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Information matrix tests for multinomial logit models

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Abstract

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. Martín Almuzara & Dante Amengual & Enrique Sentana, 2019. "Normality tests for latent variables," Quantitative Economics, Econometric Society, vol. 10(3), pages 981-1017, July.
    2. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    3. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    4. Chesher, Andrew, 1983. "The information matrix test : Simplified calculation via a score test interpretation," Economics Letters, Elsevier, vol. 13(1), pages 45-48.
    5. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    6. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    7. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
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    More about this item

    Keywords

    Hessian matrix; outer product of the score; specification test; unobserved heterogeneity.;
    All these keywords.

    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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