Estimation and prediction for spatial generalized linear mixed models using high order Laplace approximation

Evangelos Evangelou, Zhengyuan Zhu, Richard L Smith

Research output: Contribution to journalArticle

13 Citations (Scopus)
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Abstract

Estimation and prediction in generalized linear mixed models are often hampered by intractable high dimensional integrals. This paper provides a framework to solve this intractability, using asymptotic expansions when the number of random effects is large. To that end, we first derive a modified Laplace approximation when the number of random effects is increasing at a lower rate than the sample size. Second, we propose an approximate likelihood method based on the asymptotic expansion of the log-likelihood using the modified Laplace approximation which is maximized using a quasi- Newton algorithm. Finally, we define the second order plug-in predictive density based on a similar expansion to the plug-in predictive density and show that it is a normal density. Our simulations show that in comparison to other approximations, our method has better performance. Our methods are readily applied to non-Gaussian spatial data and as an example, the analysis of the rhizoctonia root rot data is presented.
Original languageEnglish
Pages (from-to)3564-3577
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume141
Issue number11
Early online date17 May 2011
DOIs
Publication statusPublished - Nov 2011

Fingerprint

Predictive Density
Laplace Approximation
Generalized Linear Mixed Model
Higher Order Approximation
Plug-in
Asymptotic Expansion
Quasi-Newton Algorithm
Likelihood Methods
Prediction
Random Effects
Sample Size
High-dimensional
Roots
Approximation
Simulation
Asymptotic expansion
Generalized linear mixed model
Predictive density
Laplace approximation
Framework

Keywords

  • spatial statistics
  • maximum likelihood estimation
  • predictive inference
  • Laplace approximation
  • generalized linear mixed models

Cite this

Estimation and prediction for spatial generalized linear mixed models using high order Laplace approximation. / Evangelou, Evangelos; Zhu, Zhengyuan; Smith, Richard L.

In: Journal of Statistical Planning and Inference, Vol. 141, No. 11, 11.2011, p. 3564-3577.

Research output: Contribution to journalArticle

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