Information Functions of Rank-2PL Models for Forced-Choice Questionnaires

This paper presents the item and test information functions of the Rank two-parameter logistic models (Rank-2PLM) for items with two (pair) and three (triplet) statements in forced-choice questionnaires. The Rank-2PLM model for pairs is the MUPP-2PLM (Multi-Unidimensional Pairwise Preference; Morillo et al., 2016), and for triplets, is the Triplet-2PLM (Fu et al., 2023a). Fisher's information and directional information are described, and the test information for Maximum Likelihood (ML), Maximum A Posterior (MAP), and Expected A Posterior (EAP) trait score estimates is distinguished. Expected item/test information indexes at various levels are proposed and plotted to provide diagnostic information on items and tests. The expected test information indexes for EAP scores may be difficult to compute due to a typical test's vast number of item response patterns. The relationships of item/test information with discrimination parameters of statements, standard error, and reliability estimates of trait score estimates are discussed and demonstrated using real data. Practical suggestions for checking the various expected item/test information indexes and plots are provided.