Testing IIA in MNLM with Hausman-McFadden


New Member
Dear all,

I'm having some problems with the IIA property violation test of Hausman McFadden.

I estimated two MNL models based on 3 predictors: one for the complete alternative choice set (9 modes of transportation) and one for the restricted alternative choice set (8 modes of transportation). I want to test whether IIA holds, i.e. that the ratios of the 7 remaining transportation modes remain the same when excluding transportation mode i.

H0: coefficients full model = coefficients restricted model.
H1: H0 is not true.

Hausman-McFadden test statistic is estimated by:

HM = (Bf - Br)' * [var(Bf) - var(Br)]^-1 * (Bf - Br)

Bf = coefficients of full model
Br = coefficients of restricted model
var(Bf) = covariance matrix of Bf
var(Br) = covariance matrix of Br

Now the problems begins because I'm having trouble with the inputs for this test:

1. Bf is a matrix with 4 rows (the beta's of the constant and the 3 predictors for each alternative) and 8 columns (the 8 different alternatives measured against the final alternative "9"), while Br is a matrix with 4 rows and 7 columns (the restricted, 7 different alternatives vs. the last alternative, now "8").

Is it correct to simply delete the column containing the beta's for the "excluded" alternative from Bf to create equally sized matrices Bf and Br?

2. The covariance matrices can be estimated from Bf and Br, right? The formula requires also the inverse of these. If i do this my matrix returns as close to singular or badly scaled (Matlab message).

How can I fix this?

3. The final statistic HM is obviously also a matrix.

Do I need to sum all the values to obtain the Chi-statistic which I can compare to the critical value assuming df = nr.rows(Br)*nr.columns(Br)?

I hope anyone can help me with this. Thank you very much for your time.

Best regards,