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# Unbalanced Random and Mixed Models

DOI link for Unbalanced Random and Mixed Models

Unbalanced Random and Mixed Models book

# Unbalanced Random and Mixed Models

DOI link for Unbalanced Random and Mixed Models

Unbalanced Random and Mixed Models book

## ABSTRACT

The purpose of this chapter is to provide a coverage of the analysis of unbalanced linear models which include random effects. As we may recall from Section 8.4, if all the effects in a model are randomly distributed, except for the overall mean, μ, then the model is called a random-effects model, or just a random model. If, however, some effects are fixed (besides the overall mean) and some are random (besides the experimental error), then the model is called a mixed-effects model, or just a mixed model. The determination of which factors in a given experimental situation have fixed effects and which have random effects depends on the nature of the factors and how their levels are selected in the experiment. A factor whose levels are of particular interest to the experimenter, and are therefore the only ones to be considered, is said to have fixed effects and is labeled as a fixed factor. If, however, the levels of the factor, which are actually used in the experiment, are selected at random from a typically large population (hypothetically infinite), P, of possible levels, then it is said to have random effects and is labeled as a random factor. In the latter case, the levels of the factor used in the experiment constitute a random sample chosen from P.