Bayesian analysis of zero-inflated regression models

• Published in: Journal of statistical planning and inference Vol. 136; no. 4; pp. 1360 - 1375
• Main Authors: Ghosh, Sujit K., Mukhopadhyay, Pabak, Lu, Jye-Chyi(JC)
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.04.2006; New York,NY Elsevier Science; Amsterdam
• Subjects: Applications; Bayesian inference; Data augmentation; Exact sciences and technology; Gibbs sampling; Insurance, economics, finance; Markov chain Monte Carlo; Mathematics; Parametric inference; Probability and statistics; Sciences and techniques of general use; Statistics; WinBUGS; Zero-inflated power series models; Zero-inflated power series models; 62P30; WinBUGS; Markov chain Monte Carlo; 62E10; Data augmentation; Bayesian inference; Gibbs sampling; 62F15; Bayes estimation; Regression analysis; Statistical decision; Poisson distribution; Geometric distribution; Statistical simulation; Power series; Statistical method; Coverage probability; 62P30 Bayesian inference; MCMC algorithm; Maximum likelihood; Likelihood function
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2004.10.008

In modeling defect counts collected from an established manufacturing processes, there are usually a relatively large number of zeros (non-defects). The commonly used models such as Poisson or Geometric distributions can underestimate the zero-defect probability and hence make it difficult to identify significant covariate effects to improve production quality. This article introduces a flexible class of zero inflated models which includes other familiar models such as the Zero Inflated Poisson (ZIP) models, as special cases. A Bayesian estimation method is developed as an alternative to traditionally used maximum likelihood based methods to analyze such data. Simulation studies show that the proposed method has better finite sample performance than the classical method with tighter interval estimates and better coverage probabilities. A real-life data set is analyzed to illustrate the practicability of the proposed method easily implemented using WinBUGS.