Longitudinal data are collected frequently in many biomedical studies, and linear and generalized linear mixed models are often used to analyze such data, where random subject specific effects are explicitly used to model the correlation in the data. A standard assumption in these models is that the random effects are normally distributed. However, this assumption may be too restrictive, yielding invalid or inefficient inference. In this talk, we propose to relax the distributional assumption of the random effects by approximating their distribution by a seminonparametric (SNP) density. Due to the special structure of an SNP density, we obtain a closed form expression for the likelihood for linear mixed models, facilitating straightforward inference on model parameters. The availability of an efficient algorithm of sampling from an SNP density allows us to carry out a Monte Carlo EM algorithm for making inference for generalized linear mixed models. We illustrate SNP approach by application to a subset of data from Framingham study and evaluate its performance via simulation studies.(This talk is based on joint work with Marie Davidian and Junliang Chen.)
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