The COUNTREG Procedure

(View the complete code for this example.)

The COUNTREG procedure is similar in use to other SAS regression model procedures. For example, the following statements are used to estimate a Poisson regression model:

proc countreg data=one;
   model y = x / dist=poisson;
run;

The response variable y is numeric and has nonnegative integer values. To allow for variance greater than the mean, specify the DIST=NEGBIN option to fit the negative binomial model instead of the Poisson.

The following example illustrates the use of PROC COUNTREG. The data are taken from Long (1997) and can be found in the SAS/ETS Sample Library. This study examines how factors such as gender (fem), marital status (mar), number of young children (kid5), prestige of the graduate program (phd), and number of articles published by the mentor (ment) of a doctoral candidate in science affect the number of articles (art) published by the scientist.

The first 10 observations are shown in Figure 1.

The following SAS statements estimate the Poisson regression model:

proc countreg data=long97data;
   model art = fem mar kid5 phd ment / dist=poisson;
run;

The "Model Fit Summary" table, shown in Figure 2, lists several details about the model. By default, the COUNTREG procedure uses the Newton-Raphson optimization technique. The maximum log-likelihood value is shown, in addition to two information measures, Akaike’s information criterion (AIC) and Schwarz’s Bayesian information criterion (SBC), which can be used to compare competing Poisson models. Smaller values of these criteria indicate better models.

The parameter estimates of the model and their standard errors are shown in Figure 3. All covariates are significant predictors of the number of articles, except for the prestige of the program (phd), which has a p-value of 0.6271.

The following statements fit the negative binomial model. Although the Poisson model requires that the conditional mean equal the conditional variance, the negative binomial model allows for overdispersion; that is, the conditional variance can exceed the conditional mean.

proc countreg data=long97data;
   model art = fem mar kid5 phd ment / dist=negbin(p=2) method=qn;
run;

The fit summary is shown in Figure 4, and parameter estimates are listed in Figure 5.

The parameter estimate for _Alpha of 0.4416 is an estimate of the dispersion parameter in the negative binomial distribution. A t test for the hypothesis is provided. It is highly significant, indicating overdispersion ().

The null hypothesis can be also tested against the alternative by using the likelihood ratio test, as described by Cameron and Trivedi (1998, pp. 45, 77–78). The likelihood ratio test statistic is equal to , where and are the log likelihoods for the Poisson and negative binomial models, respectively. The likelihood ratio test is highly significant, providing strong evidence of overdispersion.