SAS proc qlim is a procedure that models qualitative and limited dependent variables, variables with limited ranges or discrete distributions, including binary variables. The procedure can analyze both discrete univariate and multivariate models. We will illustrate how to perform a bivariate probit model analysis using proc qlim. The data set used is hsb2.sas7bdat which can be downloaded following the link. We created two binary variables, hiwrite and himath for the purpose of demonstration. The way to specify our model as a bivariate probit model is very similar to the way to specify a multivariate regression model. The only thing that we need to add is the ENDOGENOUS statement where we specify that the two outcome variables are discrete. By default with the discrete specification SAS will perform a probit regression, but logistic regression is available with the specification discrete(d=logit).
options nocenter nodate nofmterr;
libname in 'd:data';
data hsb2;
set in.hsb2;
hiwrite = (write>=60);
himath = (math>=60);
run;
proc qlim data=hsb2;
model hiwrite himath = female read;
endogenous hiwrite himath ~ discrete;
run; 1
The QLIM Procedure
Discrete Response Profile of hiwrite
Index Value Frequency Percent
1 0 147 73.50
2 1 53 26.50
Discrete Response Profile of himath
Index Value Frequency Percent
1 0 151 75.50
2 1 49 24.50
Model Fit Summary
Number of Endogenous Variables 2
Endogenous Variable hiwrite himath
Number of Observations 200
Log Likelihood -157.57872
Maximum Absolute Gradient 0.0001420
Number of Iterations 21
AIC 329.15744
Schwarz Criterion 352.24567
Algorithm converged.
Parameter Estimates
Standard Approx
Parameter Estimate Error t Value Pr > |t|
hiwrite.Intercept -5.638784 0.769722 -7.33 <.0001
hiwrite.FEMALE 0.608516 0.227431 2.68 0.0075
hiwrite.READ 0.085227 0.012885 6.61 <.0001
himath.Intercept -5.543897 0.766776 -7.23 <.0001
himath.FEMALE 0.019750 0.223054 0.09 0.9294
himath.READ 0.087772 0.013117 6.69 <.0001
_Rho 0.598763 0.109035 5.49 <.0001