One reason for the failure of the pure Poisson distribution to perfectly fit the observed CEB number of years of education completed data is that the rate of childbearing, i.e., the (eduyrs number of babies produced, P, differs across the women The univariate Poisson distribution whether the woman lives in an urban area with a mean of 1.855 does not take into account coded 1 if yes, 0 if no: the heterogeneity of the sample women in their whether the woman is a Han Chinese values of u. So we need to extend the coded 1 if yes, 0 if no univariate Poisson distribution to the poisson whether the woman's first pregnancy regression model, in which we assume that the occurred after 1979 this variable is called observed ceb count for woman i is drawn from Poisson distribution with mean u. where A policy, and is coded 1 if yes, 0 if no is estimated from observed characteristics that is, from X variables of the women Poisson regression is used to model CEB, Here are summary descriptive data with seven X variables, namely age at menarche, in ye for the dependent variable and the age at first marriage(afm), in years seven independent variables woman's exposure to the risk of childbearing sum ceb menarche afm fecund eduyrs urban han policy (fecund), which is calculated in years for each woman is the difference between her Hean std. Dev age at menarche and either, her age at sterilization, her age at menopause, or her age when the survey was conducted whichever is less:15 29 • One reason for the failure of the pure Poisson distribution to perfectly fit the observed CEB data is that the rate of childbearing, i.e., the number of babies produced, μ, differs across the women. The univariate Poisson distribution with a mean of 1.855 does not take into account the heterogeneity of the sample women in their values of μ. So we need to extend the univariate Poisson distribution to the Poisson regression model, in which we assume that the observed CEB count for woman i is drawn from a Poisson distribution with mean μ, where μi, is estimated from observed characteristics, that is, from X variables of the women. 30 Poisson regression is used to model CEB, with seven X variables, namely: • woman’s age at menarche, in years; • age at first marriage (afm), in years; • woman’s exposure to the risk of childbearing (fecund), which is calculated in years for each woman, is the difference between her age at menarche and either, her age at sterilization, her age at menopause, or her age when the survey was conducted, whichever is less; 16 31 • number of years of education completed (eduyrs); • whether the woman lives in an urban area, coded 1 if yes, 0 if no; • whether the woman is a Han Chinese, coded 1 if yes, 0 if no; • whether the woman’s first pregnancy occurred after 1979; this variable is called policy, and is coded 1 if yes, 0 if no. 32 Here are summary descriptive data for the dependent variable and the seven independent variables: sum ceb menarche afm fecund eduyrs urban han policy