The Hausman, McFadden, and Small-Hsiao tests are used to assess which assumption in multinomial logistic regression?

• A. Proportional hazards
• B. Independence of Irrelevant Alternatives (IIA)
• C. Multicollinearity among predictors
• D. Homoscedasticity

Answer: (B)

Independence of Irrelevant Alternatives (IIA) is what these tests assess. In multinomial logistic regression, IIA means the odds of choosing one option over another depend only on the attributes of those two options and are unaffected by the presence or absence of other alternatives. If you remove or add a substitute option and the estimated relative probabilities for the remaining choices change beyond what would be expected, IIA is violated.

The Hausman-McFadden approach compares the coefficient estimates from the full model (all alternatives) to those from a reduced model (a subset of alternatives). If IIA holds, these estimates should be consistent with each other; large differences indicate that the inclusion or exclusion of alternatives alters substitution patterns in a way the model cannot capture.

McFadden’s method uses a likelihood-based comparison between the full model and a restricted model with an alternative removed. A significant difference in fit or in the estimated coefficients for the remaining choices signals a violation of IIA.

Small-Hsiao provides another diagnostic by examining residual relationships across alternatives. Detecting nontrivial correlations or patterns in the residuals suggests the error structure implies substitutions among options that violate IIA.

So, these tests are all ways to check whether the IIA assumption holds, not issues like multicollinearity, heteroscedasticity, or other unrelated model properties.