Comparison of Bookmark Difficulty Locations Under Different Item Response Models

Abstract

In the bookmark standard-setting procedure, judges place “bookmarks” in a reordered test booklet containing items presented in order of increasing difficulty. Traditionally, the bookmark difficulty location (BDL) is on the trait continuum where, for dichotomous items, there is a two-thirds probability of a correct response and, for a score of k on a polytomous item, there is a two-in-three probability of a score of k or higher. General formulas for the computation of BDLs were derived for five item response theory models—namely, the 1PL and 3PL for dichotomous items and the partial credit (PC), generalized partial credit (GPC), and graded response (GR) models for polytomous items and for any response probability (RP) value. These formulas were then used to compare the ordering of items’ BDLs under the 1PL-PC, 3PL-GPC, and 3PL-GR models for RPs of 1/2, 2/3, and 4/5. Results are discussed, and guidelines for practitioners are offered. Index terms: item response theory, bookmark standard setting, item difficulty, item mapping.