In- and Equivariance for Optimal Designs in Generalized Linear Models: The Gamma Model

TL;DR

This paper explores how equivariance and invariance principles can optimize experimental designs in generalized linear models, specifically focusing on gamma distribution models, by considering transformations on settings and parameters.

Contribution

It extends the concept of equivariance to generalized linear models with gamma responses, providing methods for constructing locally optimal and maximin efficient designs.

Findings

Derived locally optimal designs for gamma models.

Developed maximin efficient design strategies.

Illustrated concepts with gamma distributed response models.

Abstract

We give an overview over the usefulness of the concept of equivariance and invariance in the design of experiments for generalized linear models. In contrast to linear models here pairs of transformations have to be considered which act simultaneously on the experimental settings and on the location parameters in the linear component. Given the transformation of the experimental settings the parameter transformations are not unique and may be nonlinear to make further use of the model structure. The general concepts and results are illustrated by models with gamma distributed response. Locally optimal and maximin efficient design are obtained for the common D- and IMSE-criterion.