D-Optimal Design for Generalized Linear Models

D-optimality is one of the most commonly used design criteria for linear regression models. In industrial experiments binary or count data often arise, for example defective/nondefective or number of defects. For such data Generalized Linear Models (GLMs) are appropriate. An analogous D-optimality design criterion can be developed using the asymptotic covariance matrix. For GLMs, this matrix is a weighted version of the covariance matrix for the linear case, and the extension of existing D-optimality algorithms is thus fairly straightforward. A number of examples compare and contrast GLM D-optimal designs to linear regression D-optimal designs. In general, the GLM D-optimal design depends on the values of the parameters being estimated. We describe a minimax approach to make the design more robust to the unknown parameters. The main example considers the design of a multifactor industrial follow-up experiment with binary data.