BayesX: Analyzing Bayesian Structural Additive Regression Models

Abstract

There has been much recent interest in Bayesian inference for generalized additive and related models. The increasing popularity of Bayesian methods for these and other model classes is mainly caused by the introduction of Markov chain Monte Carlo (MCMC) simulation techniques which allow realistic modeling of complex problems. This paper describes the capabilities of the free software package BayesX for estimating regression models with structured additive predictor based on MCMC inference. The program extends the capabilities of existing software for semiparametric regression included in S-PLUS, SAS, R or Stata. Many model classes well known from the literature are special cases of the models supported by BayesX. Examples are generalized additive (mixed) models, dynamic models, varying coefficient models, geoadditive models, geographically weighted regression and models for space-time regression. BayesX supports the most common distributions for the response variable. For univariate responses these are Gaussian, Binomial, Poisson, Gamma, negative Binomial, zero inflated Poisson and zero inflated negative binomial. For multicategorical responses, both multinomial logit and probit models for unordered categories of the response as well as cumulative threshold models for ordered categories can be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazard rate models.