Distributions of CEB, Univariate Poisson Poisson goodness of fit There is a formal "goodness of fit test we may calculate, that compares the observed empirical distribution with the distribution predicted by the Poisson regression model The null hypothesis (Ho) is that there is no difference between the obseryed data and the modeled data, indicating that the model fits the data. So we are looking for a small mber of Children Ever Born value of chi-square, with a probability >0.05 Observed CEB Distribution-+Univariate Poisson, mu =1.8 If we have a small chi-square this would mean we have a model that fits the data. a The Stata command is poisgof The predicted probabilities generated by fit chi the Poisson regression model (PRM)are only slightly worse at predicting count 0 than the predictions generated by the The goodness of fit test is good news for our univariate Poisson distribution but for the model. it tells us that the model fits the data most part the PRM only results in a ery well;; specifically, the goodness of fit Chi2 modest improvement in the predictions est indicates that given the Poisson regression Both the PRM predictions, and the model we cannot reject the null hypothesis that editions generated by the univariate observed data are poisson distributed Poisson model are still somewhat off the The Stata printout for the Poisson regression actual distribution of ceb equation also shows values of Pseudo R2 and likelihood ratio)LR Chi2, which indicate that we have a statistically significant model19 37 0 .1 .2 .3 .4 Proportion or Probability 0 1 2 3 4 5 6 7 8 9 Number of Children Ever Born Observed CEB Distribution Univariate Poisson, mu = 1.855 Prediction from PRM and Poisson Regression Model Distributions of CEB, Univariate Poisson 38 • The predicted probabilities generated by the Poisson regression model (PRM) are only slightly worse at predicting count 0 than the predictions generated by the univariate Poisson distribution; but for the most part the PRM only results in a modest improvement in the predictions. Both the PRM predictions, and the predictions generated by the univariate Poisson model, are still somewhat off the actual distribution of CEB. 20 39 Poisson Goodness of Fit • There is a formal “goodness of fit” test we may calculate, that compares the observed empirical distribution with the distribution predicted by the Poisson regression model. The null hypothesis ( H0) is that there is no difference between the observed data and the modeled data, indicating that the model fits the data. So we are looking for a small value of chi-square, with a probability > 0.05. If we have a small chi-square, this would mean we have a model that fits the data. 40 • The Stata command is poisgof • The goodness of fit test is good news for our model. It tells us that the model fits the data very well; specifically, the goodness of fit Chi2 test indicates that given the Poisson regression model we cannot reject the null hypothesis that our observed data are Poisson distributed. • The Stata printout for the Poisson regression equation also shows values of Pseudo R2 and the (likelihood ratio) LR Chi2 , which indicate that we have a statistically significant model