Open AccessAccounting for Differential Item Functioning Using Bayesian Approximate Measurement Invariance
Author(s) -
Georgios D. Sideridis,
Ioannis Tsaousis,
Abeer A. Alamri
Publication year - 2019
Publication title -
educational and psychological measurement
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.819
H-Index - 95
eISSN - 1552-3888
pISSN - 0013-1644
DOI - 10.1177/0013164419887482
Subject(s) - equivalence (formal languages) , measurement invariance , bayesian probability , statistics , invariant (physics) , mathematics , differential item functioning , structural equation modeling , econometrics , item response theory , psychology , psychometrics , confirmatory factor analysis , discrete mathematics , mathematical physics
The main thesis of the present study is to use the Bayesian structural equation modeling (BSEM) methodology of establishing approximate measurement invariance (A-MI) using data from a national examination in Saudi Arabia as an alternative to not meeting strong invariance criteria. Instead, we illustrate how to account for the absence of measurement invariance using relative compared to exact criteria. A secondary goal was to compare latent means across groups using invariant parameters only and through utilizing exact and relative evaluative-MI protocol suggested equivalence of the thresholds using prior variances equal to 0.10. Subsequent differences between groups were evaluated using effect size criteria and the prior-posterior predictive p -value (PPPP), which proved to be invaluable in attesting for differences that are beyond zero, some meaningless nonzero estimate, and the three commonly used indices of effect sizes described by Cohen in 1988 (i.e., .20, .50, and .80). Results substantiated the use of the PPPP for evaluating mean differences across groups when utilizing nonexact evaluative criteria.