Advanced discrete choice models, in particular mixed logit models, have become more and more popular these last years. While a lot of progress have been achieved in the estimation techniques, making them numerically appealing, their properties have not been examined in great details. This sometimes leads to confusing quality measurements, and misinterpretation of the estimated parameters. In this paper, we review the use of standard statistical tests on estimated parameters, in particular t-statistics, and show that there are no more valid for mixed logit models if applied in the same way as for simple models, as multinomial logit formulation. We propose alternative tests for judging the quality of parameters. In particular, instead of consider each parameter separately, we consider the whole set of parameters affecting the same factor, since they mutually influence themselves, creating correlations when using standard information matrix. The question however remains to know if some factor has to be included in the utility of the alternative, and to determine the accuracy level of the estimated parameters. We review here the use of F-tests based on likelihood ratios (see for instance McFadden and Train), as well as bootstrap resampling to determine variance and bias over the parameters. Numerical tests are performed using AMLET software. We compare obtained confidence intervals for synthetic as well as real data, and draw some guidelines for the practitioner. We finally express strength and weaknesses of the proposed method and discuss avenues for future research.

Reference

D. McFadden and K. Train, Mixed MNL Models for Discrete Response, Journal of Applied Econometrics, Vol. 15, No. 5, 2000, pp. 447-470.