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An Alternate Approach to Pseudo-Likelihood Model Selection in the Generalized Linear Mixed Modeling Framework

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  • Patrick Ten Eyck

    (The University of Iowa)

  • Joseph E. Cavanaugh

    (The University of Iowa)

Abstract

In this paper, we propose and investigate an alternate approach to pseudo-likelihood model selection in the generalized linear mixed modeling framework. The problem with the natural approach to the computation of pseudo-likelihood model selection criteria is that the pseudo-data vary for each candidate model, leading to criteria based on fundamentally different goodness-of-fit statistics, rendering them incomparable. We propose a technique that circumvents this problem. This new approach can be implemented using a SAS macro that obtains and applies the pseudo-data from the full model to fitting candidate models based on all possible subsets of predictor variables. We justify the propriety of the resulting pseudo-likelihood selection criteria through an extensive study designed as a factorial experiment. We then illustrate this new method in a modeling application pertaining to bullying in public schools. The data set for the application is taken from three waves of the Iowa Youth Survey.

Suggested Citation

  • Patrick Ten Eyck & Joseph E. Cavanaugh, 2018. "An Alternate Approach to Pseudo-Likelihood Model Selection in the Generalized Linear Mixed Modeling Framework," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(1), pages 98-122, May.
    • Handle: RePEc:spr:sankhb:v:80:y:2018:i:1:d:10.1007_s13571-017-0130-5
    DOI: 10.1007/s13571-017-0130-5
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    References listed on IDEAS

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    1. Wei Pan, 2001. "Akaike's Information Criterion in Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 57(1), pages 120-125, March.
    2. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    3. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    4. Bengtsson, Thomas & Cavanaugh, Joseph E., 2006. "An improved Akaike information criterion for state-space model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2635-2654, June.
    5. Makio Ishiguro & Yosiyuki Sakamoto & Genshiro Kitagawa, 1997. "Bootstrapping Log Likelihood and EIC, an Extension of AIC," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 411-434, September.
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    Cited by:

    1. Shuangshuang Xu & Marco A. R. Ferreira & Erica M. Porter & Christopher T. Franck, 2023. "Bayesian model selection for generalized linear mixed models," Biometrics, The International Biometric Society, vol. 79(4), pages 3266-3278, December.

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