Limited Information Model Fit Test of Binary Item Response Theory Model with Missing Responses
Year: 2026
Type: preprint
Abstract: Even though missing data are prevalent in applications of item response theory (IRT), there has been a lack of research on the global model fit of IRT models with missing data. This study proposes two limited information fit statistics under full information maximum likelihood estimation for binary IRT models, related to the M_2 statistics of Maydeu-Olivares and Joe (2005). For a baseline model, we choose a log-linear model up to pairwise interaction effects based on the observations that M_2=0 with df=0 for this model under complete data as the first- and second-order model-implied marginals exactly recover those of sample and that two-parameter logistic IRT models are special cases of the model. We develop a computationally efficient generalized expectation-maximization algorithm (Dempster et al., 1977) to estimate the log-linear model under missing data. The two proposed statistics are motivated by G^2_dif of Fuchs (1982) and D_m of Rubin (1987) in multiple imputation, referred to as G^2_dif and \tilde{M}_2. Due to exponentially increasing cells (i.e., two to the power of the number of items), we discuss poor man's data augmentation of Wei and Tanner (1990) for \tilde{M}_2. We show that the two proposed statistics perform well throughout a simulation study and an application to PISA mathematics achievement data, among which \tilde{M}_2 shows the most promising result. We complete the study by discussing several important topics for the global model fit of IRT models under missing data.
Source: PsyArXiv (OSF Preprints)
Authors: Minho Lee, Cheng Liu
Institution: University of Notre Dame
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7167377644