Design and Inference for Discriminating Between Two Competing Linear Regression Models

Abstract

The problem of discriminating between two competing simple linear regression models MI and MII is discussed in this paper. The model MI is nested within the model MII with a common linear term being present in both models with respect to an explanatory variable and an additional quadratic term with respect to the same explanatory variable being present in MII. The first criterion function for discrimination between MI and MII is in terms of minimizing the variance of the least squares estimated coefficient of the quadratic term. A lower bound is obtained for this variance. Two designs are presented satisfying this lower bound in two experimental regions. New criterion functions of discriminating between MI and MII are given based on maximizing the difference between the fitted values of n observations under MI and MII and maximizing the difference between the predicted values under MI and MII. Several results are obtained for demonstrating the performances of these designs under two new criterion functions. We also present five general classes of designs and demonstrate their sharp relative performances with respect to our criterion functions. Some results for discriminating between two competing general linear models MIII and MIV are also given.