In demography, popular count variables Thus. models other than ols models are the number of children born to a ave been used to handle count data. this woman, the number of pregnancies a lecture will cover two: (1)the Poisson regression model, and (2) the negative intercourses a person has in a week, the binomial regression model. The software number of sexual partners in a year, the ed in this le number of abortions a woman has had in regression is also available in SPSS under her lifetime the number of residential general log-linear model) Before the migrations a person makes in a lifetime discussion of the Poisson regressions the number of jobs a migrant worker has let's first take a look at the univariate done since s/he arrived. eto Poisson distribution Frequently, count variables are treated as The Univariate poisson distribution though they are continuous and The univariate poisson distribution unbounded ols models are then used to provides the benchmark for Poisson estimate the effects of x variables on their occurrence OLS is appropriate if the regression. Let Y equal a random variable that represents the number of times that dependent variable, the count, is an event has occurred during an interval independently and identically distributed of time y will have a poisson However, the use of ols for count distribution with a parameter u greater outcomes can result in inefficient inconsistent and biased estimates if one or more of the OLS assumptions are not met Pr(r=y y=0,1,2,3 5 • In demography, popular count variables are the number of children born to a woman, the number of pregnancies a woman has, the number of sexual intercourses a person has in a week, the number of sexual partners in a year, the number of abortions a woman has had in her lifetime, the number of residential migrations a person makes in a lifetime, the number of jobs a migrant worker has done since s/he arrived, etc. 6 • Frequently, count variables are treated as though they are continuous and unbounded. OLS models are then used to estimate the effects of X variables on their occurrence. OLS is appropriate if the dependent variable, the count, is independently and identically distributed. However, the use of OLS for count outcomes can result in inefficient, inconsistent and biased estimates if one or more of the OLS assumptions are not met. 4 7 • Thus, models other than OLS models have been used to handle count data. This lecture will cover two: (1) the Poisson regression model, and (2) the negative binomial regression model. The software used in this lecture is Stata. (Poisson regression is also available in SPSS under general log-linear model) Before the discussion of the Poisson regressions, let’s first take a look at the univariate Poisson distribution. 8 The Univariate Poisson Distribution • The univariate Poisson distribution provides the benchmark for Poisson regression. Let Y equal a random variable that represents the number of times that an event has occurred during an interval of time. Y will have a Poisson distribution with a parameter μ greater than 0: