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Assessing Fit of Unidimensional Graded Response Models Using Bayesian Methods
Author(s) -
Zhu Xiaowen,
Stone Clement A.
Publication year - 2011
Publication title -
journal of educational measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.917
H-Index - 47
eISSN - 1745-3984
pISSN - 0022-0655
DOI - 10.1111/j.1745-3984.2011.00132.x
Subject(s) - polytomous rasch model , item response theory , model checking , bayesian probability , predictive power , econometrics , statistics , computer science , independence (probability theory) , variety (cybernetics) , local independence , mathematics , psychometrics , algorithm , philosophy , epistemology
The posterior predictive model checking method is a flexible Bayesian model‐checking tool and has recently been used to assess fit of dichotomous IRT models. This paper extended previous research to polytomous IRT models. A simulation study was conducted to explore the performance of posterior predictive model checking in evaluating different aspects of fit for unidimensional graded response models. A variety of discrepancy measures (test‐level, item‐level, and pair‐wise measures) that reflected different threats to applications of graded IRT models to performance assessments were considered. Results showed that posterior predictive model checking exhibited adequate power in detecting different aspects of misfit for graded IRT models when appropriate discrepancy measures were used. Pair‐wise measures were found more powerful in detecting violations of the unidimensionality and local independence assumptions.