Linear mixed models with flexible distributions of random effects for longitudinal data

Normality of random effects is a routine assumption for the linear mixed mo del, but it may be unrealistic, obscuring important features of among-indiv idual variation. We relax this assumption by approximating the random effec ts density, by the seminonparameteric (SNP) representation of Gallant and N ychka (1987, Econometrics 55, 363-390), which includes normality as a speci al case and provides flexibility in capturing a broad range of nonnormal be havior, controlled by a user-chosen tuning parameter. An advantage is that the marginal likelihood may be expressed in closed form, so inference may b e carried out using standard optimization techniques. We demonstrate that s tandard information criteria may be used to choose the tuning parameter and detect departures from normality, and we illustrate the approach via simul ation and using longitudinal data from the Framingham study.