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Generalized Information Matrix Tests for Detecting Model Misspecification

Author

Listed:
  • Richard M. Golden

    (School of Behavioral and Brain Sciences, GR4.1, 800 W. Campbell Rd., University of Texas at Dallas, Richardson, TX 75080, USA)

  • Steven S. Henley

    (Martingale Research Corporation, 101 E. Park Blvd., Suite 600, Plano, TX 75074, USA
    Department of Medicine, Loma Linda University School of Medicine, Loma Linda, CA 92357, USA
    Center for Advanced Statistics in Education, VA Loma Linda Healthcare System, Loma Linda, CA 92357, USA)

  • Halbert White

    (Department of Economics, University of California San Diego, La Jolla, CA 92093, USA
    Halbert White sadly passed away before this article was published.)

  • T. Michael Kashner

    (Department of Medicine, Loma Linda University School of Medicine, Loma Linda, CA 92357, USA
    Office of Academic Affiliations (10A2D), Department of Veterans Affairs, 810 Vermont Ave. NW (10A2D), Washington, DC 20420, USA
    Center for Advanced Statistics in Education, VA Loma Linda Healthcare System, Loma Linda, CA 92357, USA
    Department of Psychiatry, University of Texas Southwestern Medical Center at Dallas, Dallas, TX 75390, USA)

Abstract

Generalized Information Matrix Tests (GIMTs) have recently been used for detecting the presence of misspecification in regression models in both randomized controlled trials and observational studies. In this paper, a unified GIMT framework is developed for the purpose of identifying, classifying, and deriving novel model misspecification tests for finite-dimensional smooth probability models. These GIMTs include previously published as well as newly developed information matrix tests. To illustrate the application of the GIMT framework, we derived and assessed the performance of new GIMTs for binary logistic regression. Although all GIMTs exhibited good level and power performance for the larger sample sizes, GIMT statistics with fewer degrees of freedom and derived using log-likelihood third derivatives exhibited improved level and power performance.

Suggested Citation

  • Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, vol. 4(4), pages 1-24, November.
    • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:4:p:46-:d:82838
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    References listed on IDEAS

    as
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    Cited by:

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    2. Verhagen, Mark D., 2021. "Identifying and Improving Functional Form Complexity: A Machine Learning Framework," SocArXiv bka76, Center for Open Science.
    3. Lijuan Huo & Jin Seo Cho, 2021. "Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 293-317, June.
    4. Qian M. Zhou, 2024. "Information matrix equivalence in the presence of censoring: a goodness-of-fit test for semiparametric copula models with multivariate survival data," Statistical Papers, Springer, vol. 65(7), pages 4677-4713, September.
    5. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2019. "Consequences of Model Misspecification for Maximum Likelihood Estimation with Missing Data," Econometrics, MDPI, vol. 7(3), pages 1-27, September.
    6. Francesca Iorio & Riccardo Lucchetti & Rosaria Simone, 2024. "Testing distributional assumptions in CUB models for the analysis of rating data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 669-701, September.

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