Linear mixed models with flexible distributions of random effects for longitudinal data. (English) Zbl 1209.62087

Summary: Normality of random effects is a routine assumption for the linear mixed model, but it may be unrealistic, obscuring important features of among-individual variation. We relax this assumption by approximating the random effects density by the seminonparameteric (SNP) representation of A. R. Gallant and D. W. Nychka [Econometrics 55, 363–390 (1987)], which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may be carried out using standard optimization techniques. We demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simulation and using longitudinal data from the Framingham study.


62G08 Nonparametric regression and quantile regression
62J05 Linear regression; mixed models
90C90 Applications of mathematical programming
62P10 Applications of statistics to biology and medical sciences; meta analysis
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