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Information matrix tests for multinomial logit models

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We show that the influence functions of the information matrix test for the multinomial logit model are the Kronecker product of the outer product of the generalised residuals minus their covariance matrix conditional on the explanatory variables times the outer product of those variables. Thus, it resembles a multivariate heteroskedasticity test à la White (1980), which confirms Chesher’s (1984) unobserved heterogeneity interpretation. Our simulation experiments indicate that using theoretical expressions for the conditional covariance matrices involved substantially reduces size distortions, while the parametric bootstrap practically eliminates them. We also show that the test has good power against several relevant alternatives.

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  • Dante Amengual & Gariele Fiorentini & Enrique Sentan, 2024. "Information matrix tests for multinomial logit models," Working Papers wp2024_2406, CEMFI.
    • Handle: RePEc:cmf:wpaper:wp2024_2406
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    1. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    2. Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.
    3. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    4. Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2024. "The information matrix test for Gaussian mixtures," Working Papers wp2024_2401, CEMFI.
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    7. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
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    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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