Generalized Poisson-Poisson Mixture Model for Misreported Counts with an Application to Smoking Data

Abstract

The assumption that is usually made when modeling count data is that the response variable, which is the count, is correctly reported. Some counts might be over-or under-reported. We derive the Generalized Poisson-Poisson mixture regression (GPPMR) model that can handle accurate, un-derreported and overreported counts. The parameters in the model will be estimated via the maximum likelihood method. We apply the GPPMR model to a real-life data set.