4.16 Regression-Based Specification Tests for
the Multinomial Logit Model

Diagnostic tests for omitted variables or
functional misspecification in the multinomial
logit (MNL) model can be performed conveniently
by testing the significance of auxiliary
regressions of residuals on included and
excluded variables. In particular, Lagrange
Multiplier (LM) and Hausman-McFadden (HM) tests
of the Independence from Irrelevant Alternatives
(IIA) Property of the MNL model can be carried
out by the regression method using suitably
defined excluded variables. Using this method,
it is straightforward to test jointly against
several sources of misspecification, and to
diagnose the structure of deviations from the
MNL model.