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

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

Computational Statistics & Data Analysis, 2014, vol. 73, issue C, 146-162

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).

Keywords: EM algorithm; Fully exponential Laplace approximation; Joint model; Multiple membership; Multivariate; Sparse matrix (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:73:y:2014:i:c:p:146-162

DOI: 10.1016/j.csda.2013.11.019

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