New Challenges and Strategies in Robust Optimal Design for Multicategory Logit Modelling

Applied researchers often use multi-category logit (MCL) regression models such as the proportional odds model or baseline category logit model in representing their system or process, and these researchers require practical guidelines regarding the associated experimental designs. Previously-provided results for optimal designs for the proportional odds and two variants of the continuation ratio MCL models are of limited usefulness since in general they typically yield designs which are efficient only for the specified MCL model. This expository paper provides key model-robust design strategies using a derived larger unifying MCL model and the strategy of model nesting introduced in Atkinson (Biometrika 59:275–93, 1972). These strategies are also extended to incorporate geometric and uniform designs. As such, these designs are useful for both parameter estimation and model discrimination via checking for goodness-of-fit. Key representative examples are provided from the fields of bioassay and toxicology to illustrate these results.