Abstract
Generalized linear mixed models are popular for regressing a discrete response when there is clustering, e.g. in longitudinal studies or in hierarchical data structures. It is standard to assume that the random effects have a normal distribution.
Recently, it has been examined whether wrongly assuming a normal distribution for the random effects is important for the estimation of the fixed effects parameters. Since it is unclear whether the normality assumption is truly satisfied in practice, it is important that generalized mixed models are available which relax the normality assumption.
A replacement of the normal distribution with a mixture of Gaussian distributions specified on a grid whereby only the weights of the mixture components are estimated using a penalized approach ensuring a smooth distribution for the random effects is proposed. The parameters of the model are estimated in a Bayesian context using MCMC techniques.