paste(p_names_mean_function, collapse = " + "), " ~ 1,\n",
-    "  random = ", random_spec, "\n",
-    "  start = p_start_mean_function)\n")
-
-  f_nlme <- eval(parse(text = nlme_call_text))
-
-  return(f_nlme)
-}