The Linear Model: II. The ‘Mixed’ Model

Abstract

In a classical context, a ‘mixed model’ consists of a set of fixed effects and covariates plus one or more random effects, plus a random error term. In Chap. 1, Sect. 1.5, we have explained the differences between fixed and random effects in a frequentist context. However, as we said in Chap. 6, in a Bayesian context, all effects are random; thus, there is no distinction between fixed models, random models or mixed models. Nevertheless, we keep the nomenclatures ‘fixed’ and ‘random’ for the effects that are considered so in a frequentist model, because it is widely extended and it facilitates the understanding of the model. Later we will see which type of Bayesian random effects are what we call ‘fixed’ effects in the frequentist school. We will also consider here that the data are normally distributed, although other distributions of the data can be considered, and the procedure would be the same. In this chapter, we examine a common mixed model in animal production, the model with repeated records and the most widely used mixed model in genetic evaluation. We end the chapter with an introduction to multitrait models.