The QLIM Procedure

(View the complete code for this example.)

Cameron and Trivedi (1986, 1998) studied the number of doctor visits from the Australian Health Survey, 1977–1978. In the following data set, the dependent variable, DVISITS, contains the number of doctor visits in the past 2 weeks (0, 1, or more than 2). The explanatory variables are as follows: SEX indicates if the patient is female; AGE is the age in years divided by 100; INCOME is the annual income ($10,000); LEVYPLUS indicates if the patient has private health insurance; FREEPOOR indicates free government health insurance due to low income; FREEREPA indicates free government health insurance for other reasons; ILLNESS is the number of illnesses in the past 2 weeks; ACTDAYS is the number of days the illness caused reduced activity; HSCORE is a questionnaire score; CHCOND1 indicates a chronic condition that does not limit activity; and CHCOND2 indicates a chronic condition that limits activity.

title1 'Estimating an Ordinal Probit Model';

data docvisit;
   input sex age agesq income levyplus freepoor freerepa
         illness actdays hscore chcond1 chcond2 dvisits;
   y = (dvisits > 0);
   if ( dvisits > 8 ) then dvisits = 8;
datalines;

   ... more lines ...   

1 0.37 0.1369 0.25  0  0  1  1  0  1  0  0  0
1 0.52 0.2704 0.65  0  0  0  0  0  0  0  0  0
0 0.72 0.5184 0.25  0  0  1  0  0  0  0  0  0
;

The dependent variable, DVISITS, has nine ordered values. The following SAS statements estimate the ordinal probit model:

/*-- Ordered Discrete Responses --*/
proc qlim data=docvisit;
   model dvisits = sex age agesq income levyplus
                   freepoor freerepa illness actdays hscore
                   chcond1 chcond2 / discrete;
run;

The output of the QLIM procedure for ordered data modeling is shown in Output 27.1.1.

By default, ordinal probit/logit models are estimated assuming that the first threshold or limit parameter () is 0. However, this parameter can also be estimated when the LIMIT1=VARYING option is specified. The probability that belongs to the jth category is defined as

where is the logistic or standard normal CDF, and . Output 27.1.2 lists ordinal probit estimates computed in the following program. Note that the intercept term is suppressed for model identification when is estimated.

/*-- Ordered Probit --*/
proc qlim data=docvisit;
   model dvisits = sex age agesq income levyplus
                   freepoor freerepa illness actdays hscore
                   chcond1 chcond2 / discrete(d=normal) limit1=varying;
run;