Notes on Poisson Regression and Some Extensions

. tab yy | Freq. Percent Cum.------------+-----------------------------------0 | 359 23.92 23.921 | 266 17.72 41.642 | 404 26.92 68.553 | 247 16.46 85.014 | 128 8.53 93.545 | 48 3.20 96.746 | 20 1.33 98.077 | 8 0.53 98.608 | 21 1.40 100.00------------+-----------------------------------Total | 1,501 100.00. tab y, sum(PrY_pois) mean| Summary of| PrY_poisy | Mean------------+------------0 | .143793971 | .278870252 | .270416833 | .174813094 | .084756995 | .032875096 | .010626187 | .002944028 | .00071369------------+------------Total | .19380861Incidentally, the estimated mean and variance of y are respectively 1.94 and 2.79, suggesting adeparture from the usual Poisson sampling assumptions.Full Model. Next we add several covariates to the model. For example, coho10 is a linear effectof 10-year birth cohort to capture secular trends toward fewer children among later birth cohorts;married is a dummy variable to capture the tendency for women to postpone childbearing untilafter marriage. 1 The models also control for respondent’s education, income and race.. xi:glm childs coh10 married i.deg nonwht income, family(p)i.deg _Ideg_1-3 (naturally coded; _Ideg_1 omitted)Generalized linear models No. of obs = 1496Optimization : ML Residual df = 1489Scale parameter = 1Deviance = 1934.104383 (1/df) Deviance = 1.298928Pearson = 1661.586326 (1/df) Pearson = 1.1159081 Note that this measure reflects current marital status, not necessarily the marital status at the time of childbearing.5