Abstract
Item Relational Structure (IRS) analysis (Takeya, 1980) is frequently used to analyze test data. IRS analysis counts the frequency of examinees who answered correctly to one item and incorrectly to another item. It assesses the mutual dependence between the two items by comparing this frequency to the expected frequency under hypothetical independence. However, IRS analysis entails two problems: (1) the threshold of dependence is arbitrary and the results depend on the threshold; (2) when two items are conditionally independent given the examinees' ability variable, IRS analysis sometimes detects dependence between these items if the ability variable affects them strongly. This paper introduces a revised IRS analysis that uses the expected frequency described by Chen and Thissen (1997), which determines the threshold of dependence statistically and which controls the effect of the ability variable. Through numerical experiments, the revised IRS analysis detected fewer incorrect dependences and incorrect independences than traditional IRS analysis with various thresholds. However, the error ratio of detecting incorrect dependence is not controlled sufficiently. Applications to actual data must be analyzed carefully when the test includes many dependent items.
