Lang, S. and Fahrmeir, Ludwig
Bayesian generalized additive mixed models. A simulation study.
Collaborative Research Center 386, Discussion Paper 230
Generalized additive mixed models extend the common parametric predictor of generalized linear models by adding unknown smooth functions of different types of covariates as well as random effects. From a Bayesian viewpoint, all effects as well as smoothing parameters are random. Assigning appropriate priors, posterior inference can be based on Markov chain Monte Carlo techniques within a unified framework. Given observations on the response and on covariates, questions like the following arise: Can the additive structure be recovered? How well are unknown functions and effects estimated? Is it possible to discriminate between different types of random effects? The aim of this paper is to obtain some answers to such questions through a careful simulation study. Thereby, we focus on models for Gaussian and categorical responses based on smoothness priors as in Fahrmeir and Lang (2001). The result of the study provides valuable insight into the facilities and limitations of the models when applying them to real data.