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SAS FAQ
How can I perform a Bivariate Probit Analysis Using Proc QLIM in SAS 9.1?

SAS proc qlim is a new procedure in SAS/ETS released in SAS 9. It analyzes 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. The only type of model that SAS does for two discrete outcome variables will be a biprobit model. Therefore it is sufficient to just specify that the two outcome variables are discrete.

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

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