The QLIM Procedure

(View the complete code for this example.)

The following example illustrates the use of PROC QLIM. The 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 (inlf ). Explanatory variables are the number of children ages 5 or younger (kidslt6 ), the number of children ages 6 to 18 (kidsge6 ), the woman’s age (age ), the woman’s years of schooling (educ ), wife’s labor experience (exper ), square of experience (expersq ), and the family income excluding the wife’s wage (nwifeinc ). The program (with data values omitted) is as follows:

/*-- Binary Probit --*/
proc qlim data=mroz plots=predicted;
   model inlf = nwifeinc educ exper expersq
                age kidslt6 kidsge6  / discrete;
run;

Results of this analysis are shown in the following four figures. In the first table, shown in Figure 1, PROC QLIM provides frequency information about each choice. In this example, 428 women participate in the labor force (inlf = 1).

The second table is the estimation summary table shown in Figure 2. Included are the number of dependent variables, names of dependent variables, the number of observations, the log-likelihood function value, the maximum absolute gradient, the number of iterations, the optimization method, AIC, and Schwarz criterion.

Goodness-of-fit measures are displayed in Figure 3. All measures except McKelvey-Zavoina’s definition are based on the log-likelihood function value. The likelihood ratio test statistic has chi-square distribution conditional on the null hypothesis that all slope coefficients are zero. In this example, the likelihood ratio statistic is used to test the hypothesis that kidslt6 = kidge6 = age = educ = exper = expersq nwifeinc = 0.

The parameter estimates and standard errors are shown in Figure 4.

Finally, the QLIM procedure profiles the predicted outcome with respect to the regressors. For example, Figure 5 shows the predicted values profiled with respect to nwifeinc, educ, exper, expersq, age, and kidslt6.

Figure 5: Predictions by Regressors: nwifeinc, educ, exper, expersq, age, and kidslt6

When the error term has a logistic distribution, the binary logit model is estimated. To specify a logistic distribution, add the D=LOGIT option as follows:

/*-- Binary Logit --*/
proc qlim data=mroz;
   model inlf = nwifeinc educ exper expersq
                age kidslt6 kidsge6  / discrete(d=logit);
run;

The estimated parameters are shown in Figure 6.

The heteroscedastic logit model can be estimated using the HETERO statement. If the variance of the logit model is a function of the family income level excluding wife’s income (nwifeinc), the variance can be specified as

where is normalized to 1 because the dependent variable is discrete. The following SAS statements estimate the heteroscedastic logit model:

/*-- Binary Logit with Heteroscedasticity --*/
proc qlim data=mroz;
  model inlf = nwifeinc educ exper expersq
               age kidslt6 kidsge6 / discrete(d=logit);
  hetero inlf ~ nwifeinc / noconst;
run;

The parameter estimate, , of the heteroscedasticity variable is listed as _H.nwifeinc; see Figure 7.