Polytomous Item Explanatory IRT Models with Random Item Effects

Abstract This paper proposes three polytomous item explanatory models with random item errors in Item Response Theory (IRT), which are also regarded as polytomous random item effects models. As in the Linear Logistic Test Model with item error (LLTM + ε) approach, the proposed models can take the uncertainty in explanation and/or the random nature of item parameters into account for polytomous items. For estimation of the proposed models with crossed random effects, available estimation methods are reviewed, and a Bayesian inference is adopted for data analysis. To examine how the proposed models work in different explanatory conditions, two simulation studies evaluate model comparison and parameter recovery as well as the effects of model misspecification. In addition, two empirical studies demonstrate practical implications and applications of the proposed models to two real data sets, the Carbon Cycle assessment data and the verbal aggression data. The simulation findings suggest that the proposed polytomous item explanatory models with random item errors perform better than the models without item error terms for making accurate statistical inferences, such as estimation or hypothesis testing for the item property effects. The empirical findings show that the proposed models outperform the models without random item errors in terms of the goodness-of-fit and reconstructing the step difficulties, and also demonstrate methodological and practical differences between the two polytomous item explanatory approaches, Many-Facet Rasch Model (MFRM) and Linear Partial Credit Model (LPCM).

Dr. Jinho Kim is a 2018 doctoral graduate of the Quantitative Methods and Evaluation (QME) program in the Graduate School of Education, University of California at Berkeley. He received his M.A. in Education from Korea University, South Korea in 2011. Currently he is a postdoctoral scholar at the Berkeley Evaluation and Assessment Research (BEAR) Center, where he is working for California Department of Education's Desired Results Developmental Profile (DRDP) project. His main research interests include explanatory measurement modeling, random item effects models, structural equation models, causal inference methods, multilevel modeling and longitudinal data analysis. He is particularly interested in applying quantitative methods to educational measurement, evaluation and policy.

Tuesday, October 2, 2018 - 2:00pm
2121 Berkeley Way
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