Estimating the well-known Multinomial Logit model
The Multinomial Logit (MNL) model was introduced by Daniel McFadden in his seminal paper from 1973, http://eml.berkeley.edu/reprints/mcfadden/zarembka.pdf.
The model is based on fairly restrictive assumptions: the Independent and Identically Distributed (IID) error terms and the Independence from Irrelevant Alternatives (IIA).
The IID assumes that the error terms of utility functions of all the alternatives are independent (uncorrelated) and follow the same distribution. (For MNL, it is the Extreme Value Type I Distribution, commonly known as Gumbel distribution after E. J. Gumbel who derived and analyzed it.)
The IIA, on the other hand, assumes that the ratios of probabilities between alternatives are constant, that is, removing one or more alternatives from the consideration set does not change the ratio between the remaining alternatives. Consider the following situation: you are choosing between a bike, train, and car to get to work. For...
