An Optimal Experimental Design Criterion for Discriminating Between Non-Normal Models

Abstract

Typically "T"-optimality is used to obtain optimal designs to discriminate between homoscedastic models with normally distributed observations. Some extensions of this criterion have been made for the heteroscedastic case and binary response models in the literature. In this paper, a new criterion based on the Kullback-Leibler distance is proposed to discriminate between rival models with non-normally distributed observations. The criterion is coherent with the approaches mentioned above. An equivalence theorem is provided for this criterion and an algorithm to compute optimal designs is developed. The criterion is applied to discriminate between the popular Michaelis-Menten model and a typical extension of it under the log-normal and the gamma distributions. Copyright 2007 Royal Statistical Society.

Discriminating Among Several Semiparametric Models

“…When the discrimination between two binary response models then the KL-criterion and generalized T-criterion are identical, see López-Fidalgo et al (2007). Otsu (2008) proposed the KL-optimal criterion by using López-Fidalgo et al (2007) to a semiparametric setup to discriminate two regression models. Tomasi (2007) used a generalized KL-criterion to discriminate more than two non-normal models.…”

“…The KL-criterion function includes the T-optimality criterion as a special case and is applicable to any parametric regression models. López-Fidalgo et al (2007) applied KL-optimality criterion under non-normal distributions, as the lognormal and gamma distributions. When the discrimination between two binary response models then the KL-criterion and generalized T-criterion are identical, see López-Fidalgo et al (2007).…”

“…López-Fidalgo et al (2007) applied KL-optimality criterion under non-normal distributions, as the lognormal and gamma distributions. When the discrimination between two binary response models then the KL-criterion and generalized T-criterion are identical, see López-Fidalgo et al (2007). Otsu (2008) proposed the KL-optimal criterion by using López-Fidalgo et al (2007) to a semiparametric setup to discriminate two regression models.…”

Bayesian Optimum Design Criterion for Multi Models Discrimination

“…A more general criterion so-called KL-optimality is introduced by López-Fidalgo et al (2007). This criterion, which covers T-optimality and all its generalizations, is based on the Kullback-Leibler (KL) distance and it is useful for discriminating between non-normal and more generally nonlinear models.…”

Designs for Generalized Linear Models

“…Ponce de Leon and Atkinson (1992) and Waterhouse et al (2008) extend T-optimality to GLMs. A general design criterion for discrimination between models using Kullback-Leibler distances is that of López-Fidalgo et al (2007). A potential disadvantage of these designs is that they focus exclusively on model discrimination.…”