CONFIDENCE INTERVALS FOR CHOICE PROBABILITIES OF THE MULTINOMIAL LOGIT MODEL

This paper describes three methods for developing confidence intervals for the choice probabilities in multinomial logit models. The confidence intervals reflect the effects of sampling errors in the parameters of the models. The first method is based on the asymptotic sampling distribution of the choice probabilities and leads to a joint confidence region for these probabilities. This confidence region is not rectangular and is useful mainly for testing hypotheses about the values of the choice probabilities. The second method is based on an asymptotic linear approximation of the relation between errors in models' parameters and errors in choice probabilities. The method yields confidence intervals for individual choice probabilities as well as rectangular joint confidence regions for all of the choice probabilities. However, the linear approximation on which the method is based can yield erroneous results, thus limiting the applicability of the method. A procedure for setting an upper bound on the error caused by the linear approximation is described. The third method is based on nonlinear programming. This method also leads to rectangular joint confidence regions for the choice probabilities. The nonlinear programming method is exact and, therefore, more generally applicable than the linear approximation method. However, when the linear approximation is accurate, it tends to produce narrower confidence intervals than does the nonlinear programming method, except in cases where the number of alternatives in the choice set is either two or very large. Several numerical examples are given in which the nonlinear programming method is illustrated and compared with the linear approximation method. (Author)

Media Info

  • Media Type: Print
  • Features: References; Tables;
  • Pagination: pp 23-29
  • Monograph Title: Passenger travel forecasting
  • Serial:

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Filing Info

  • Accession Number: 00310698
  • Record Type: Publication
  • ISBN: 0309029813
  • Files: TRIS, TRB
  • Created Date: May 21 1980 12:00AM