How Good is Art Estimated Logit Model? Estimation Accuracy Analysed by Monte Carlo Simulations



How Good is Art Estimated Logit Model? Estimation Accuracy Analysed by Monte Carlo Simulations

Authors

BRUNDELL-FREIJ, University of Lund, Sweden

Description

Members of the Logit model family have for a long time been widely used in

Abstract

Members of the Logit model family have for a long time been widely used in
transportation planning for forecasting purposes. The estimated parameters of such
models have been interpreted to contain valuable information on individual
assessment.

The parameters of logit models are usually Maximum-Likelihood estimated. At
infinitely large sample sizes we know that such estimates are unbiased, normal
distributed and effective (have the "smallest possible" variance). The corresponding
properties of the estimates for finite sample sizes are, however, not covered by theory,
and not analysed in literature.

As our data sets in reality will always comprise a - larger or smaller - finite number of
observations, there is in fact very little knowledge about the quality of the estimated
model, and to which extent it applies to the underlying behavioural process. This
uncertainty comes on top of the doubts that have been expressed by several authors
about the applicability of the assumptions (micro-economic and stochastic) from
which the logit model form as such may be derived 1.

This paper is based on the estimation of logit models from data sets in which the
underlying choice processes are under control - data sets formed by Monte Carlo
simulation. The work is inspired by a paper of Ortuzar, J. D. & William.% H. C.
(1982), but covers a wider range of model quality issues. A more comprehensive
description of my Monte Carlo simulations is presented in Brundell-Freij, K. (1995).
Any conclusions presented in this paper without supporting evidence, would be based
on results presented there.

The aim of this paper is to discuss the following questions:

* What kind of errors - concerning individual assessment as well as prediction of
policy effects - would result from use of the estimated model(s)?

* How would the answer to the above question depend on basic model
imperfections and factors such as sample size etc.?

The estimated models - as well as the underlying data set - focuses modal split models
for regional commuting. There is however all reason to believe that the results
concerning modelling errors and problems that are reported in this paper are far more
general, and applies to all kinds of logit model use.

Publisher

Association for European Transport