Designs for generalized linear models with random block effects

Tim Waite, University of Southampton

For an experiment measuring independent discrete responses, a generalized linear model, such as the logistic or log-linear, is typically used to analyse the data. In blocked experiments, where observations from the same block are potentially correlated, it may be appropriate to include random effects in the predictor, thus producing a generalized linear mixed model. Selecting optimal designs for such models is complicated by the fact that the Fisher information matrix, on which most optimality criteria are based, is computationally expensive to evaluate. In addition, the dependence of the information matrix on the unknown values of the parameters must be overcome by, for example, use of a pseudo-Bayesian approach. For the first time, we evaluate the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix, derived from marginal quasi-likelihood and generalized estimating equations. It is found that, for binary-response models, naive application of these approximations may result in inefficient designs. However, a simple correction for the marginal attenuation of parameters yields much improved designs when the intra-block dependence is moderate. For stronger intra-block dependence, our adjusted marginal modelling approximations are sometimes less effective. Here, more efficient designs may be obtained from a novel asymptotic approximation. The use of approximations from this suite reduces the computational burden of design search substantially, enabling straightforward selection of multi-factor designs.