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

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.

Optimal designs for two-parameter nonlinear models with application to survival models

“…Our assumptions are somewhat less restrictive and easier to check than those provided by Yang and Stufken (2009) for more general models. Our results were then applied to the proportional hazards parameterisation of the exponential regression model (1.1), for the cases of Type I and random censoring.…”

“…In particular, these results are not applicable to model (1.1). Yang and Stufken (2009) consider Loewner optimality and an even more general class of models. They obtain a series of excellent results, showing that under some conditions, for each given design there is always a design from a simple class which is better in the Statistica Sinica: Preprint doi: 10.5705/ss.2011.271 Loewner sense.…”

“…The aim of this paper is to provide characterisations of D-and c-optimal designs under assumptions which are less restrictive and easier to verify than those in Yang and Stufken (2009) and which are satisfied by a large class of models, including model (1.1). In section 2 we develop this approach for D-optimality.…”

On Optimal Designs for Nonlinear Models: A General and Efficient Algorithm

“…Recently, Yang and Stufken (2009), Yang (2010), and Dette and Melas (2011) convincingly demonstrated that unifying results for multiple models, multiple optimality criteria and multiple objectives can be obtained in the context of nonlinear models. They show that we can focus on a subclass of designs with a simple form, no matter what type of optimal designs we are looking for, including optimal multi-stage designs.…”

Design Admissibility, Invariance and Optimality in Multiresponse Linear Models

“…One may then restrict oneself to this subclass Ξ com . Along this line, a series of remarkable papers by Yang and Stufken (2009), Yang (2010), Dette and Melas (2011), Yang and Stufken (2012) and Dette and Schorning (2013) derived several complete classes of designs for single response models with respect to the Loewner ordering of the information matrices, based on considerations of admissibility and invariance.…”