Invariance of Comparisons—Separation of Person and Item Parameters

Abstract

In the Rasch model, the probability that a person answers one of two dichotomous items correctly, on the condition that only one is answered correctly and the other incorrectly, depends only on the relative difficulties $$ \delta_{1} $$and $$ \delta_{2} $$of the items and is independent of the proficiency $$ \beta $$of the person. Because the Rasch model implies statistical independenceStatistical independenceof responses, the probability of answering both items correctly equals the product of the probabilities of answering the separate items correctly. The measurementMeasurementrequirement of invariance of comparisonsInvariance of comparisonsis met in the Rasch model; the comparison of the difficulties between two items can be made independently of the proficiency of any person, and the comparison between persons can be made independently of the difficulties of the items. This invariance is a property of the Rasch model and instruments must be constructed to achieve this invariance in assessments—they are not present just because assessments are analysed with the Rasch model.