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Information Ratio Test for Model Misspecification in Quasi-Likelihood Inference


  • Qian M. Zhou
  • Peter X.-K. Song
  • Mary E. Thompson


In this article, we focus on the circumstances in quasi-likelihood inference that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment, but the estimation efficiency could be diminished due to misspecification of the second moment. We propose an information ratio (IR) statistic to test for model misspecification of the variance/covariance structure through a comparison between two forms of information matrix: the negative sensitivity matrix and the variability matrix. We establish asymptotic distributions of the proposed IR test statistics. We also suggest an approximation to the asymptotic distribution of the IR statistic via a perturbation resampling method. Moreover, we propose a selection criterion based on the IR test to select the best fitting variance/covariance structure from a class of candidates. Through simulation studies, it is shown that the IR statistic provides a powerful statistical tool to detect different scenarios of misspecification of the variance/covariance structures. In addition, the IR test as well as the proposed model selection procedure shows substantial improvement over some of the existing statistical methods. The IR-based model selection procedure is illustrated by analyzing the Madras Longitudinal Schizophrenia data. Appendices are included in the supplemental materials, which are available online.

Suggested Citation

  • Qian M. Zhou & Peter X.-K. Song & Mary E. Thompson, 2012. "Information Ratio Test for Model Misspecification in Quasi-Likelihood Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 205-213, March.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:205-213
    DOI: 10.1080/01621459.2011.645785

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    Cited by:

    1. Xu, Jianwen & Wang, You-Gan, 2014. "Intra-cluster correlation structure in longitudinal data analysis: Selection criteria and misspecification tests," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 70-77.
    2. repec:eee:csdana:v:56:y:2012:i:12:p:3975-3987 is not listed on IDEAS
    3. Schepsmeier, Ulf, 2015. "Efficient information based goodness-of-fit tests for vine copula models with fixed margins: A comprehensive review," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 34-52.
    4. Kwon, Yongchan & Choi, Young-Geun & Park, Taesung & Ziegler, Andreas & Paik, Myunghee Cho, 2017. "Generalized estimating equations with stabilized working correlation structure," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 1-11.
    5. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    6. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, Open Access Journal, vol. 4(4), pages 1-15, October.
    7. Shulin Zhang, & Ostap Okhrin, & Qian M. Zhou & Peter X.-K. Song, 2013. "Goodness-of-fit Test for Specification of Semiparametric Copula Dependence Models," SFB 649 Discussion Papers SFB649DP2013-041, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, Open Access Journal, vol. 4(4), pages 1-24, November.

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