On the Applicability of the Multinomial Probit Model

On the Applicability of the Multinomial Probit Model


MUNIZAGA M A, University of Chile and ORTUZAR J, Pontificia Universidad de Chile, Chile


It has been known for many years that the multinomial Logit (MNL) model is not


It has been known for many years that the multinomial Logit (MNL) model is not
appropriate when the assumptioa.of independent and identically distributed error termg
is not reasonable. Alternative model functions, such as the hierarchical logit (IIL)
model, have been proposed to deal with the problem of correlation among certa;n
options but only the multinomial Probit CMNP) model is free from all deficiencies. It is
interesting to mention that although the MNP estimation is now perfectly plausible the
model has only been shyly incorporated into practice.

In this paper we will attempt to clarify some aspects, that maybe obscure, related to the
use of MNP models in order to sthnulate its use orto provide .arguments to avoid its use
depending on the case. To do this we have identified fairly simple structures of the
covariance matrix of the error terms in some common practical cases, and study how
different models (including the MNP) behave in those conditions using Monte Carlo
simulation. Our results allow us to recommend the use ofProbit modelsin the presence
of correlation when large databases are available. Probit or HeternsceAa~*fio Extreme
Value (HEVL) models may be nsed when heteroscedasticity between alternatives is
expected. Finally, in the presence of pure heteroscedastioity, the lVlNL model seems to
work fine but with a Single Element Nested Logit (SENL) or a MNP model, the ratio
between standard deviations can also be estimated. This may be very important if mixed
revealed (RP) and stated preference (SP) models are required.

The rest of the paper is organised as follows. In section 2 we describe the models and
their estimation. In section 3 we identify the structure of the covariance matrix in some
common practical cases. The empirical evidence is shown in section 4, and the main
conclusions of the paper are snmmarised ill section 5.


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