# Application of Random Coefficient Logit Model

## Application of Random Coefficient Logit Model

### Authors

KIM K S, University of Leeds, UK

### Description

This paper aims to introduce and estimate a random coefficient logit model by mixed logit specification. This is a generalisation of the standard logit model. To estimate the random coefficient logit model, a simulation method is applied to approximate mu

### Abstract

This paper aims to introduce and estimate a random coefficient logit model by mixed logit specification. This is a generalisation of the standard logit model. To estimate the random coefficient logit model, a simulation method is applied to approximate multi dimensional integrals and we maximlse a simulated log likelihood function instead of true log likelihood function. This is analogous error component logit model (Daly[1997]) because the unobserved part of a utility function consists of several components. More details are explained subsequently.

Logit models have become firmly established in the travel demand research. Bhat[1997] identified the following important assumptions for multinominal logit model(MNL), leading to the simple structure and presenting well known restrictions. First, the coefficients of variables have same values (taste variations) for all people. This assumption implies that different people have the same utility parameters for each factor entering the model. Second, the unobserved part of utility is distributed independently and identically across alternatives. Because of these assumption, logit models predict that a change in the attributes of one alternative changes the probabilities of the other alternatives being chosen proportionally. Furthermore, logit models assume that the unobserved part of utility is independent for each response when there are repeated choices by an individual.

Many researchers have been known to relax either of these assumptions, see Bhat[1997] for a good review of these. The multinominal probit model(MNP) relaxes most of the logit model assumptions, but its estimation is still difficult. Munizaga and Ortuzar[1997] recently estimated the MNP using GHK simulator.

#### Publisher

Association for European Transport