Cumulative Logit---Poisson and Cumulative Logit---Negative Binomial Compound Regression Models for Count Data

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 4, 2008 : 10:30 AM to 12:20 PM
• Sponsor: ENAR
• Author(s): Mark VanRaden*+ and John M. Lachin
• Companies: National Institutes of Health and The George Washington University
• Keywords: count data ; poisson ; regression ; hurdle ; negative binomial ; ordinal regression

Abstract

Count data are often analyzed by Poisson regression, generalized to negative binomial (NB) models in overdispersed cases. When zeroes are much too frequent or infrequent, hurdle models use a binary model to predict 0 vs. >0 and a count model (e.g. conditional Poisson or NB) for the exact positive count. Model departures might still occur for very low counts. Thus we extend the binary part to a cumulative logit (CL) ordinal regression model, the conditional count model predicting exact counts within the CL's highest category, say count>L where L>0 (case L=0 is a hurdle model). Exposure time is incorporated. Parameters estimates by ML are asymptotically normal. A simple type of effect sharing between the two parts can reduce dimension. An individual Pearson type statistic crudely assesses fit. A proper, categorized chi square fit test is possible. Models were readily fit in application.