Quantifying Response Dependence Between Two Dichotomous Items Using the Rasch Model

Abstract

Models of modern test theory imply statistical independence among responses, generally referred to as local independence. One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model, this article shows how the magnitude of this violation can be estimated as a change in the location of the second item caused by its dependence on the first. It is suggested that this index is relatively more tangible in interpretation than other indices of dependence that are either a weight in the interaction term in a model or a correlation coefficient. The prime function of this method of assessing dependence is likely to be in the development of tests where evidence of the degree of dependence of one item on another in a pilot study can be used as part of the evidence in deciding which items will be retained in a final version of a test.