Designs for generalized linear models with random block effects

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Description/Abstract

For an experiment measuring a discrete response, a generalized linear model such as the logistic or Poisson model is typically used to analyse the data. However these models assume that the responses are independent. In blocked experiments, where responses in the same block are potentially correlated, it may be appropriate to include random effects in the predictor, thus producing a generalized linear mixed model (GLMM). Optimising 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.

We consider the use of analytical approximations such as marginal quasi-likelihood, and penalized quasi-likelihood, as the basis of computationally cheap surrogates for the information matrix when obtaining D-optimal designs. This reduces the computational burden substan- tially, enabling us to find multifactor designs in a much shorter time frame. The accuracy of the analytical approximations is explored in simple cases using a novel computational approximation. A pseudo-Bayesian approach is employed to address the dependence of the D-optimal design on the unknown values of the parameters