Statistical tests of conditional independence between responses and/or response times on test items

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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.
Original languageEnglish
Pages (from-to)120-139
Issue number1
Publication statusPublished - 2010


  • METIS-272629
  • Lagrange multiplier tests
  • lognormal model
  • Response time
  • Item response theory (IRT)
  • Hierarchical modeling
  • Conditional independence
  • IR-85852

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