University of Illinois at Chicago
We consider D-optimal designs with ordered categorical responses and cumulative link models. In addition to theoretically characterizing locally D-optimal designs, we develop efficient algorithms for obtaining both approximate designs and exact designs. For ordinal data and general link functions, we obtain a simplified structure of the Fisher information matrix, and express its determinant as a homogeneous polynomial. For a predetermined set of design points, we derive the necessary and sufficient conditions for an allocation to be locally D-optimal. 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. We also provide EW D-optimal designs as a highly efficient surrogate to Bayesian D-optimal designs with ordinal data.
More information about Jie Yang may be found at http://www.math.uic.edu/~jyang06.