DFIT: Differential Functioning of Items and Tests framework


DFIT provides functions for calculating the differential item and test functioning proposed by Raju et al. (1995).


DFIT provides a set of functions to calculate the noncompensatory (NCDIF), compensatory (CDIF) and test level (DTF) differential functioning indices for items and tests under Raju's (Raju, et al. 1995) DFIT framework. It also provides functions for obtaining cut-off points for identifying differential functioning for these indices following the Monte Carlo Item Parameter Replication approach proposed by Oshima et al. (2006).

This package also improves upon available DFIT software by allowing the covariance matrices for both focal and reference groups to be used. This improves the obtained cut-off points, which result in type I error rates at the nominal level, and increased power, when compared to the cut-off points obtained when using only the focal group item parameter estimates and their estimate covariances (Cervantes, 2012). Furthermore, this package includes functions for obtaining the asymptotic covariance matrices of item parameter estimates (currently only for dichotomous IRT models) and for calculating the DFIT indices base on the focal group distribution as well as ability estimates for a sample from the focal population are included; these enable ad hoc and a priori power calculations for given item parameters and sample sizes to be possible with this package.


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Cervantes, V. H. (2012). On using the Item Parameter Replication (IPR) approach for power calculation of the noncompensatory differential item functioning (NCDIF) index (pp. 206-207). Proceedings of the V European Congress of Methodology. Santiago de Compostela, Spain: Universidade de Santiago de Compostela.

Cervantes, V. H. (2017). DFIT: An R Package for Raju's Differential Functioning of Items and Tests Framework. Journal of Statistical Software, 76(5), 1-24. doi:10.18637/jss.v076.i05

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Oshima, T., Raju, N. & Nanda, A. (2006). A new method for assessing the statistical significance in the Differential Functioning of Items and Tests (DFIT) framework. Journal of educational measurement, 43(1), 1–17. doi:10.1111/j.1745-3984.2006.00001.x

Raju, N. (1988). The area between two item characteristic cureves. Psychometricka, 53(4), 495–502. doi:10.1007/bf02294403

Raju, N., Fortmann-Johnson, K., Kim, W., Morris, S., Nering, M. & Oshima, T. (2009). The item parameter replication method for detecting differential functioning in the polytomous DFIT framework. Applied psychological measurement, 33(2), 133–147. doi:10.1177/0146621608319514

Raju, N. S., van der Linden, W. J., & Fleer, P. F. (1995). IRT-based internal measures of differential functioning of items and tests. Applied Psychological Measurement, 19, 353–368. doi:10.1177/014662169501900405

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Wright, K. (2011). Improvements for Differential Funtioning of Items and Tests (DFIT): Investigating the addition of reporting an effect size measure and power (Unpublished doctoral dissertation). Georgia State University, USA.

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