A disaggregate negative binomial regression procedure for count data analysis

Various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations. The authors present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross-sections, possibly over some fixed time periods. This procedure simultaneously pools or groups cross-sections while estimating a separate negative binomial regression model for each group. An E-M algorithm is described within a maximum likelihood framework to estimate the group proportions, the group-specific regression coefficients, and the degree of overdispersion in event rates within each derived group. The proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases (events) for a frequently bought consumer good.