Do Items Order? The Psychology in IRT Models

Invariant item ordering refers to the statement that if one item is harder than another for one person, then it is harder for all people. Whether item ordering holds is a psychological statement because it describes how people may qualitatively vary. Yet, modern item response theory (IRT) makes an a priori commitment to item ordering. The Rasch model, for example, posits that items must order. Conversely, the 2PL model posits that items never order. Needed is an IRT model where item ordering or its violation is a function of the data rather than an *a priori* commitment. We develop two-parameter shift-scale models for this purpose, and find that the two-parameter uniform offers many advantages. We show how item ordering may be assessed using Bayes factor model comparison, and discuss computational issues with shift-scale IRT models.