Seleção de efeitos aleatórios em modelos lineares mistos

Abstract

Experiments with longitudinal data have a characteristic that differs from experiments with cross-sectional data in that the sample units are observed more than once through pre-established evaluation conditions in the study. Consequently, the statistical analysis of these data is more complex; for example, both inter-unit and intra-unit dispersion must be taken into account in the analysis and it is extremely important to choose the covariance structure well. With regard to modeling longitudinal data, a very common alternative is the use of latent variable models, such as the class of linear mixed models, or two-stage models, as described by Laird and Ware (1982, Biometrics), which is a class of regression models in which fixed and random coefficients make up their functional structure. This class has gained popularity and much of the effort put into the modeling process is in selecting efficient fixed and random terms to make up the model. Some techniques have been proposed for this purpose, but Singer and Rocha (2017, Journal of Applied Statistics) comment that they should not be used exclusively but should be used together. In this context, we present a set of techniques proposed by the authors to select fixed and random coefficients in linear mixed models by means of hypothesis testing.