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

TL;DR

This paper introduces two novel approximation methods to efficiently evaluate the Fisher information matrix for optimal design in generalized linear mixed models, especially logistic models, reducing computational costs and improving design efficiency.

Contribution

It presents new asymptotic and Kriging-based approximations for the information matrix, enabling more efficient optimal design selection for generalized linear mixed models.

Findings

Asymptotic approximation is accurate with strong within-block dependence.

Interpolation via Kriging effectively finds pseudo-Bayesian designs.

Correcting marginal model attenuation improves design efficiency.

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.