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A High-dimensional Multinomial Choice Model

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  • Didier Nibbering

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Abstract

The number of parameters in a standard multinomial choice model increases linearly with the number of choice alternatives and number of explanatory variables. Since many modern applications involve large choice sets with categorical explanatory variables, which enter the model as large sets of binary dummies, the number of parameters easily approaches the sample size. This paper proposes a new method for data-driven parameter clustering over outcome categories and explanatory dummy categories in a multinomial probit setting. A Dirichlet process mixture encourages parameters to cluster over the categories, which favours a parsimonious model specification without a priori imposing model restrictions. An application to a dataset of holiday destinations shows a decrease in parameter uncertainty, an enhancement of the parameter interpretability, and an increase in predictive performance, relative to a standard multinomial choice model.

Suggested Citation

  • Didier Nibbering, 2019. "A High-dimensional Multinomial Choice Model," Monash Econometrics and Business Statistics Working Papers 19/19, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2019-19
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp19-2019.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    large choice sets; Dirichlet process prior; multinomial probit model; high-dimensional models;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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