Count Data Regression Using Series Expansions: with Applications

A new class of parametric regression models for both underand overdispersed count data is proposed. These models are based on squared polynomial expansions around a Poisson baseline density. The approach is similar to that for continuous data using squared Hermite polynomials proposed by Gallant and Nychka and applied to ®nancial data by, among others, Gallant and Tauchen. The count models are applied to underdispersed data on the number of takeover bids received by targeted ®rms, and to overdispersed data on the number of visits to health practitioners. The models appear to be particularly useful for underdispersed count data. # 1997 by John Wiley & Sons, Ltd.