Optimal designs for models with covariates

Abstract

The model refers to a treatment design with one treatment at v levels and first Order regression on K continuous covariates attached to each experimental unit. The Problem is that of constructing optimal completely randomized design plans for estimating both the treatment effect parameters and the covariate value parameters. The attention is for the classes of designs with N = i (mod4); i = 0, 1, 2, 3. The D-criterion has been used to judge the goodness of the design for estimating the parameters in this model. Design plans with equal replications have been developed for which N = v x R where N is the total number of observations. Hadamard Matrices and Symmetric Conference Matrices playa central role in this study. Keywords: Completely Randomized designs, information matrix, Hadamard Matrix, Symmetric Conference Matrix, Covariates, Designs with equal replications.