Elsevier

Journal of Econometrics

Volume 64, Issues 1–2, September–October 1994, Pages 207-240
Journal of Econometrics

An exact likelihood analysis of the multinomial probit model

https://doi.org/10.1016/0304-4076(94)90064-7Get rights and content

Abstract

We develop new methods for conducting a finite sample, likelihood-based analysis of the multinomial probit model. Using a variant of the Gibbs sampler, an algorithm is developed to draw from the exact posterior of the multinomial probit model with correlated errors. This approach avoids direct evaluation of the likelihood and, thus, avoids the problems associated with calculating choice probabilities which affect both the standard likelihood and method of simulated moments approaches. Both simulated and actual consumer panel data are used to fit six-dimensional choice models. We also develop methods for analyzing random coefficient and multiperiod probit models.

References (40)

  • D.S. Bunch

    Estimability in the multinomial probit model

    Transportation Research

    (1991)
  • B. Dansie

    Parameter estimability in the multinomial probit model

    Transportation Research

    (1985)
  • A. Zellner et al.

    Bayesian analysis of dichotomous quantal response models

    Journal of Econometrics

    (1984)
  • J. Albert et al.

    Bayesian analysis of binary and polychotomous data

    Journal of the American Statistical Association

    (1993)
  • A. Borsch-Supan et al.

    Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models

    Journal of Econometrics

    (1990)
  • A. Borsch-Supan et al.

    Health, children, and elderly living arrangements: A multiperiod-multinomial probit model with unobserved heterogeneity and autocorrelated errors

  • B.P. Carlin et al.

    Monte Carlo Bayesian methods for discrete regression models and categorial time series

  • G. Casella et al.

    Explaining the Gibbs sampler

    American Statistician

    (1992)
  • S. Chib et al.

    Bayesian inference for regressions with ARMA (p,q) errors

    (1992)
  • C. Daganzo

    Multinomial probit

    (1980)
  • L. Devroye

    Non-uniform random variate generation

    (1986)
  • A.R. Gallant

    Nonlinear statistical models

    (1987)
  • A. Gelfand et al.

    Sampling-based approaches to calculating marginal densities

    Journal of the American Statistical Association

    (1990)
  • A. Gelfand

    Illustration of Bayesian inference in normal data models using Gibbs sampling

    Journal of the American Statistical Association

    (1990)
  • A. Gelfand et al.

    Bayesian analysis of constrained parameter and truncated data problems using Gibbs sampling

    Journal of the American Statistical Association

    (1992)
  • A. Gelman et al.

    A single series from the Gibbs sampler provides a false sense of security

  • A. Gelman et al.

    Inference from iterative simulation using multiple sequences

    Statistical Science

    (1992)
  • S. Geman et al.

    Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images

    IEEE Transactions on Pattern Analysis and Machine Intelligence

    (1984)
  • J. Geweke

    Efficient simulation from the multivariate normal and Student-t distributions subject to linear constraints and the evaluation of constraint probabilities

  • J. Geweke

    Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments

  • Cited by (348)

    • Bayesian forecasting in economics and finance: A modern review

      2024, International Journal of Forecasting
    View all citing articles on Scopus
    View full text