On local optimality of vertex type designs in generalized linear models

Locally optimal designs are derived for generalized linear models with first order linear predictors. We consider models including a single factor, two factors and multiple factors. Mainly, the experimental region is assumed to be a unit cube. In particular, models without intercept are considered on arbitrary experimental regions. Analytic solutions for optimal designs are developed under the D- and A-criteria, and more generally, for Kiefer’s $$\Phi _k$$ Φ k -criteria. The focus is on the vertex type designs. That is, the designs are only supported by the vertices of the respective experimental regions. By the equivalence theorem, necessary and sufficient conditions are developed for the local optimality of these designs. The derived results are applied to gamma and Poisson models.