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A Comparison of Estimation Methods for Multilevel Logistic Models

Author

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  • Mirjam Moerbeek

    (Utrecht University)

  • Gerard J. P. Breukelen

    (Maastricht University)

  • Martijn P. F. Berger

    (Maastricht University)

Abstract

Summary In this paper a comparison between Penalized Quasi Likelihood (PQL) and estimation by numerical integration is made for the analysis of two-level experimental binary data with two treatment conditions. The comparison between the estimation methods is made for three situations: randomization to treatment conditions at the cluster level, randomization at the person level with treatment by cluster interaction, and without such interaction. Criteria for comparison are convergence of the estimation process and improper estimates (i.e. unrealistic high point estimates), criteria concerning the point estimation (bias, variance, and mean squared error) and testing (bias of the point estimates and of the variances as reported by the software) of the treatment effect. The results show that non-convergence occurs more often when estimation is done by numerical integration. This method may also lead to improper estimates. First order PQL performs best in terms of point estimation of the treatment effect, but should not be used for testing. For the latter purpose second order PQL is more applicable.

Suggested Citation

  • Mirjam Moerbeek & Gerard J. P. Breukelen & Martijn P. F. Berger, 2003. "A Comparison of Estimation Methods for Multilevel Logistic Models," Computational Statistics, Springer, vol. 18(1), pages 19-37, March.
    • Handle: RePEc:spr:compst:v:18:y:2003:i:1:d:10.1007_s001800300130
    DOI: 10.1007/s001800300130
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    References listed on IDEAS

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    1. Harvey Goldstein & Jon Rasbash, 1996. "Improved Approximations for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 159(3), pages 505-513, May.
    2. Germán Rodríguez & Noreen Goldman, 2001. "Improved estimation procedures for multilevel models with binary response: a case‐study," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 164(2), pages 339-355.
    3. Germáan Rodríguez & Noreen Goldman, 1995. "An Assessment of Estimation Procedures for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(1), pages 73-89, January.
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    Cited by:

    1. H. Abebe & F. Tan & G. Breukelen & M. Berger, 2014. "Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation," Computational Statistics, Springer, vol. 29(6), pages 1667-1690, December.
    2. Gerard Breukelen, 2005. "Psychometric Modeling of response speed and accuracy with mixed and conditional regression," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 359-376, June.
    3. Abebe, Haftom T. & Tan, Frans E.S. & Van Breukelen, Gerard J.P. & Berger, Martijn P.F., 2014. "Bayesian D-optimal designs for the two parameter logistic mixed effects model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1066-1076.
    4. Ippel, L. & Kaptein, M.C. & Vermunt, J.K., 2019. "Online estimation of individual-level effects using streaming shrinkage factors," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 16-32.

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