In many ELS contexts, count data are noted over-dispersion. In many legal settings this issue presents in the form of a "zeros-problem." When such a "skewed, count" dependent variable arises, various approaches include: negative binomial, Poisson, and zero-inflated regression estimations. A recent discussion of this general topic on the StataList (here) includes a robust back-and-forth about the relative strengths and weaknesses of various approaches. The claim that Poisson regression is not inappropriate when there is overdispersion in the dependent variable is forcefully defended. (For an earlier discussion of this general topic click here.)
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