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Multivariate Normal Utility Function
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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 17.12 and Figure 17.13. The test for ttime = 0 is rejected at the 1% significance level.
Figure 17.12
Constrained Probit Estimation Summary
The MDC Procedure
Multinomial Probit Estimates
decision |
50 |
150 |
-33.88604 |
-54.93061 |
0.0002380 |
8 |
Dual Quasi-Newton |
71.77209 |
75.59613 |
100 |
11 |