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A Class of Random Utility Models Generating the Exploded Logit

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  • Karim Kilani

    (LIRSA - Laboratoire interdisciplinaire de recherche en sciences de l'action - CNAM - Conservatoire National des Arts et Métiers [CNAM])

Abstract

We reexamine a family of distributions in random utility models introduced by David Strauss, which generates ranking probabilities consistent with the exploded logit model, thus implying the multinomial logit model for the choice probabilities. We explore the necessary and sufficient conditions for its validity within copula theory, a robust analytical framework. By specifying minimal assumptions required for the support of the marginal utility distributions, we clarify and reinforce the fundamental structure of the model, demonstrating that it is based on strict archimedean copulas. Additionally, we provide a new mathematical proof by induction confirming that these utility distributions indeed generate the exploded logit model.

Suggested Citation

  • Karim Kilani, 2024. "A Class of Random Utility Models Generating the Exploded Logit," Working Papers hal-04704755, HAL.
    • Handle: RePEc:hal:wpaper:hal-04704755
    Note: View the original document on HAL open archive server: https://cnam.hal.science/hal-04704755v1
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    File URL: https://cnam.hal.science/hal-04704755v1/document
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    Keywords

    Exploded Logit Model; Multinomial Logit Model; Ranking Probabilities; Random Utility Models JEL Classification: C25; D01; Archimedean Copulas Choice Probabilities Copula Theory Exploded Logit Model Multinomial Logit Model Ranking Probabilities Random Utility Models JEL Classification: C25 D01; Archimedean Copulas; Choice Probabilities; Copula Theory;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles

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