# Poisson Regression

**Topics:**Regression analysis, Normal distribution, Statistical hypothesis testing

**Pages:**2 (1642 words)

**Published:**May 1, 2013

This page shows an example of poisson regression analysis with footnotes explaining the output. The data collected were academic information on 316 students. The response variable is days absent during the school year (daysabs), from which we explore its relationship with math standardized tests score (mathnce), language standardized tests score (langnce) and gender . As assumed for a Poisson model our response variable is a count variable and each subject has the same length of observation time. Had the observation time for subjects varied, the Poisson model would need to be adjusted to account for the varying length of observation time per subject. This point is discussed later in the page. Also, the Poisson model, as compared to other count models (i.e., negative binomial or zero-inflated models), is assumed the appropriate model. In other words, we assume that the dependent variable is not over-dispersed and does not have an excessive number of zeros. The first half of this page interprets the coefficients in terms of Poisson regression coefficients and the second half interprets the coefficients in terms of incidence rate ratios.

We also run the estat ic command to calculate the likelihood ratio chi-square statistic.

poisson daysabs mathnce langnce gender

Iteration 0: log likelihood = -1547.9709

Iteration 1: log likelihood = -1547.9709

Poisson regression Number of obs = 316 LR chi2(3) = 175.27 Prob > chi2 = 0.0000 Log likelihood = -1547.9709 Pseudo R2 = 0.0536

------------------------------------------------------------------------------ daysabs | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- mathnce | -.0035232 .0018213...

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