D-optimal Designs with Ordered Categorical Data

TL;DR

This paper develops methods for constructing D-optimal experimental designs for ordered categorical data modeled by cumulative link models, improving efficiency over uniform allocations and providing robust alternatives.

Contribution

It derives conditions for locally D-optimal designs, introduces algorithms for their construction, and explores minimally supported and EW D-optimal designs for ordered categorical responses.

Findings

Support points depend only on predictors, not parameters.

D-optimal minimally supported designs are often non-uniform.

EW D-optimal designs are efficient and robust.

Abstract

Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider D-optimal designs with ordered categorical responses and cumulative link models. For a predetermined set of design points, we derive the necessary and sufficient conditions for an allocation to be locally D-optimal and develop efficient algorithms for obtaining approximate and exact designs. We prove that the number of support points in a minimally supported design only depends on the number of predictors, which can be much less than the number of parameters in the model. We show that a D-optimal minimally supported allocation in this case is usually not uniform on its support points. In addition, we provide EW D-optimal designs as a highly efficient surrogate to Bayesian D-optimal designs. Both of them can be much more robust than uniform designs.