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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Copyright Owner
Elsevier B.V.
Copyright Date
2011
Language
en
File Format
application/pdf
Recommended Citation
Evangelou, Evangelos; Zhu, Zhengyuan; and Smith, Richard L., "Estimation and prediction for spatial generalized linear mixed models using high order Laplace approximation" (2011). Statistics Publications. 128.
https://lib.dr.iastate.edu/stat_las_pubs/128
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.