$ D $-optimal designs for Poisson regression with synergetic interaction effect

TL;DR

This paper characterizes D-optimal experimental designs for two-dimensional Poisson regression models with synergetic interactions, simplifying the design process through reparameterization and extending results to higher dimensions.

Contribution

It provides an explicit characterization of D-optimal designs in Poisson regression with interaction effects, using a novel reparameterization approach that reduces complexity.

Findings

Explicit D-optimal designs for 2D Poisson regression with interactions

Reparameterization simplifies the analysis of sensitivity functions

Extensions to higher-dimensional models are proposed

Abstract

We characterize $D$-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of constant intensity. This approach leads to a substantial reduction of complexity as properties of the sensitivity can be treated along and across the contours separately. Furthermore, some extensions of this result to higher dimensions are presented.