Random effects models

Abstract

This chapter is concerned with random effects models for analyzing non-normal data that are assumed to be clustered or correlated. The clustering may be due to repeated measurements over time, as in longitudinal studies, or to subsampling the primary sampling units, as in cross-sectional studies. In each of these cases the data consist of repeated observations (y _it , x _it ), t = 1,..., T _i , for each individual or unit i = 1,..., n, where y denotes a response variable of primary interest and x a vector of covariates. Typical examples include panel data, where the cluster-specific data $\left( {y_i ,\,x_i } \right) = \left( {y_{i1} ,...,\,y_i T_i ,\,x_{i1} ,...,x_i T_i } \right)$ correspond to a time series of length T _i , or large-scale health studies, where (y _i , x _i ) represents the data of a primary sampling unit, say a hospital or a geographical region