D-optimal Factorial Designs under Generalized Linear Models

TL;DR

This paper extends the theory of D-optimal factorial designs in generalized linear models to include responses from the exponential family and multi-level factors, broadening their applicability.

Contribution

It generalizes previous work on D-optimal designs for binary responses to more complex response types and multi-level predictors within GLMs.

Findings

Extended D-optimal design theory to exponential family responses

Developed methods for multi-level predictor designs

Provided theoretical foundations for broader experimental design applications

Abstract

Generalized linear models (GLMs) have been used widely for modelling the mean response both for discrete and continuous random variables with an emphasis on categorical response. Recently Yang, Mandal and Majumdar (2013) considered full factorial and fractional factorial locally D-optimal designs for binary response and two-level experimental factors. In this paper, we extend their results to a general setup with response belonging to a single-parameter exponential family and for multi-level predictors.