Linear Mixed Eﬀects Models with Flexible Generalized Skew-Elliptical Random Eﬀects
The linear mixed eﬀects model is a popular framework for analysis of continuous longitudinal responses from a sample of individuals in biomedical, agricultural, environmental, and social science applications. Inter-individual heterogeneity in features of the longitudinal proﬁles, such as (error-free) baseline response or rate of change, is represented explicitly by individualspeciﬁc random eﬀects, so that inference on questions involving population or individual characteristics is possible. A standard assumption is that the random eﬀects and within-individual errors are normally distributed, and software such as SAS proc mixed (Littell, Milliken, Stroup, and Wolﬁnger, 1996) or Splus lme() (Pinheiro and Bates, 2000) incorporates this assumption. Although normality of within-individual deviations may be a reasonable model for many continuous measurements, perhaps on a transformed scale, normality of the random eﬀects implies a belief about inter-individual heterogeneity that may be unrealistic. For example, a common feature in biological contexts is skewness or heavy-tailedness of features underlying individual proﬁles.