Scaling distortion in numerical conjoint measurement

Abstract

Proponents of numerical conjoint measurement gen-erally assume that the technique’s goodness-of-fit mea-sure will detect an inappropriate composition rule or the presence of random response error. In this paper a number of hypothetical and real preference rank order-ings are analyzed using both axiomatic conjoint mea-surement and numerical conjoint measurement to dem-onstrate that this assumption is not warranted and may result in a distorted scaling. Axiomatic conjoint measurement and numerical conjoint measurement (often called conjoint anal-ysis) have been described as two complementary approaches to the study of composition rules in psychology (Green & Wind, 1973; Krantz & Tver-sky, 1971). Axiomatic conjoint measurement be-gins with an ordering of the dependent variable and tests the properties or axioms that this ordering must satisfy if it is to be represented numerically according to a proposed composition rule. In con-trast, numerical conjoint measurement does not test the ordinal properties of the data but instead searches (usually through an iterative computer algorithm) for an appropriate monotonic transformation of the dependent variable that best satisfies an assumed composition rule; then it evaluates the correspon-dence between the assumed rule and the scaled data with a goodness-of-fit (or badness-of-fit) measure. The functions of axiomatic conjoint measuremen