Mullahy, John, "Specification and Testing of Some Modified Count Data Models", Journal of Econometrics, Vol. 33, No. 3, (December 1986), pp. 341-365.
Abstract: This paper explores the specification and testing of some modified count data models. These alternatives permit more flexible specification of the data-generating process (dgp) than do familiar count data models (e.g., the Poisson), and provide a natural means for modeling data that are over- or underdispersed by the standards of the basic models. In the cases considered, the familiar forms of the distributions result as parameter-restricted versions of the proposed modified distributions. Accordingly, score tests of the restrictions that use only the easily-computed ML estimates of the standard models are proposed. The tests proposed by Hausman (1978) and White (1982) are also considered. The tests are then applied to count data models estimated using survey microdata on beverage consumption.