Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent outsourcing rates

This paper focuses on an extension of zero-inflated generalized Poisson (ZIGP) regression models for count data. We discuss generalized Poisson (GP) models where dispersion is modelled by an additional model parameter. Moreover, zero-inflated models, in which overdispersion is assumed to be caused by an excessive number of zeros, are discussed. In addition to ZIGP models considered by several authors, we now allow for regression on the overdispersion and zero-inflation parameters. Consequently, we propose tools for an exploratory data analysis on the dispersion and zero-inflation level. An application dealing with outsourcing of patent filing processes will be used to compare these nonnested models. The model parameters are fitted by maximum likelihood using our R package 'ZIGP' available on the Comprehensive R Archive Network (CRAN). Asymptotic normality of the Maximum Likelihood (ML) estimates in this non-exponential setting is proven. Standard errors are estimated using the asymptotic normality of the estimates. Appropriate exploratory data analysis tools are developed. Also, a model comparison using Akaike Information Criterion (AIC) statistics and Vuong tests is carried out. For the given data, our extended ZIGP regression model will prove to be superior over GP and zero-inflated Poisson (ZIP) models, and even over ZIGP models, with constant overall dispersion and zero-inflation parameters demonstrating the usefulness of our proposed extensions.