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 18.12 and Figure 18.13. The test for ttime
= 0 is rejected at the 1% significance level.
Figure 18.12: Constrained Probit Estimation Summary
Model Fit Summary  

Dependent Variable  decision 
Number of Observations  50 
Number of Cases  150 
Log Likelihood  33.88604 
Log Likelihood Null (LogL(0))  54.93061 
Maximum Absolute Gradient  0.0002380 
Number of Iterations  8 
Optimization Method  Dual QuasiNewton 
AIC  71.77209 
Schwarz Criterion  75.59613 
Number of Simulations  100 
Starting Point of Halton Sequence  11 
Figure 18.13: Multinomial Probit Estimates with Unit Variances
Parameter Estimates  

Parameter  DF  Estimate  Standard Error 
t Value  Approx Pr > t 
ttime  1  0.2307  0.0472  4.89  <.0001 
RHO_21  1  0.4820  0.3135  1.54  0.1242 