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Designs for generalized linear models with random block effects via information matrix approximations

Designs for generalized linear models with random block effects via information matrix approximations
Designs for generalized linear models with random block effects via information matrix approximations
The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur.
blocks, binary data, bayesian design, generalized linear mixed model, grouped data, logistic regression, mixed effects models
0006-3444
677-693
Waite, T.W.
67ff61af-f85f-4cc7-a7b8-4f188b624266
Woods, D.C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Waite, T.W.
67ff61af-f85f-4cc7-a7b8-4f188b624266
Woods, D.C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c

Waite, T.W. and Woods, D.C. (2015) Designs for generalized linear models with random block effects via information matrix approximations. Biometrika, 102 (3), 677-693. (doi:10.1093/biomet/asv005).

Record type: Article

Abstract

The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur.

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More information

Accepted/In Press date: 2015
e-pub ahead of print date: 7 July 2015
Published date: September 2015
Keywords: blocks, binary data, bayesian design, generalized linear mixed model, grouped data, logistic regression, mixed effects models
Organisations: Statistical Sciences Research Institute

Identifiers

Local EPrints ID: 342216
URI: http://eprints.soton.ac.uk/id/eprint/342216
ISSN: 0006-3444
PURE UUID: ea49d5d0-ac79-4029-a854-4155c8216162
ORCID for D.C. Woods: ORCID iD orcid.org/0000-0001-7648-429X

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Date deposited: 16 Aug 2012 08:53
Last modified: 15 Mar 2024 03:05

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Contributors

Author: T.W. Waite
Author: D.C. Woods ORCID iD

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