On the applicability of algebraic statistics to regression models with errors in variables
Suela Ruffa · PORTO Publications Open Repository TOrino (Politecnico di Torino) · 2005
In this paper we study the applicability of algebraic statistics methods to regression linear models with errors in variables (EIV models). In fact the advantage in the algebraic statistics methods is that we can find saturated linear models identifiable with designs which are not regular fractions of full factorial designs. First we introduce the main concepts of algebraic statistics applied to the design of experiments and next we formulate the model of interest: the Berkson’s model in the case of a polynomial linear regression problem. By mean of simple designs we illustrate the main issues met in the generalization of algebraic statistic theory to EIV models. Mainly these are due to the fact that the design points are unknown realizations of random variables. For the application we have in mind, the assumption of normality is natural. The generalization from these simple designs to higher dimensional and non regular fractional designs is straightforward. The paper concludes with a discussion on the applicability of currently available software for algebraic statistics analysis to designs with errors in variables.