By William Greene
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Additional info for Functional Form and Heterogeneity in Models for Count Data
4. 30), so the hypothesis that the same model applies to males and females is rejected for the Poisson model. The Poisson speciﬁcation is, itself, rejected in favor of a model with heterogeneity, so we repeated the homogeneity test with the log gamma (negative binomial) results. 3. Poisson models and heterogeneity in poisson (t ratios in parentheses). 7 n 27326 14243 13083 Notes: Estimated coeﬃcients for year dummy variables, excluding year 1984, are not reported; θ = the estimated parameter for the log gamma (NB) model; κ = 1/θ = Var[h] for log gamma model; σ(ε) = ψ (θ) = Var(ln hi ) for the log gamma model.
This model speciﬁes the NB2 functional form with, in addition, λi = exp(xi β + σεi ), where εi has a standard normal distribution. One way to view the model would be as a Poisson model with a compound disturbance in it, λi = exp(xi β + σn εni + εgi ), where εni is the standard normally distributed component and εgi is the log of hi , which has the log gamma distribution that produces the NB model. If εni and εgi are statistically independent, then the unconditional (on εgi ) density will be the NB2 model, still with latent normally distributed heterogeneity.
The outcome variables of interest in the study were doctor visits in the last three months and number of hospital visits last year. 2. 3.. 1. was truncated at 20 visits. 2. was truncated at 10. 1 The Data 171 Fig. 2. Histograms for DocVis. The base case count model used by the authors included the following variables in addition to the constant term: xit = (Age, Agesq, HSat, Handdum, Handper, M arried, Educ, Hhninc, Hhkids, Self, Civil, Bluec, W orking, P ublic, AddOn) and a set of year eﬀects, t = (Year 1985, Year 1986, Year 1987, Year 1988, Year 1991, Year 1994).
Functional Form and Heterogeneity in Models for Count Data by William Greene