Hallo all,
I am new to the list an not an econometrician (double apologies!).
I have a problem with the test for the Independence of Irrelevant
Alternatives (IIA) in a Multinomial Logit Model (MNL).
I am using the Hausmann McFadden test . The test statistic is:
(b_r - b_u)' [VC_r - VC_u]^(-1) (b_r - b_u)
where
b_u estimated parameters of the full choice set
VC_r estimated variance and covariance matrix of the full choice
set
b_r estimated parameters of the restricted choice set
VC_r estimated variance and covariance matrix of the restricted
choice set
Although quadratic, the statistic is sometimes negative (because
the restricted model has less observations than the unrestricted).
Hausmann and McFadden (Econometrica, 1984, p.1226), suggest an
asymptotically equivalent estimate of VC_r for a conditional logit model
that guarantees positive semidefiniteness of [VC_r - VC_u].
Algebraically the conditional and multinomial logit models are the same,
so I guess I could use the same logic to obtain an alternative estimate
to obtain a poitive test statistic.
Do you know where I could find a specification I could use for the MNL?
Has anybody encountered the same problem before?
I will be happy to make a summary for the list of the replies I receive.
Thank you very much for your help
Alberto Bacchiega
University of York (UK)
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