HPCOUNTREG Procedure

(View the complete code for this example.)

Except for its ability to operate in the multithreaded environment, the HPCOUNTREG procedure is similar to other regression model procedures in the SAS System. For example, the following statements are used to estimate a Poisson regression model:

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

The response variable y is numeric and has nonnegative integer values.

This section illustrates two simple examples that use PROC HPCOUNTREG. The data are taken from Long (1997). 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 a scientist’s mentor (ment) 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. The model is executed in single-machine mode with two threads.

/*-- Poisson Regression --*/
proc hpcountreg data=long97data;
   model art = fem mar kid5 phd ment / dist=poisson method=quanew;
   performance nthreads=2  details;
run;

The "Model Fit Summary" table that is shown in Figure 2 lists several details about the model. By default, the HPCOUNTREG 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.

Figure 3 shows the parameter estimates of the model and their standard errors. 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.

To allow for variance greater than the mean, you can fit the negative binomial model instead of the Poisson model by specifying the DIST=NEGBIN option, as shown in the following statements. Whereas the Poisson model requires that the conditional mean and conditional variance be equal, the negative binomial model allows for overdispersion, in which the conditional variance can exceed the conditional mean.

/*-- Negative Binomial Regression --*/
proc hpcountreg data=long97data;
   model art = fem mar kid5 phd ment / dist=negbin(p=2) method=quanew;
   performance nthreads=2 details;
run;

Figure 4 shows the fit summary and Figure 5 shows the parameter estimates.

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 , which is highly significant, providing strong evidence of overdispersion.