Testing Weak Item Independence for the Constant Latent Odds-Ratios Model Using Kendall's W

Abstract

The Constant Latent Odds Ratios (CLORs) model is a newly developed generalization of the Rasch model with powerful measurement properties. From the assumptions of the CLORs model, the property of weak item independence follows. Weak item independence states that the ordering of the item probabilities is the same at every level of the total score, a property that only holds for a small selection of IRT models. By testing for weak item independence, it becomes possible to see whether applying a CLORs model instead of e.g. a Birnbaum model would be appropriate. To this purpose, a test of weak item independence is proposed that makes use of Kendall's W as a measure of concordance. The sensitivity of this test in differentiating between the CLORs model and the Birnbaum model is evaluated through simulation study, and a parametric bootstrap procedure is used to apply the test to empirical data.