Sparse Nonparametric Graphical Models for Random Effect Distribution in GLMMs

A generalized linear mixed model with a nonparametric distribution for the random effect is proposed. The normality assumption for the random effects may be too restrictive to represent the between-subject distribution, especially when the longitudinal response is non-Gaussian. Starting from nonparametric graphical models, we take advantage of the nonparanormal approach to build a flexible la- tent, individual-specific structure for the longitudinal profiles. The nonparanormal method is particularly appealing since it acts on transformations of multivariate non- Gaussian random variables, and assumes that these transformations are multivariate Gaussian. Moreover, it is particularly convenient to handle the joint distribution for high-dimensional variables.