Parisa Parsamaram, Otto-von-Guericke University

• Title: Approximation of the quasi Fisher information matrix for designing experiments in ordinal mixed models

• Abstract: In the present work we want to determine optimum designs in the situation of ordinal outcomes with individual subject effects. To describe this situation we use a mixed ordinal regression model where, on the individual level, cumulative ordinal response is assumed based on a logit or probit link. To measure the quality of the design, usually the Fisher information matrix is used. However, in the case of mixed ordinal regression models, there is no closed form of the marginal likelihood and, hence, no closed form of the Fisher information. To avoid this problem, we consider the quasi Fisher information related to the concept of quasi-likelihood estimation. For the quasi Fisher information matrix only the first and second order moments of the model equations are needed which is much simpler than the full likelihood. But even these moments are not readily accessible because of the missing closed form of the corresponding integrals. To solve this, we propose two new concurring approximations for the quasi Fisher information which both show a quite similar performance. Based on these approximations, D-optimum designs are calculated for the specific case of a mixed binary regression model. These results can readily be extended to more complicated model situations.