DIF is often classified as CTT or IRT based approach. I will like to know the bases for this classification.
I'm not sure what exactly you are asking but to my knowledge, the term "differential item functioning" (DIF) is primarily used within the context of item response theory (IRT). In classical test theory (CTT), we typically deal with scale (sum, composite) scores that constitute continuous/metrical/interval-scale test score variables rather than binary or ordinal items. With continuous data, multigroup confirmatory factor analysis (mCFA) is often use to examine measurement equivalence (aka measurement invariance), a concept that is strongly related to DIF.
In mCFA, we can specify, test, and compare various models of CTT (e.g., the models of tau-parallel, tau-equivalent, tau-congeneric variables) in different groups, thereby examining equivalence of factor loadings, intercepts, and/or error variances across groups. Factor analysis can also be applied to binary/ordinal data, so there is some overlap between DIF in IRT and measurement equivalence testing using mCFA.
IRT models are typically "full information" approaches that are based on the entire information contained in the observed item response pattern frequencies, whereas factor analytic methods tend to be "limited information" approaches, using only covariances, correlations, and/or means as input.
Thank you Prof. Christian,
In all honesty, you have given me a great insight and a broad desire to explore the DIF concept deeply. I sincerely appreciate your contribution.
Different classifications also exist:
1) Empirically based methods vs. methods based on IRT models (Gamerman, Gonçalves & Soares, 2018; Wainer, 1993)
2) observed-score based & model-based (Elosua & Wells, 2013):
Article Detecting DIF in polytomous items using MACS, IRT and ordina...
Elosua, P., & Wells, C. S. (2013). Detecting DIF in polytomous items using MACS, IRT and ordinal logistic regression. Psicológica, 34(2), 327-342.
Gamerman, D., Gonçalves, F. B., & Soares, T. M. (2018). Differential item functioning. In W. J. van der Linden (Ed.), Handbook of item response theory (pp. 67-84). CRC Press.
Wainer, H. (1993). Model-based standardized measurement of an item’s differential impact. In P. W. Holland & H. Wainer (Eds.), Differential item functioning (pp. 123-135). Lawrence Erlbaum Associates.
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