**SAS proc qlim** is a procedure that models **q**ualitative and **l**imited 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