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A generalized dimensionality discrepancy measure for dimensionality assessment in multidimensional item response theory
Author(s) -
Levy Roy,
Svetina Dubravka
Publication year - 2011
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711010x500483
Subject(s) - curse of dimensionality , measure (data warehouse) , conditional independence , covariance , item response theory , independence (probability theory) , mathematics , perspective (graphical) , computer science , econometrics , statistics , artificial intelligence , data mining , psychometrics
A generalized dimensionality discrepancy measure is introduced to facilitate a critique of dimensionality assumptions in multidimensional item response models. Connections between dimensionality and local independence motivate the development of the discrepancy measure from a conditional covariance theory perspective. A simulation study and a real‐data analysis demonstrate the utility of the discrepancy measure's application at multiple levels of analysis in a posterior predictive model checking framework.