Campus Units

Statistics

Document Type

Article

Publication Version

Accepted Manuscript

Publication Date

11-2011

Journal or Book Title

Journal of Statistical Planning and Inference

Volume

141

Issue

11

First Page

3564

Last Page

3577

DOI

10.1016/j.jspi.2011.05.008

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.

Comments

This is a manuscript of an article published as Evangelou, Evangelos, Zhengyuan Zhu, and Richard L. Smith. "Estimation and prediction for spatial generalized linear mixed models using high order Laplace approximation." Journal of Statistical Planning and Inference 141, no. 11 (2011): 3564-3577. DOI: 10.1016/j.jspi.2011.05.008. Posted with permission.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Copyright Owner

Elsevier B.V.

Language

en

File Format

application/pdf

Published Version

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