The hypothesis is rejected, once again.

The nested logit model was reestimated under assumptions of the heteroscedastic extreme value model. The results are shown in Table 21.15. This model is less restrictive than the nested logit model. To make them comparable, we note that we found that Gair = n/(Tairj6) = 2.1886 and Gtrain = Gbus = Gear = n/{xgmundj6) = 3.2974. The heteroscedastic extreme value (HEV) model thus relaxes one variance restriction, because it has three free variance parameters instead of two. On the other hand, the important degree of freedom here is that the HEV model does not impose the IIA assumption anywhere in the choice set, whereas the nested logit does, within each branch.

A primary virtue of the HEV model, the nested logit model, and other alternative models is that they relax the IIA assumption. This assumption has implications for the cross elasticities between attributes in the different probabilities. Table 21.16 lists the estimated elasticities of the estimated probabilities with respect to changes in the generalized cost variable. Elasticities are computed by averaging the individual sample values rather than computing them once at the sample means. The implication of the IIA

TABLE 21.16 Estimated Elasticities with Respect to Generalized Cost

Cost Is That of Alternative

TABLE 21.16 Estimated Elasticities with Respect to Generalized Cost

Cost Is That of Alternative

Effect on |
Air |
Train |
Bus |
Car |

Multinomial Logit |

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