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

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


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1093/biomet/asv005
Keywords: blocks, binary data, bayesian design, generalized linear mixed model, grouped data, logistic regression, mixed effects models
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics
Divisions : Faculty of Social and Human Sciences > Southampton Statistical Sciences Research Institute
ePrint ID: 342216
Accepted Date and Publication Date:
Date Deposited: 16 Aug 2012 08:53
Last Modified: 27 Oct 2016 16:18
Statistical Design of Experiments for Complex Nonparametric and Mechanistic Models
Funded by: EPSRC (EP/J018317/1)
Led by: David Woods
30 September 2012 to 29 September 2017

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