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The COUNTREG Procedure

Example 10.1 Basic Models

Data Description and Objective

The data set docvisit contains information for approximately 5,000 Australian individuals about the number and possible determinants of doctor visits that were made during a two-week interval. This data set contains a subset of variables taken from the Racd3 data set used by Cameron and Trivedi (1998). The docvisit data set can be found in the SAS/ETS Sample Library.

The variable doctorco represents doctor visits. Additional variables in the data set that you want to evaluate as determinants of doctor visits include sex (coded 0=male, 1=female), age (age in years divided by 100), illness (number of illnesses during the two-week interval, with five or more coded as five), income (annual income in Australian dollars divided by 1,000), and hscore (a general health questionnaire score, where a high score indicates bad health). Summary statistics for these variables are computed in the following statements and presented in Output 10.1.1.

proc means data=docvisit;
   var doctorco sex age illness income hscore;
run;

Output 10.1.1 Summary Statistics

The MEANS Procedure

Variable	N	Mean	Std Dev	Minimum	Maximum
doctorco sex age illness income hscore	5190 5190 5190 5190 5190 5190	0.3017341 0.5206166 0.4063854 1.4319846 0.5831599 1.2175337	0.7981338 0.4996229 0.2047818 1.3841524 0.3689067 2.1242665	0 0 0.1900000 0 0 0	9.0000000 1.0000000 0.7200000 5.0000000 1.5000000 12.0000000

 proc countreg data=docvisit;
    model doctorco=sex illness income hscore / dist=poisson printall;
 run;

 proc countreg data=docvisit;
    class sex;
    model doctorco=sex illness income hscore / dist=poisson;
 run;

If the CLASS statement is present, the COUNTREG procedure creates as many indicator or dummy variables as there are categories in a class variable and uses them as independent variables. In order to avoid collinearity with the intercept, the last-created dummy variable is assigned a zero coefficient by default. This means that only the dummy variable associated with the first level of sex (male=0) is used as a regressor. Consequently, the estimated coefficient for this dummy variable is the negative of the one for the original SEX variable in Output 10.1.2 because the reference level has switched from male to female.

Now consider a more practical task. The previous example implicitly assumed that each additional illness during the two-week interval has the same effect. In other words, this variable was thought of as a continuous variable. But this variable has only six values, and it is quite possible that the number of illnesses has a nonlinear effect on doctor visits. In order to check this conjecture, the following statements specify ILLNESS in the CLASS statement so that it is represented in the model by a set of six dummy variables that can account for any type of nonlinearity.

 proc countreg data=docvisit;
    class sex illness;
    model doctorco=sex illness income hscore / dist=poisson;
 run;

The parameter estimates are displayed in Output 10.1.4.

Each ILLNESS parameter in this model represents the difference between each effect of ILLNESS and ILLNESS=5. Note that these estimates for different ILLNESS categories do not increase linearly, but instead show a relatively large jump from zero illnesses to one followed by relatively smaller increases.

 proc countreg data=docvisit;
    model doctorco=sex illness income hscore / dist=zip;
    zeromodel doctorco ~ age;
 run;

The estimates of the zero-inflated intercept (Inf_Intercept) and the zero-inflated regression coefficient for AGE (Inf_age) are approximately 0.99 and –2.09, respectively. Since the zero-inflation model uses a logistic link by default, you can estimate the probabilities for individuals of ages 20, 50, and 70 as follows:

That is, the estimated probability of belonging to the low-risk group is about 0.64 for a 20-year-old individual, 0.49 for a 50-year-old individual, and only 0.38 for a 70-year-old individual. This supports the suspicion that older individuals are more likely to have a positive number of doctor visits.

Alternative models to account for the overdispersion are the negative binomial and the zero-inflated negative binomial models, which can be fit using the DIST=NEGBIN and DIST=ZINB options, respectively.

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