Abstract:
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Multinomial logistic models have been widely used for categorical responses or multinomial responses, including baseline-category logit model for nominal responses, cumulative logit model and adjacent-categories logit model for ordinal responses, and continuation-ratio logit model for hierarchical responses. In order to construct a general framework towards D-optimal designs for these models, we unify all the four models into a common form and extend them to fit different model assumptions, including proportional odds (po), non-proportional odds (npo), and partial proportional odds (ppo). We explore the design space of these models, derive a simplified form of the Fisher information matrix, and obtain explicit formulas of its determinant. We derive necessary and sufficient conditions for a minimally supported design to be D-optimal. We also develop efficient numerical algorithms for searching D-optimal designs.
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