The Rank-2PL IRT Models for Forced-Choice Questionnaires: Maximum Marginal Likelihood Estimation with an EM Algorithm

The rank two-parameter logistic (Rank-2PL) item response theory models refer to a set of models applying the 2PL model in a sequential ranking process that occurs in forced-choice questionnaires. The multi-unidimensional pairwise preference with 2PL model (MUPP-2PL) is a Rank-2PL model for items with two statements. Focusing on items with three statements, we develop a maximum marginal likelihood estimation with an expectation-maximization algorithm to estimate item parameters and their standard errors. A simulation study is conducted to check parameter recovery, and then the model is applied to a real dataset. Finally, the findings are summarized and discussed, and future research is suggested.