The Rasch Model, the Law of Comparative Judgment and Additive Conjoint Measurement

Relationships between the Rasch model and both the law of comparative judgment and additive conjoint measurement are discussed. The distance between the ability of Person a and the difficult of Item i is, in the Rasch model, the baseline value corresponding to the probability that a will respond correctly to i, where this probability is interpreted as the area under a logistic curve (which is substantially equivalent to the normal curve) and is thus an application of the law of comparative judgment. Under certain assumptions, the Rasch model is also a special case of additive conjoint measurement and, properly reinterpreted, may be usefully applied in contexts other than individual differences.