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Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects

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  • Karl, Andrew T.
  • Yang, Yan
  • Lohr, Sharon L.

Abstract

Estimation of generalized linear mixed models (GLMMs) with non-nested random effects structures requires the approximation of high-dimensional integrals. Many existing methods are tailored to the low-dimensional integrals produced by nested designs. We explore the modifications that are required in order to adapt an EM algorithm with first-order and fully exponential Laplace approximations to a non-nested, multiple response model. The equations in the estimation routine are expressed as functions of the first four derivatives of the conditional likelihood of an arbitrary GLMM, providing a template for future applications. We apply the method to a joint Poisson–binary model for ranking sporting teams, and discuss the estimation of a correlated random effects model designed to evaluate the sensitivity of value-added models for teacher evaluation to assumptions about the missing data process. Source code in R is provided in the online supplementary material (see Appendix C).

Suggested Citation

  • Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2014. "Computation of maximum likelihood estimates for multiresponse generalized linear mixed models with non-nested, correlated random effects," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 146-162.
    • Handle: RePEc:eee:csdana:v:73:y:2014:i:c:p:146-162
    DOI: 10.1016/j.csda.2013.11.019
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    1. M. Jamshidian & R. I. Jennrich, 2000. "Standard errors for EM estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 257-270.
    2. Louis T. Mariano & Daniel F. McCaffrey & J. R. Lockwood, 2010. "A Model for Teacher Effects From Longitudinal Data Without Assuming Vertical Scaling," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 253-279, June.
    3. Andrew T. Karl & Yan Yang & Sharon L. Lohr, 2013. "A Correlated Random Effects Model for Nonignorable Missing Data in Value-Added Assessment of Teacher Effects," Journal of Educational and Behavioral Statistics, , vol. 38(6), pages 577-603, December.
    4. Dimitris Rizopoulos & Geert Verbeke & Emmanuel Lesaffre, 2009. "Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 637-654, June.
    5. Steffen Fieuws & Geert Verbeke, 2006. "Pairwise Fitting of Mixed Models for the Joint Modeling of Multivariate Longitudinal Profiles," Biometrics, The International Biometric Society, vol. 62(2), pages 424-431, June.
    6. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    7. Page, Katie & Page, Lionel, 2010. "Alone against the crowd: Individual differences in referees' ability to cope under pressure," Journal of Economic Psychology, Elsevier, vol. 31(2), pages 192-199, April.
    8. Karl, Andrew T. & Yang, Yan & Lohr, Sharon L., 2013. "Efficient maximum likelihood estimation of multiple membership linear mixed models, with an application to educational value-added assessments," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 13-27.
    9. Annis David H. & Craig Bruce A., 2005. "Hybrid Paired Comparison Analysis, with Applications to the Ranking of College Football Teams," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 1(1), pages 1-33, October.
    10. Rizopoulos, Dimitris, 2010. "JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i09).
    11. Manuel Eugster & Jochen Knaus & Christine Porzelius & Markus Schmidberger & Esmeralda Vicedo, 2011. "Hands-on tutorial for parallel computing with R," Computational Statistics, Springer, vol. 26(2), pages 219-239, June.
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