Analysis of pairwise preference data using integrated B-splines

Abstract

Pairwise preference data are represented as a monotone integral transformation of difference on the underlying stimulus-object or utility scale. The class of monotone transformations considered is that in which the kernel of the integral is a linear combination of B-splines. Two types of data are analyzed: binary and continuous. The parameters of the transformation and the underlying scale values or utilities are estimated by maximum likelihood with inequality constraints on the transformation parameters. Various hypothesis tests and interval estimates are developed. Examples of artificial and real data are presented.