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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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    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.
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