The LOGISTIC Procedure

(View the complete code for this example.)

The following data were originally published by Mroz (1987) and downloaded from Wooldridge (2002). This data set is based on a sample of 753 married white women. The dependent variable is a discrete variable of labor force participation (InLaborForce). Explanatory variables are the number of children age 5 or younger (KidsLt6); the number of children ages 6 to 18 (KidsGe6); the woman’s age (Age); the woman’s years of schooling (Education); the wife’s labor experience (Experience); the square of experience (SqExperience); and the family income, excluding the wife’s wages (IncomeExcl).

data Mroz;
   input InLaborForce IncomeExcl Education Experience
         SqExperience Age KidsLt6 KidsGe6 lWage;
   datalines;
1 10.91006    12 14  196   32  1   0   1.210154
1 19.49998    12 5   25    30  0   2   0.3285121

   ... more lines ...   

0 9.952       12 4   16    43  0   0   .
0 24.984      12 15  225   60  0   0   .
0 28.363      9  12  144   39  0   3   .
;

The following program sets aside about 30% of the data set to be used for testing the model. To do this, a new response variable, InLaborForce2, is set to missing for the test data; otherwise it is set to the original value of InLaborForce.

data Mroz;
   set Mroz;
   if (ranuni(3939)<.3) then InLaborForce2=.;
   else InLaborForce2=InLaborForce;
run;

In the following statements, the GOF option modifies the "Model Fitting Statistics" table by displaying a single column with more statistics in Output 79.19.1, displays more tests in the "Goodness-of-Fit" table, displays the results of the Hosmer-Lemeshow test, and displays a calibration plot because ODS Graphics is enabled. The SHOWOBS option modifies the calibration plot by displaying a bar chart of the events in the upper margin of the plot and a bar chart of the nonevents in the bottom margin. The CLM option displays confidence intervals for the mean loess fit as a band around the loess curve. The OUTPUT statement creates a data set that contains the linear predictors and the original InLaborForce variable.

ods graphics on;
proc logistic data=Mroz plots=calibration(clm showobs);
   model InLaborForce2 = IncomeExcl Education Experience
                         SqExperience Age KidsLt6 KidsGe6  / gof;
   id InLaborForce;
   output out=Scored xbeta=XBeta;
run;

Because of the continuous predictors, the Pearson and deviance tests in Output 79.19.1 cannot be trusted. However, all the other tests remain valid and do not reject the null hypothesis that the fit is adequate.

The "Model Fit Statistics" table displays an assortment of statistics in Output 79.19.2 that are most useful when you compare this model to other models. The misclassification rate and the average square error are of moderate size.

The Hosmer-Lemeshow test is computed using 10 groups for an 8-degrees-of-freedom chi-square test, and you do not reject the null hypothesis that the fit is adequate. The results are shown in Output 79.19.3.

The calibration plot in Output 79.19.4 shows you how well the predicted probabilities align with the observed responses. The smoothing parameter that the procedure selects seems rather small; you can change the smoothing parameter for the loess fit by specifying the PLOTS=CALIBRATION(SMOOTH=) option. The confidence band is not a simultaneous band, so you cannot use the fact that the band does or does not contain the diagonal line as a calibration test. The displayed Spiegelhalter z statistic is a standard normal; its squared value is reported in Output 79.19.1.

Now that the model has been fit to the training data, refit the testing data by using the original response variable versus the linear predictor (Harrell 2015). Ideally, the intercept parameter should be near 0, and the slope parameter should be near 1. In the following statements, the WHERE data set option extracts the test data from the Scored data set, and the TEST statement performs a Wald test of this joint hypothesis. The calibration plot of this fit should also be close to the diagonal.

proc logistic data=Scored(where=(InLaborForce2=.))
              plots=calibration(clm showobs);
   model InLaborForce = XBeta;
   test intercept = 0, XBeta = 1;
run;

The TEST result in Output 79.19.5 shows that you do not reject the null that the intercept parameter is 0 and the slope parameter is 1.

The calibration plot displayed in Output 79.19.6 follows the diagonal quite well.