Doubly Inflated Poisson (DIP) and Related Regression Models

• Activity Number: 519
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Manasi Sheth*+ and N. Rao Chaganty
• Companies: Old Dominion University and Old Dominion University
• Keywords: Count Data ; Doubly Inflated Poisson ; Maximum Likelihood ; Method of Moments ; Relative Efficiency

Abstract

Usually over-dispersed count data consists of certain values occurring more frequently than allowed by the common parametric families of distributions. For dealing with zero-inflated count data with covariates, Lambert (Technometrics, 1992, pp. 1 - 14) proposed the zero-inflated Poisson (ZIP) regression model. In this talk, we introduce Doubly Inflated Poisson (DIP) models for count data situations where there is another inflated value k > 0. We present the distributional properties of these models. For the data consisting of un-grouped as well as grouped frequencies, with and without covariates, we discuss parameter estimation using maximum likelihood (ML) and method of moments. Asymptotic and small sample comparisons show that the ML estimators are far superior than the moment estimators. We illustrate the application of DIP models to analyze length of stay (LOS) in the hospital for patients with pancreatic disorder. Parameter estimation and analysis of count data with a negative binomial data-generating process will also be presented using a Doubly Inflated Negative Binomial (DINB) Model.