On Efficient Design of Pilot Experiment for Generalized Linear Models

Abstract: The experimental design for a generalized linear model (GLM) is important but challenging since the design criterion often depends on model specification including the link function, the linear predictor, and the unknown regression coefficients. Prior to constructing locally or globally optimal designs, a pilot experiment is usually conducted to provide some insights on the model specifications. In pilot experiments, little information on the model specification of GLM is available. Surprisingly, there is very limited research on the design of pilot experiments for GLMs. In this work, we obtain some theoretical understanding of the design efficiency in pilot experiments for GLMs. Guided by the theory, we propose to adopt a low-discrepancy design with respect to some target distribution for pilot experiments. The performance of the proposed design is assessed through several numerical examples.