Designs for mixed models with binary response
Seminar Room 1, Newton Institute
For an experiment measuring a binary response, a generalized linear model such as the logistic or probit is typically used to model 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). Obtaining designs for such models is complicated by the fact that the information matrix, on which most optimality criteria are based, is computationally expensive to evaluate (indeed if one computes naively, the search for an optimal design is likely to take several months).
When analyzing GLMMs, it is common to use analytical approximations such as marginal quasi-likelihood (MQL) and penalized quasi-likelihood (PQL) in place of full maximum likelihood. In this talk, we consider the use of such computationally cheap approximations as surrogates for the true information matrix when producing designs. This reduces the computational burden substantially, and enables us to obtain designs within a much shorter time frame. However, other issues also need to be considered such as the accuracy of the approximations and the dependence of the optimal design on the unknown values of the parameters. In particular, we evaluate the effectiveness of designs found using these analytic approximations through comparison to designs that are found using a more computationally expensive numerical approximation to the likelihood.