Spherical radial approximation for nested mixed effects models

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• 作者：Jacob Gagnon ; Hua Liang ; Anna Liu
• 关键词：AIDS ; Nonparametric random effects ; Likelihood approximation ; Generalized linear mixed models ; Generalized additive mixed models ; Laplace ; Quadrature ; Spherical radial ; Nested random effects
• 刊名：Statistics and Computing
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：26
• 期：1-2
• 页码：119-130
• 全文大小：645 KB
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• 作者单位：Jacob Gagnon (1)
  Hua Liang (2)
  Anna Liu (3)
  
  1. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, 01609, USA
  2. Department of Statistics, George Washington University, Rome Hall, 801 22nd street NW, Washington, DC, 20052, USA
  3. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA, 01003, USA
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics Computing and Software
  Statistics
  Numeric Computing
  Mathematics
  Artificial Intelligence and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-1375

文摘

We consider a likelihood approximation in generalized linear mixed-effects models (GLMM) with multilevel nested random effects. Likelihood evaluation in such models is difficult, hindered by the need for high dimensional integration, where the dimension is proportional to the number of units per level and the number of random effects per unit. Various integration approaches have been proposed, including the penalized quasi-likelihood method, Laplace approximation, quadrature approximation, simulation, and MCMC algorithms. We propose a new quadrature approximation method, which is based on the spherical radial integration approach of Monahan and Genz (J Am Stat Assoc 92:664–674 1997), and at the same time takes advantage of the hierarchical structure of the integration. Our new hierarchical spherical radial method has a time complexity that is linear in the number of units per level and the number of random effects per unit, in contrast to the exponential complexity of the adaptive Gaussian quadrature method of Pinheiro and Chao (J Comput Graph Stat 15:58–81 2006) for the same problem. Using a spline approximation, the generalized additive mixed models (GAMM) are GLMMs with two levels of nested random effects. We apply our method to estimation of GAMMs. We compare it with competing methods through simulations and apply our method to analyze virologic and immunologic responses in an AIDS clinical trial. An R package is written and available at http://​users.​wpi.​edu/​~jgagnon/​software.​html. Keywords AIDS Nonparametric random effects Likelihood approximation Generalized linear mixed models Generalized additive mixed models Laplace Quadrature Spherical radial Nested random effects