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Testing the difficulty theory of the SON‐R 5 1 2 –17, a non‐verbal test of intelligence
Author(s) -
Geerlings Hanneke,
Laros Jacob A.,
Tellegen Peter J.,
Glas Cees A. W.
Publication year - 2014
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 - 10.1111/bmsp.12017
Subject(s) - statistics , residual , covariate , variance (accounting) , mathematics , test (biology) , bayesian probability , econometrics , logistic regression , robustness (evolution) , predictive power , item response theory , psychometrics , algorithm , paleontology , biochemistry , chemistry , accounting , gene , business , biology , philosophy , epistemology
Fischer's (1973) linear logistic test model can be used to test hypotheses regarding the effect of covariates on item difficulty and to predict the difficulty of newly constructed test items. However, its assumptions of equal discriminatory power across items and a perfect prediction of item difficulty are never absolutely met. The amount of misfit in an application of a Bayesian version of the model to two subtests of the SON‐R 5 1 2–17 is investigated by means of item fit statistics in the framework of posterior predictive checks and by means of a comparison with a model that allows for residual (co)variance in the item parameters. The effect of the degree of residual (co)variance on the robustness of inferences is investigated in a simulation study.