Notes on Poisson Regression and Some Extensions

Density0 1 2 3 4 5.8 1 1.2 1.4vhat1Figure 4: Distribution of Empirical Bayes Estimates of Random EffectThe distribution of random effects from this model can be shown a couple of ways. A graphicalrepresentation is given in Fig. 4. The commands to fit the model and compute the subject-specificrandom effect estimates are given below.xi: xtpois childs boomer married i.deg nonwht income, i(idnum)xtpois, irrpredict xb, xbgen lambda1 = exp(xb)scalar alpha = 1/(exp([lnalpha]_cons))gen vhat1 = (y + alpha)/(lambda1 + alpha)sum vhat1, detailhistogram vhat1-------------------------------------------------------------vhat1-------------------------------------------------------------Percentiles Smallest1% .822471 .75523535% .8726416 .780816610% .8964401 .7998554 Obs 149625% .9296511 .8005092 Sum of Wgt. 149650% .9884257 Mean 1Largest Std. Dev. .094407175% 1.053683 1.38304790% 1.123672 1.383047 Variance .008912795% 1.170076 1.420766 Skewness .803510299% 1.288011 1.431209 Kurtosis 4.09398Thus, based on this data, the propensity for childbearing (net of covariates) is about 1.25 timeshigher for women at the 90% percentile of the random effects distribution relative to those at the10th percentile, which is not much of a difference.Extensions. It is also possible to combine both zero-inflation with the negative binomialdistributional assumption. What you get, of course, is the zero-inflated negative binomial model(zinb). There are many extensions of these extensions that have not made their way into canned15