Effects of local item dependence on the fit and equating performance of the three-parameter logistic model

Abstract

Unidimensional item response theory (IRT) has become widely used in the analysis and equating of educational achievement tests. If an IRT model is true, item responses must be locally independent when the trait is held constant. This paper presents several measures of local dependence that are used in conjunction with the three-parameter logistic model in the analysis of unidimensional and two-dimensional simulated data and in the analysis of three mathematics achievement tests at Grades 3 and 6. The measures of local dependence (called Q₂ and Q₃) were useful for identifying subsets of items that were influenced by the same factors (simulated data) or that had similar content (real data). Item pairs with high Q₂ or Q₃ values tended to have similar item parameters, but most items with similar item parameters did not have high Q₂ or Q₃ values. Sets of locally dependent items tended to be difficult and discriminating if the items involved an accumulation of the skills involved in the easier items in the rest of the test. Locally dependent items that were independent of the other items in the test did not have unusually high or low difficulties or discriminations. Substantial unsystematic errors of equating were found from the equating of tests involving collections of different dimensions, but substantial systematic errors of equating were only found when the two tests measured quite different dimensions that were presumably taught sequentially.