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 language | English |
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Pages (from-to) | 3564-3577 |
Number of pages | 14 |
Journal | Journal of Statistical Planning and Inference |
Volume | 141 |
Issue number | 11 |
Early online date | 17 May 2011 |
DOIs | |
Publication status | Published - Nov 2011 |
Keywords
- spatial statistics
- maximum likelihood estimation
- predictive inference
- Laplace approximation
- generalized linear mixed models
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