The PROBIT Procedure

In this example, a series of people are asked whether or not they would subscribe to a new newspaper. For each person, the variables sex (Female, Male), age, and subs (1=yes, 0=no) are recorded. The PROBIT procedure is used to fit a logistic regression model to the probability of subscribing (subs = 1) as a function of the variables sex and age. Specifically, the probability of subscribing is modeled as

where F is the cumulative logistic distribution function.

By default, the PROBIT procedure models the probability of the lower response level. The following statements format the values of subs as 1 = ’accept’ and 0 = ’reject’, and model by using the EVENT= response variable option. The STORE statement saves the fitted model in an item store named LogitModel. The results are shown in Output 93.3.1.

data news;
   input sex $ age subs @@;
   datalines;
Female     35    0   Male       44    0
Male       45    1   Female     47    1
Female     51    0   Female     47    0
Male       54    1   Male       47    1
Female     35    0   Female     34    0
Female     48    0   Female     56    1
Male       46    1   Female     59    1
Female     46    1   Male       59    1
Male       38    1   Female     39    0
Male       49    1   Male       42    1
Male       50    1   Female     45    0
Female     47    0   Female     30    1
Female     39    0   Female     51    0
Female     45    0   Female     43    1
Male       39    1   Male       31    0
Female     39    0   Male       34    0
Female     52    1   Female     46    0
Male       58    1   Female     50    1
Female     32    0   Female     52    1
Female     35    0   Female     51    0
;

proc format;
   value subscrib 1 = 'accept' 0 = 'reject';
run;

proc probit data=news;
   class sex;
   model subs(event="accept")=sex age / d=logistic itprint;
   format subs subscrib.;
   store out=LogitModel;
run;

Output 93.3.1 shows that there appears to be an effect due to both the variables sex and age. The positive coefficient for age indicates that older people are more likely to subscribe than younger people. The negative coefficient for sex indicates that females are less likely to subscribe than males.

You can use the SCORE statement in the PLM procedure to score new observations based on the fitted model saved by the STORE statement above. For example, to compute the probability of subscribing for one new observation with sex = ‘Female’ and age = 35 in the data set test, you can use the following statements:

data test;
   input sex $ age;
   datalines;
Female     35
;

proc plm restore=LogitModel;
   score data=test out=testout predicted / ilink;
run;

proc print data=testout;
run;

The ILINK option in the SCORE statement applies the inverse of the logit link to provide an estimate on the mean (probability) scale. Output 93.3.2 shows the predicted probability for the new observation.