Support points of locally optimal designs for nonlinear models with two parameters

TL;DR

This paper introduces an algebraic approach to identify support points of locally optimal designs for nonlinear models with two parameters, applicable to various models and experimental settings.

Contribution

It presents a novel algebraic method for determining support points in locally optimal designs, offering advantages over traditional geometric approaches.

Findings

Applicable to logistic, probit, and other models for binary data

Works with constrained and unconstrained design regions

Relatively easy to implement in practice

Abstract

We propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model. In contrast to the commonly used geometric approach, we use an approach based on algebraic tools. Considerations are restricted to models with two parameters, and the general results are applied to often used special cases, including logistic, probit, double exponential and double reciprocal models for binary data, a loglinear Poisson regression model for count data, and the Michaelis--Menten model. The approach, which is also of value for multi-stage experiments, works both with constrained and unconstrained design regions and is relatively easy to implement.