A Mixed Poisson Regression Model for Analysis of Patent Data

We analyze cross-sectional patent data using a finite mixed Poisson regression model with covariates in Poisson rates and mixing probabilities. Maximum likelihood estimation based on the EM and quasi-Newton algorithms, a model selection procedure, residual analysis and goodness-of-fit tests are discussed. This model is applied to data on the relationship between technological innovation and R&D research. Results are compared in several ways to those obtained using alternative models for overdispersion. Monte Carlo studies show among other things that the selection criteria usually choose the correct model and that when the mixing distribution is incorrectly specified, estimates of parameters remain unbiased but are inefficient.