R: Bayesian variable selection for a Poisson-Logistic model

pogit-package {pogit}

R Documentation

Bayesian variable selection for a Poisson-Logistic model

Description

This package provides Bayesian variable selection for regression models of under-reported count data as well as for (overdispersed) Poisson, negative binomial and binomial logit regression models using spike and slab priors. For posterior inference, MCMC sampling schemes are used that rely on data augmentation and/or auxiliary mixture sampling techniques. Details can be found in Dvorzak and Wagner (2016).

Details

The main function is pogitBvs which provides Bayesian variable selection for a Poisson-Logistic (Pogit) model to account for potential under-reporting of count data. The Pogit model, introduced by Winkelmann and Zimmermann (1993), is specified by combining a Poisson model for the data generating process of counts and a logit model for the fallible reporting process, where the outcomes of both processes may depend on a set of potential covariates. By augmenting the observed data with the unobserved counts, the model can be factorized into a Poisson and a binomial logit model part. Hence, the MCMC sampling algorithm for this two-part model is based on data augmentation and sampling schemes for a Poisson and a binomial logit model.

Though part of the main function, the functions poissonBvs and logitBvs can be used separately to perform Bayesian variable selection for Poisson or binomial logit regression models. An alternative to poissonBvs is provided by the function negbinBvs to deal with overdispersion of count data. The sampling algorithms are based on auxiliary mixture sampling techniques.

All functions return an object of class "pogit" with methods print.pogit, summary.pogit and plot.pogit to summarize and display the results.

Author(s)

Michaela Dvorzak <m.dvorzak@gmx.at>, Helga Wagner

Maintainer: Michaela Dvorzak <m.dvorzak@gmx.at>

References

Dvorzak, M. and Wagner, H. (2016). Sparse Bayesian modelling of underreported count data. Statistical Modelling, 16(1), 24 - 46, doi:10.1177/1471082x15588398.

Winkelmann, R. and Zimmermann, K. F. (1993). Poisson-Logistic regression. Department of Economics, University of Munich, Working Paper No. 93 - 18.

Examples

## see examples for pogitBvs, logitBvs, poissonBvs and negbinBvs