Analysis of Patent Data—A Mixed-Poisson-Regression-Model Approach

Abstract

Count-data models are used to analyze the relationship between patents and research and development spending at the firm level, accounting for overdispersion using a finite mixed Poisson regression model with covariates in both Poisson rates and mixing probabilities. Maximum likelihood estimation using the EM and quasi-Newton algorithms is discussed. Monte Carlo studies suggest that (a) penalized likelihood criteria are a reliable basis for model selection and can be used to determine whether continuous or finite support for the mixing distribution is more appropriate and (b) when the mixing distribution is incorrectly specified, parameter estimates remain unbiased but have inflated variances.