  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.
