Title: Investigating the Invariant Ordering of Clustered Items Using Nonparametric Item Response Theory
Abstract: Invariant item ordering (IIO) is a property of a test or questionnaire, in which the items have the same order in difficulty (or popularity) for all values of a unidimensional latent variable. An IIO allows for the arrangement of items from easy to difficult, better interpretation of test scores, and comparison of response patterns. For tests with clustered items, the usefulness of the IIO definition and existing methods for investigation is limited. First, I explain alternative ordering structures in the form of a weak and strong invariant cluster ordering. In addition, I elaborate on our proposed procedure for investigating the ordering structure of a clustered item set, to guide analysis on test data. We applied this procedure to test data from the Norwegian version of the Test for Reception of Grammar. Suggestions for practice, further methodological developments, and future research are discussed.