Statistical model assumptions achieved by linear models: classics and generalized mixed

Abstract

When an agricultural experiment is completed and the data about the response variable is available, it is necessary
to perform an analysis of variance. However, the hypothesis testing of this analysis shows validity only if the assumptions of the
statistical model are ensured. When such assumptions are violated, procedures must be applied to remedy the problem. The present
study aimed to compare and investigate how the assumptions of the statistical model can be achieved by classical linear model
and generalized linear mixed model, as well as their impact on the hypothesis test of the analysis of variance. The data used in
this study was obtained from a genetic breeding program on the cooking time of segregating populations. The following solutions
were proposed: i) Classical linear model with data transformation and ii) Generalized linear mixed models. The assumptions
of normality and homogeneity were tested by Shapiro-Wilk and Levene, respectively. Both models were able to achieve the
assumptions of the statistical model with direct impact on the hypothesis testing. The data transformations were effective in
stabilizing the variance. However, several inappropriate transformations can be misapplied and meet the assumptions, which
would distort the hypothesis test. The generalized linear mixed models may require more knowledge about the identification of
lines of programming, compared to the classical method. However, besides the separation of fixed from random effects, they
allow for the specification of the type of distribution of the response variable and the structuring of the residues.