Bayesian Zero-Inflated Negative Binomial Regression Based on Pólya-Gamma Mixtures
Open Access
- 1 September 2019
- journal article
- research article
- Published by Institute of Mathematical Statistics in Bayesian Analysis
- Vol. 14 (3), 829-855
- https://doi.org/10.1214/18-ba1132
Abstract
Motivated by a study examining spatiotemporal patterns in inpatient hospitalizations, we propose an efficient Bayesian approach for fitting zero-inflated negative binomial models. To facilitate posterior sampling, we introduce a set of latent variables that are represented as scale mixtures of normals, where the precision terms follow independent Pólya-Gamma distributions. Conditional on the latent variables, inference proceeds via straightforward Gibbs sampling. For fixed-effects models, our approach is comparable to existing methods. However, our model can accommodate more complex data structures, including multivariate and spatiotemporal data, settings in which current approaches often fail due to computational challenges. Using simulation studies, we highlight key features of the method and compare its performance to other estimation procedures. We apply the approach to a spatiotemporal analysis examining the number of annual inpatient admissions among United States veterans with type 2 diabetes.Keywords
This publication has 17 references indexed in Scilit:
- Understanding predictive information criteria for Bayesian modelsStatistics and Computing, 2013
- Bayesian Inference for Logistic Models Using Pólya–Gamma Latent VariablesJournal of the American Statistical Association, 2013
- Associations Between Reduced Hospital Length of Stay and 30-Day Readmission Rate and Mortality: 14-Year Experience in 129 Veterans Affairs HospitalsAnnals of Internal Medicine, 2012
- Use of outpatient care in VA and Medicare among disability-eligible and age-eligible veteran patientsBMC Health Services Research, 2012
- A Bayesian model for repeated measures zero-inflated count data with application to outpatient psychiatric service useStatistical Modelling, 2010
- Adding Spatially-Correlated Errors Can Mess Up the Fixed Effect You LoveThe American Statistician, 2010
- Bias in 2-part mixed models for longitudinal semicontinuous dataBiostatistics, 2009
- Deviance information criteria for missing data modelsBayesian Analysis, 2006
- Bayesian analysis of zero-inflated regression modelsJournal of Statistical Planning and Inference, 2006
- Zero-Inflated Poisson Regression, with an Application to Defects in ManufacturingTechnometrics, 1992