Theory of conjoint measurement
The theory of conjoint measurement (also known as conjoint measurement or additive conjoint measurement) is a general, formal theory of continuous quantity. It was independently discovered by the French economist Gérard Debreu (1960) and by the American mathematical psychologist R. Duncan Luce and statistician John Tukey (Luce & Tukey 1964).
The theory concerns the situation where at least two natural attributes, A and X, non-interactively relate to a third attribute, P. It is not required that A, X or P are known to be quantities. Via specific relations between the levels of P, it can be established that P, A and X are continuous quantities. Hence the theory of conjoint measurement can be used to quantify attributes in empirical circumstances where it is not possible to combine the levels of the attributes using a side-by-side operation or concatenation. The quantification of psychological attributes such as attitudes, cognitive abilities and utility is therefore logically plausible. This means that the scientific measurement of psychological attributes is possible. That is, like physical quantities, a magnitude of a psychological quantity may possibly be expressed as the product of a real number and a unit magnitude.
Application of the theory of conjoint measurement in psychology, however, has been limited. It has been argued that this is due to the high level of formal mathematics involved (e.g., Cliff 1992) and that the theory cannot account for the "noisy" data typically discovered in psychological research (e.g., Perline, Wright & Wainer 1979). It has been argued that the Rasch model is a stochastic variant of the theory of conjoint measurement (e.g., Brogden 1977; Embretson & Reise 2000; Fischer 1995; Keats 1967; Kline 1998; Scheiblechner 1999), however, this has been disputed (e.g., Karabatsos, 2001; Kyngdon, 2008). Order restricted methods for conducting probabilistic tests of the cancellation axioms of conjoint measurement have been developed in the past decade (e.g., Karabatsos, 2001; Davis-Stober, 2009).
The theory of conjoint measurement is (different but) related to conjoint analysis, which is a statistical-experiments methodology employed in marketing to estimate the parameters of additive utility functions. Different multi-attribute stimuli are presented to respondents, and different methods are used to measure their preferences about the presented stimuli. The coefficients of the utility function are estimated using alternative regression-based tools.
