LOCALLY D-OPTIMAL DESIGNS FOR HIERARCHICAL RESPONSE EXPERIMENTS

Categorical responses with a hierarchical structure are common in social sciences, public health, and marketing. The continuation ratio model is one of the most common models used to characterize such hierarchical data. Despite the wealth of research on this model, few studies have considered its design in the data collection step. Here, we study locally D-optimal designs for models with general link functions under the partial proportional odds assumption. The necessary and sufficient conditions for the positive definiteness of the Fisher information matrix are derived, which show that a feasible design may contain fewer supports than the number of parameters in the model. Based on some deduced characteristics of the D-optimal criterion, an efficient algorithm is proposed to search for optimal designs that can deal with both discrete and continuous design fields. Lastly, numerical examples illustrate the advantages of the proposed designs over some existing designs.