A BAYESIAN RANDOM EFFECTS MODEL FOR TESTLETS

Eric T. Bradlow · Howard Wainer · Xiaohui Wang

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

ABSTRACT Standard item response theory (IRT) models fit to dichotomous examination responses ignore the fact that sets of items (testlets) often come from a single common stimuli (e.g. a reading comprehension passage). In this setting, all items given to an examinee are unlikely to be conditionally independent (given examinee proficiency). Models that assume conditional independence will overestimate the precision with which examinee proficiency is measured. Overstatement of precision may lead to inaccurate inferences such as prematurely ending an examination in which the stopping rule is based on the estimated standard error of examinee proficiency (e.g an adaptive test). To model examinations that may be a mixture of independent items and testlets, we modified one standard IRT model to include an additional random effect for items nested within the same testlet. We use a Bayesian framework to facilitate posterior inference via a Data Augmented Gibbs Sampler (DAGS, Tanner and Wong 1987). The modified and standard IRT models are both applied to a data set from a disclosed form of the SAT. We also provide simulation results that indicates that the degree of precision bias is a function of the variability of the testlet effects, as well as the testlet design.

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References

1969Statistical Theories of Mental Test Scores 1993Scaling Performance Assessments: Strategies for Managing Local Item Dependence 1987Item Clusters and Computerized Adaptive Testing: A Case for Testlets 1990BILOG 3 : item analysis and test scoring with binary logistic models 1981The dimensionality of tests and items 1987A Nonparametric Approach for Assessing Latent Trait Unidimensionality 1992Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling 1990A New Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation

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