| We propose Bayesian generalized additive mixed models for correlated data, which arise frequently in studies involving clustered, hierarchical and spatial designs. The models allow for additive functional dependence of a continuous or discrete outcome variable on covariates by using nonparametric regression and account for correlation between observations using random effects. Partially improper integrated Wiener priors are used for the nonparametric functions and the resulting estimators are cubic smoothing splines. When the distribution of the random effects is normal, a Gibbs sampling algorithm is provided for the estimation of all model parameters and inference for fixed effects, random effects, and nonparametric functions. Systematic inference can be made within a modified generalized linear mixed model framework. We also propose a generalized additive mixed model which relaxes the normality assumption for the distribution of the random effects. A Dirichlet process prior distribution is assumed for the random effects. Computation is carried out using Gibbs sampling. Systematic inference on model parameters can be made within a modified generalized linear mixed model framework without parametric distributional assumption on random effects. We illustrate the proposed approaches by analyzing two real-world data sets and evaluate their performance through simulations. |
