Statistical Tests of Conditional Independence Between Responses and/or Response Times on Test Items

Wim J. van der Linden · Cees A. W. Glas

83 citations0/0 files storedPsychometrika

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

Abstract

Three plausible assumptions of conditional independence in a hierarchical model for responses and response times on test items are identified. For each of the assumptions, a Lagrange multiplier test of the null hypothesis of conditional independence against a parametric alternative is derived. The tests have closed-form statistics that are easy to calculate from the standard estimates of the person parameters in the model. In addition, simple closed-form estimators of the parameters under the alternatives of conditional dependence are presented, which can be used to explore model modification. The tests were applied to a data set from a large-scale computerized exam and showed excellent power to detect even minor violations of conditional independence.

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References

1969Statistical Theories of Mental Test Scores 2012Applications of Item Response Theory To Practical Testing Problems 1968Some latent trait models and their use in inferring an examinee's ability 2010Psychological Science 1997Local Dependence Indexes for Item Pairs Using Item Response Theory 1984Effects of Local Item Dependence on the Fit and Equating Performance of the Three-Parameter Logistic Model 2000Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models 2007A Hierarchical Framework for Modeling Speed and Accuracy on Test Items

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