MULTIPLE-INFLATION POISSON MODEL WITH L1 REGULARIZATION

A multiple-inflation Poisson (MIP) model is put forward for analyzing count data that have multiple inflated values. Analogous to the zero-inflated Poisson model (ZIP; Lambert (1992)), MIP assumes a mixture distribution of Poisson and degenerate distributions, where the probabilities for the inflated values are from a cumulative logit model. We explore the properties of the proposed model, with a detailed treatment given to its maximum likelihood estimation. Moreover, we address variable selection by adopting an L-1 regularization scheme. Both simulation experiments and an analysis of a health care data set are provided to illustrate the multiple-inflation Poisson model.