Bias in Discrete Choice Models Estimates
MAHER M, ROSA A and KONTOLEMAKIS J, Napier University, UK
It is well known that the multinomial logit (MNL) model suffers from certain weaknesses when used in discrete choice modelling, principally when the errors are not independent. The most extreme form of this is in the so-called Òred bus, blue bus paradoxÓ
It is well known that the multinomial logit (MNL) model suffers from certain weaknesses when used in discrete choice modelling, principally when the errors are not independent. The most extreme form of this is in the so-called Òred bus, blue bus paradoxÓ (Mayberry 1973). Nevertheless, software implementing the MNL model (such as ALOGIT Daly 1992)) continues to be widely used. The hierarchical logt (HI,) model has been proposed as a means of allowing for correlated errors between alternatives but, whilst the form of the HL model suggests that it should overcome some of the MNLÕs deficiencies, it is by no means clear that it will overcome all of them and, in any case, the user must spec% the hierarchical structure rather than allow the data to reveal the location and extent of any correlation.
The multinomial probit (MNP) model specifically allows for correlated errors and, at least in principle, these correlations can be inferred from the data rather than needing to be specified at the input stage. Given the appreciable advantages which MNP models have over their MNL counterparts, it is perhaps curious that they have not found their way into commercial sohare for estimation in discrete choice modelling. The reasons presumably include the fact that MNL models are simple to understand and to use for estimation and that, by comparison, MNP models are more complex and their use in estimation softwae has been perceived to be computationally demanding.
Recently developed methods for the estimation of MNP models use Monte Carlo simulation techniques. Tests on these methods have confirmed their superiority over MNL methods in certain circumstances, especially in the presence of correlation, but these tests also demonstrate that the computation times required are many times more than for MNL estimation.
One purpose of this paper is to investigate the extent of the bias in parameter estimates from MNL estimation and how this bias depends on the degree of correlation in the errors. This is carried out through the application of MNL estimation to many artiscially generated data sets, with known values of the parameters. The other purpose is to develop and test (on the same artificial data sets) a numerical MNP estimation method (as opposed to the previous simulation-based methods) which requires computation times that are no greater than those for MNL estimation.
The structure of the paper is as follows: Section 2 will review the various models and previous literature, as well as the proposed MNP algorithm. In Section 3, the methodology for the artificial data generation process will be described. Then, the programme of tests and the results obtained will be described in Section 4, before conclusions are drawn in Section 5.
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