A General Model for Item Dependency
Terry A. Ackerman, Judith A. Spray · 1986
The purpose of this paper is to define a model of item dependency and to use it to illustrate the effect that violations of local independence have on the behavior of item characteristic curves. The dependency model is flexible enough to simulate the interaction of a number of factors including item difficulty and discrimination, varying degrees of item dependence and item order or sequence effects. The model also provides for an ability-by-dependence interaction. Results suggest that the shift in an item's characteristic curve can be fairly dramatic, producing nonlogistic response probability curves. Suggestions for future work with the model and its implications are made. A General Model for Item Dependency Local independence is an assumption of all of the current item response theory (IRT) models. The violation of this assumption certainly can occur in situations where items are nested (i.e., multiple part questions where the correct solution to one part or item must be achieved before the solution to subsequent parts can be achieved — see the example in Figure 1). Further more, the violation of the independence assumption could occur in other situations which are much less obvious. In fact one of the justifications for considering IRT models that would allow for the violation of the local inde pendence assumption would be to be able to detect and possibly eliminate or modify items that would inadvertently cue” the correct response to other items on the same test. The purpose of this paper is to define a model of item dependency (in which local independence between item responses is a special case) and use it to illustrate what happens to typical test items, as represented by the behavior of their item characteristic curves (iCC's) when varying degrees of dependency exist. The item dependency model proposed is flexible enough to simulate or describe the interaction of a number of factors such as item difficulty and discrimination, the amount and direction of the dependency, and item order or sequence effects. An underlying assumption of the model is that each item within a sequence of k. items is dependent only on the previous item (i.e., a one-item-back dependency, the simplest situation). However, other itemlags are possible to describe with the proposed m o d e l .