Dave Woods (University of Southampton)

Design of experiments for Generalised Linear (Mixed) Models

Generalised Linear and Generalised Linear Mixed Models (GLMs and GLMMs) may be used to describe data from a range of experiments in science, technology and industry. Example experiments with binary data come from areas such as crystallography, food science and aeronautical engineering. If the experiment is performed in blocks, eg subjects in a clinical trial or batches in manufacturing, a mixed model with random block effects allows the estimation of either subject-specific or population averaged treatment effects and induces an intra-block correlation structure for the response.

Finding optimal or efficient designs for GLMs and variants is complicated by the dependence of design performance on the values of the unknown model parameters. We describe methods for finding (pseudo) Bayesian designs that average a function of the information matrix across a prior distribution, and assess the resulting designs using simulation. The methods can also be extended to account for uncertainty in the linear predictor and link function, or to find designs for models with nonlinear predictors.

For GLMMs, the search for designs is complicated by the fact that the information matrix is not available in closed form. We make use of analytic and computational approximations, and also an alternative marginal model and generalised estimation equations.