Evangelou, E., Zhu, Z. and Smith, R. L., 2011. Estimation and prediction for spatial generalized linear mixed models using high order Laplace approximation. Journal of Statistical Planning and Inference, 141 (11), pp. 3564-3577.
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.
|Item Type ||Articles|
|Creators||Evangelou, E., Zhu, Z. and Smith, R. L.|
|Uncontrolled Keywords||spatial statistics, maximum likelihood estimation, predictive inference, laplace approximation, generalized linear mixed models|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||Evangelou.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Statistical Planning and Inference. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Evangelou, E., Zhu, Z. and Smith, R. L., 2011. Forthcoming. Estimation and prediction for spatial generalized linear mixed models using high order laplace approximation. Journal of Statistical Planning and Inference. http://dx.doi.org/10.1016/j.jspi.2011.05.008|
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