Techniques for Deriving Extendible Linear Parameter Spaces

The aim of this paper is to describe a constructive method for generating linear parameter spaces that have a certain desirable invariance property, called “extendibility”. Extendibility of the parameter space is defined as the unambiguity of extensions of the parameter space as a result of inherent symmetries underlying the structure of the covariates or statistical units. Common extensions are the relabelling of treatments, the addition or deletion of statistical units, the inclusion of alternative covariate levels and the use of alternative measurement scales. Group representation theory is introduced to describe some of these extendibility conditions and to devise a method to deduce extendible linear parameter spaces.