Elemental information matrices and optimal experimental design for generalized regression models

The construction of optimal experimental designs for regression models requires knowledge of the information matrix of a single observation. The latter can be found if the elemental information matrix corresponding to the distribution of the response is known. We present tables of elemental information matrices for distributions that are often used in statistical work. The tables contain matrices for one- and two-parameter distributions. Additionally we describe multivariate normal and multinomial cases. The parameters of response distributions can themselves be parameterized to provide dependence on explanatory variables, thus leading to regression formulations for wide classes of models. We present essential results from optimal experimental design and illustrate our approach with a few examples including bivariate binary responses and gamma regression.