A New Algorithm for D-optimal Designs under General Parametric Statistical Models with Mixed Factors

In this paper, we consider experiments involving both discrete factors and continuous factors under general parametric statistical models. To search for optimal designs under the D-criterion, we propose a new algorithm, called the ForLion algorithm, which performs an exhaustive search in a design space with discrete and continuous factors while keeping high efficiency and a reduced number of design points. Its optimality is guaranteed by the general equivalence theorem. We show its advantage using a real-life experiment under multinomial logistic models, and further specialize the algorithm for generalized linear models to show the improved efficiency with model-specific formulae and iterative steps.