The QLIM Procedure

Cameron and Trivedi (1986, 1998) studied the number of doctor visits from the Australian Health Survey 1977-78. 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: 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.

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;
1 0.19 0.0361 0.55  1  0  0  1  4  1  0  0  1
1 0.19 0.0361 0.45  1  0  0  1  2  1  0  0  1

   ... 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 22.1.1.

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 22.1.2 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;