Multinominal logit models: multicollinearity and its consequences on parameter estimation and on independence from irrelevant alteratives tests

The Multinomial Logit Model is one of the most used Discrete Choice Models and it has been widely used to study the transportation system. This model has a closed form and so it is computationally cheap, but it needs some restrictive assumptions. The Independence from Irrelevant Alternatives (IIA) property for example, is not always respected and the tests used to verify it can lead to opposed results almost when there is multicollinearity between explicative variables. Furthermore, the presence of multicollinearity can generate problems in the parameter estimation. In this paper we study the effects of the multicollinearity on the results of the IIA tests and we propose a new method to estimate the parameters of the multinomial logit model. The data used for the analysis concern the choice of the residence in the Zurich area