Fundamentals Of Discrete Choice Part 2-the Nested Logit Model

摘要

In part 1 (TEC October 2008) of this article, we considered the multinomial logit model, its properties and its ability to model people's choice making behaviour. However it has one important set of limitations. Consider the choice between two modes of transport; car and bus where 75% chose car and 25% chose bus (ie they are in the ratio: 3:1). If we now add a new mode: train, then we would expect to attract train passengers from both car and bus so that the split could end up as 60% car, 20% bus and 20% train. Note that we have not changed the car or bus modes at all, so we would expect their split to be in the same ratio as before (ie 3:1). The multinomial logit model would correctly preserve this split, making train abstract from car and bus so as to preserve the existing ratio of car to bus. This is called the Independence from Irrelevant Alternatives (IIA) property because the choice between car and bus is irrelevant to the choice between car and train and between bus and train. The IIA assumption asserts that the ratio of any two alternatives is independent of the presence or absence of other alternatives. The mutinomial logit model assumes the independence from irrelevant alternatives holds. However sometimes this is not always the case.