Example 72.3 Logistic Regression

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 a positive response (subscribing) as a function of the variables sex and age. Specifically, the probability of subscribing is modeled as

where is the cumulative logistic distribution function.

By default, the PROBIT procedure models the probability of the lower response level for binary data. One way to model is to format the response variable so that the formatted value corresponding to is the lower level. The following statements format the values of subs as 1 = ’accept’ and 0 = ’reject’, so that PROBIT models . They produce Output 72.3.1.

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 subs sex;
   model subs=sex age / d=logistic itprint;
   format subs subscrib.;
run;

Output 72.3.1 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.