The MDC Procedure

Multivariate Normal Utility Function

Consider the random utility function

where

The correlation coefficient () between and represents commonly neglected attributes of public transportation modes, 1 and 2. The following SAS statements estimate this trinomial probit model:

/*-- homoscedastic mprobit --*/
proc mdc data=newdata;
   model decision = ttime /
            type=mprobit
            nchoice=3
            unitvariance=(1 2 3)
            covest=hess;
   id pid;
run;

The UNITVARIANCE=(1 2 3) option specifies that the random component of utility for each of these choices has unit variance. If the UNITVARIANCE= option is specified, it needs to include at least two choices. The results of this constrained multinomial probit model estimation are displayed in Figure 24.12 and Figure 24.13. The test for ttime = 0 is rejected at the 1% significance level.

Figure 24.12: Constrained Probit Estimation Summary

The MDC Procedure
 
Multinomial Probit Estimates

Model Fit Summary
Dependent Variabledecision
Number of Observations50
Number of Cases150
Log Likelihood-33.88604
Log Likelihood Null (LogL(0))-54.93061
Maximum Absolute Gradient0.0002380
Number of Iterations8
Optimization MethodDual Quasi-Newton
AIC71.77209
Schwarz Criterion75.59613
Number of Simulations100
Starting Point of Halton Sequence11


Figure 24.13: Multinomial Probit Estimates with Unit Variances

The MDC Procedure
 
Multinomial Probit Estimates

Parameter Estimates
ParameterDFEstimateStandard
Error
t ValueApprox
Pr > |t|
ttime1-0.23070.0472-4.89<.0001
RHO_2110.48200.31351.540.1242