Exploring the Effects of Item-Specific Factors in Sequential and IRTree Models

Test items for which the item score reflects a sequential or IRTree modeling outcome are considered. For such items, we argue that item-specific factors, although not empirically measurable, will often be present across stages of the same item. In this paper, we present a conceptual model that incorporates such factors. We use the model to demonstrate how the varying conditional distributions of item-specific factors across stages become absorbed into the stage-specific item discrimination and difficulty parameters, creating ambiguity in the interpretations of item and person parameters beyond the first stage. We discuss implications in relation to various applications considered in the literature, including methodological studies of (1) repeated attempt items; (2) answer change/review, (3) on-demand item hints; (4) item skipping behavior; and (5) Likert scale items. Our own empirical applications, as well as several examples published in the literature, show patterns of violations of item parameter invariance across stages that are highly suggestive of item-specific factors. For applications using sequential or IRTree models as analytical models, or for which the resulting item score might be viewed as outcomes of such a process, we recommend (1) regular inspection of data or analytic results for empirical evidence (or theoretical expectations) of item-specific factors; and (2) sensitivity analyses to evaluate the implications of item-specific factors for the intended inferences or applications.