Title: Bayesian model choice in semi-parametric regression approaches
Abstract: Semiparametric regression methods can be utilized in regression analysis where covariates cannot anymore be assumed to have a linear effect (or polynomial functions thereof) on the outcome. However, if we want to formally test for the existence of one or multiple non-parametric effects (of any specific covariates) in order to accomplish a model selection, there are no straightforward approaches, and existing methods are computationally expensive. We accomplish model selection in a Bayesian framework, utilizing Markov Chain Monte Carlo techniques. In this case, Bayesian P-Splines are used for the non-parametric effects since they have some nice properties. This methodology enables us to perform the model selection and the estimation of the regression parameters simultaneously. Two approaches are presented: To start with, we use an inverse gamma prior for the covariance of the random effects. We then reformulate the model and apply a conditionally conjugated normal prior on the Cholesky factors of the covariance matrices. We employ simulation studies to compare the properties and performance of the two versions. The procedures are illustrated with analyses of two real datasets.