Abstract
When item characteristic curves are nondecreasing functions of a latent variable, the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses. This general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves. The proposed tests are simple, have known asymptotic null distributions, and possess certain optimal properties. In an example, the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves.
Keywords
MathematicsMonotonic functionLocal independenceConditional independenceIndependence (probability theory)Monotone polygonConditional varianceItem response theoryEconometricsApplied mathematicsParametric statisticsConditional probability distributionSimple (philosophy)Latent variable modelSet (abstract data type)Latent variableStatisticsPsychometricsComputer scienceMathematical analysis
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Publication Info
- Year
- 1984
- Type
- article
- Volume
- 49
- Issue
- 3
- Pages
- 425-435
- Citations
- 202
- Access
- Closed
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Cite This
Paul R. Rosenbaum
(1984).
Testing the Conditional Independence and Monotonicity Assumptions of Item Response Theory.
Psychometrika
, 49
(3)
, 425-435.
https://doi.org/10.1007/bf02306030
Identifiers
- DOI
- 10.1007/bf02306030