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 regression introduced by
Famoye and Singh (2003), 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.
Asymptotic normality of the 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 AIC
statistics and Vuong tests (see Vuong (1989)) is carried out. For
the given data, our extended ZIGP regression model will prove to be
superior over GP and ZIP models and even ZIGP models with constant
overall dispersion and zero-inflation parameters demonstrating the
usefulness of our proposed extensions.