Statistical Modelling 7 (2007), 125153
Zero-inflated generalized Poisson models with regression effects on the mean,
dispersion and zero-inflation level applied to patent outsourcing rates
Claudia Czado
Center for Mathematical Sciences,
Munich University of Technology
Germany
Vinzenz Erhardt
Center for Mathematical Sciences,
Munich University of Technology,
Boltzmannstrasse 3,
D85747 Garching
Germany
eMail:
erhardt@ma.tum.de
Aleksey Min
Center for Mathematical Sciences,
Munich University of Technology
Germany
Stefan Wagner
Institute for Innovation Research,
Technology Management and Entrepreneurship,
University of Munich
Germany
Abstract:
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 RArchive
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.
Keywords:
maximum likelihood estimator; overdispersion; patent outsourcing;
Vuong test; zero-inflated generalized Poisson regression; zero-inflation
Downloads:
Data and R-code in
zipped
archive.
The ZIGP package is available for download from
CRAN.
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