BayesX: Analyzing Bayesian Structural Additive Regression Models

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.

BayesX: Analysing Bayesian structured additive regression models

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 the estimation of very complex and realistic models. This paper describes the capabilities of the public domain software BayesX for estimating complex regression models with structured additive predictor. The program extends the capabilities of existing software for semiparametric regression. 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 and 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 may be estimated. Moreover, BayesX allows the estimation of complex continuous time survival and hazardrate models

Variational inference for count response semiparametric regression

© 2015 International Society for Bayesian Analysis. Fast variational approximate algorithms are developed for Bayesian semiparametric regression when the response variable is a count, i.e., a nonnegative integer. We treat both the Poisson and Negative Binomial families as models for the response variable. Our approach utilizes recently developed methodology known as non-conjugate variational message passing. For concreteness, we focus on generalized additive mixed models, although our variational approximation approach extends to a wide class of semiparametric regression models such as those containing interactions and elaborate random effect structure

Nonparametric checks for count data models: an application to demand for health care in Spain

This paper presents model specification checking procedures for count data regression models which are consistent in the direction of nonparametric alternatives. The discussion is motivated in the context of a model of demand for health care in Spain. The parameters of the regression model are estimated by maximum likelihood based on Poisson and Negative Binomial specifications as well as by ordinary least squares and semiparametric generalized least squares. However, our interest is not only centered on the estimation ofthe regression parameters, but also the conditional probabilities of counts. Therefore, the specification of the conditional distribution function of counts is the main focus of attention. A useful preliminary diagnosis tool consists of comparing the conditional probabilities estimates by nonparametric regression and by maximum likelihood methods based on alternative models. We present formal specification procedures based on new developed testing methods for regression model checking. The test statistics are based on marked empirical processes which are not distribution free, but their critical values are well approximated by bootstrap. Such tests are valid for testing the functional form of the conditional mean and conditional probabilities resulting from alternative distributional specifications. In our health care demand model, the linear exponential regression model with a Negative Binomial seems to be appropiate for this data set

BayesX: Analyzing Bayesian Structural Additive Regression Models

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

Count data models with variance of unknown form: an application to a hedonic model of worker absenteeism

We examine an econometric model of counts of worker absences due to illness in a sluggishly adjusting hedonic labor market. We compare three estimators that parameterize the conditional variance?least squares, Poisson, and negative binomial pseudo maximum likelihood?to generalized least squares (GLS) using nonparametric estimates of the conditional variance. Our data support the hedonic absenteeism model. Semiparametric GLS coefficients are similar in sign, magnitude, and statistical significance to coefficients where the mean and variance of the errors are specified ex ante. In our data, coefficient estimates are sensitive to a regressor list but not to the econometric technique, including correcting for possible heteroskedasticity of unknown form.Publicad

Count data models with variance of unknown form: an application to a hedonic model of worker absenteeism

We examined an econometric model of counts of worker absences due to illness. The underlying theoretical model is of a sluggishly adjusting hedonic labor market. We compared results fromı three parametric estimators, nonlinear least squares plus Poissonand negative binomial pseudo maximum likelihood, to generalized least squares using nonparametric estimates of the conditional variance. Our data support the hedonic model of worker absenteeism. Semiparametric generalized least squares coefficients are similar in sign, magnitude, and statistical significance to their econometric analogs where the mean and variance of the errors were specified ex ante. Overdispersion test reject the Poisson specification. Robustness checks confirm that in our dataı parameter estimates are sensitive to regressor list but are not sensitive to econometric technique, including how we corrected for possible heteroskedasticity of unknown form