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+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/loftest.R
+\name{loftest}
+\alias{loftest}
+\alias{loftest.mkinfit}
+\title{Lack-of-fit test for models fitted to data with replicates}
+\usage{
+loftest(object, ...)
+
+\method{loftest}{mkinfit}(object, ...)
+}
+\arguments{
+\item{object}{A model object with a defined loftest method}
+
+\item{\dots}{Not used}
+}
+\description{
+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.
+}
+\details{
+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.
+}
+\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)
+}
+}
+\seealso{
+lrtest
+}