  We consider optimal designs for general multinomial logistic models, which
cover baseline-category, cumulative, adjacent-categories, and
continuation-ratio logit models, with proportional odds, non-proportional odds,
or partial proportional odds assumption. We derive the corresponding Fisher
information matrices in three different forms to facilitate their calculations,
determine the conditions for their positive definiteness, and search for
optimal designs. We conclude that, unlike the designs for binary responses, a
feasible design for a multinomial logistic model may contain less experimental
settings than parameters, which is of practical significance. We also conclude
that even for a minimally supported design, a uniform allocation, which is
typically used in practice, is not optimal in general for a multinomial
logistic model. We develop efficient algorithms for searching D-optimal
designs. Using examples based on real experiments, we show that the efficiency
of an experiment can be significantly improved if our designs are adopted.
