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+#' Lack-of-fit test for models fitted to data with replicates
+#'
+#' This is a generic function with a method currently only defined for mkinfit
+#' objects. It fits an anova model to the data contained in the object and
+#' compares the likelihoods using the likelihood ratio test
+#' \code{\link[lmtest]{lrtest.default}} from the lmtest package.
+#'
+#' The anova model is interpreted as the simplest form of an mkinfit model,
+#' assuming only a constant variance about the means, but not enforcing any
+#' structure of the means, so we have one model parameter for every mean
+#' of replicate samples.
+#'
+#' @param object A model object with a defined loftest method
+#' @param \dots Not used
+#' @export
+loftest <- function(object, ...) {
+  UseMethod("loftest")
+}
+
+#' @rdname loftest
+#' @importFrom stats logLik lm dnorm coef
+#' @seealso lrtest
+#' @examples
+#' \dontrun{
+#' test_data <- subset(synthetic_data_for_UBA_2014[[12]]$data, name == "parent")
+#' sfo_fit <- mkinfit("SFO", test_data, quiet = TRUE)
+#' plot_res(sfo_fit) # We see a clear pattern in the residuals
+#' loftest(sfo_fit)  # We have a clear lack of fit
+#' #
+#' # We try a different model (the one that was used to generate the data)
+#' dfop_fit <- mkinfit("DFOP", test_data, quiet = TRUE)
+#' plot_res(dfop_fit) # We don't see systematic deviations, but heteroscedastic residuals
+#' # therefore we should consider adapting the error model, although we have
+#' loftest(dfop_fit) # no lack of fit
+#' #
+#' # This is the anova model used internally for the comparison
+#' test_data_anova <- test_data
+#' test_data_anova$time <- as.factor(test_data_anova$time)
+#' anova_fit <- lm(value ~ time, data = test_data_anova)
+#' summary(anova_fit)
+#' logLik(anova_fit) # We get the same likelihood and degrees of freedom
+#' #
+#' test_data_2 <- synthetic_data_for_UBA_2014[[12]]$data
+#' m_synth_SFO_lin <- mkinmod(parent = list(type = "SFO", to = "M1"),
+#'   M1 = list(type = "SFO", to = "M2"),
+#'   M2 = list(type = "SFO"), use_of_ff = "max")
+#' sfo_lin_fit <- mkinfit(m_synth_SFO_lin, test_data_2, quiet = TRUE)
+#' plot_res(sfo_lin_fit) # not a good model, we try parallel formation
+#' loftest(sfo_lin_fit)
+#' #
+#' m_synth_SFO_par <- mkinmod(parent = list(type = "SFO", to = c("M1", "M2")),
+#'   M1 = list(type = "SFO"),
+#'   M2 = list(type = "SFO"), use_of_ff = "max")
+#' sfo_par_fit <- mkinfit(m_synth_SFO_par, test_data_2, quiet = TRUE)
+#' plot_res(sfo_par_fit) # much better for metabolites
+#' loftest(sfo_par_fit)
+#' #
+#' m_synth_DFOP_par <- mkinmod(parent = list(type = "DFOP", to = c("M1", "M2")),
+#'   M1 = list(type = "SFO"),
+#'   M2 = list(type = "SFO"), use_of_ff = "max")
+#' dfop_par_fit <- mkinfit(m_synth_DFOP_par, test_data_2, quiet = TRUE)
+#' plot_res(dfop_par_fit) # No visual lack of fit
+#' loftest(dfop_par_fit)  # no lack of fit found by the test
+#' #
+#' # The anova model used for comparison in the case of transformation products
+#' test_data_anova_2 <- dfop_par_fit$data
+#' test_data_anova_2$variable <- as.factor(test_data_anova_2$variable)
+#' test_data_anova_2$time <- as.factor(test_data_anova_2$time)
+#' anova_fit_2 <- lm(observed ~ time:variable - 1, data = test_data_anova_2)
+#' summary(anova_fit_2)
+#' }
+#' @export
+loftest.mkinfit <- function(object, ...) {
+
+  name_function <- function(x) {
+    object_name <- paste(x$mkinmod$name, "with error model", x$err_mod)
+    if (length(x$bparms.fixed) > 0) {
+      object_name <- paste(object_name,
+        "and fixed parameter(s)",
+        paste(names(x$bparms.fixed), collapse = ", "))
+    }
+    return(object_name)
+  }
+
+  # Check if we have replicates in the data
+  if (max(aggregate(object$data$observed,
+    by = list(object$data$variable, object$data$time), length)$x) == 1) {
+    stop("Not defined for fits to data without replicates")
+  }
+
+  data_anova <- object$data
+  data_anova$time <- as.factor(data_anova$time)
+  data_anova$variable <- as.factor(data_anova$variable)
+  if (nlevels(data_anova$variable) == 1) {
+    object_2 <- lm(observed ~ time - 1, data = data_anova)
+  } else {
+    object_2 <- lm(observed ~ variable:time - 1,
+      data = data_anova)
+  }
+
+  object_2$mkinmod <- list(name = "ANOVA")
+  object_2$err_mod <- "const"
+  sigma_mle <- sqrt(sum(residuals(object_2)^2)/nobs(object_2))
+  object_2$logLik <- sum(dnorm(x = object_2$residuals,
+      mean = 0, sd = sigma_mle, log = TRUE))
+  object_2$data <- object$data # to make the nobs.mkinfit method work
+  object_2$bparms.optim <- coef(object_2)
+  object_2$errparms <- 1 # We have estimated one error model parameter
+  class(object_2) <- "mkinfit"
+
+  lmtest::lrtest.default(object_2, object, name = name_function)
+}