The recent study of Oshima, Raju, and Nanda proposes the item parameter replication (IPR) method for assessing statistical significance of the noncompensatory differential item functioning (NCDIF) index within the differential functioning of items and tests (DFIT) framework. Previous Monte Carlo simulations have found that the appropriate cutoff values for determining statistical significance of NCDIF depend on sample size and the item response theory (IRT) model used for the analysis. The IPR method simplifies the process of identifying cutoff values that are tailored to a particular research setting. This approach has been shown to be effective for detecting differential item functioning (DIF) in dichotomous items. The current article extends the IPR method to the polytomous case.
Baker, F.B. (1993). EQUATE2: Computer program for equating two metrics in item response theory [Computer program]. Madison: University of Wisconsin, Laboratory of Experimental Design.
2.
Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
3.
Bolt, D.M. (2002). A Monte Carlo comparison of parametric and nonparametric polytomous DIF detection methods. Applied Measurement in Education , 2, 113-141.
4.
Chamblee, M.C. (1998). A Monte Carlo investigation of conditions that impact type 1 error rates of differential functioning of items and tests. Unpublished doctoral dissertation, Georgia State University .
5.
Cohen, A.S., Kim, S., & Baker, F.B. (1993). Detection of differential item functioning in the graded response model. Applied Psychological Measurement , 17, 335-350.
6.
Drasgow, F., & Kanfer, R. (1985). Equivalence of psychological measurement in heterogeneous populations. Journal of Applied Psychology, 70, 662-680.
7.
Fleer, P.F. (1993). A Monte Carlo assessment of a new measure of item and test bias. Unpublished doctoral dissertation, Illinois Institute of Technology.
8.
Flowers, C.P., Oshima, T.C., & Raju, N.S. (1999). A description and demonstration of the polytomous-DFIT framework. Applied Psychological Measurement, 23, 309-326.
9.
Graybill, F.A. (1969). Introduction to matrices with applications in statistics. Belmont, CA: Wadsworth .
10.
Kim, S.-H., & Cohen, A.S. (1991). A comparison of two area measures for detecting differential item functioning. Applied Psychological Measurement , 15, 269-278.
11.
Li, Y.H., & Lissitz, R.W. (2004). Applications of the analytically derived asymptotic standard errors of item response theory item parameter estimates. Journal of Educational Measurement, 41, 85-117.
12.
Lord, F.M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Erlbaum.
13.
Morris, S.B., Fortmann, K.A., & Oshima, T.C. (2007, April). An evaluation of the item parameter replication method for DFIT analysis of polytomous items. Paper presented at the annual conference of the National Council on Measurement in Education, Chicago.
14.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159-176.
15.
Muraki, E., & Bock, R.D. (1997). PARSCALE: IRT based test scoring and item analysis for graded, open-ended exercises and performance tasks [Computer software] . Chicago: Scientific Software International .
16.
Oshima, T.C., Raju, N.S., & Flowers, C.P. (1997). Development and demonstration of multidimensional IRT-based internal measures of differential functioning of items and tests . Journal of Educational Measurement, 34, 253-272.
17.
Oshima, T.C., Raju, N.S., & Nanda, A.O. (2006). A new method for assessing the statistical significance in the differential functioning of items and tests (DFIT) framework. Journal of Educational Measurement, 43, 1-17.
18.
Raju, N.S. (1988). The area between two item characteristic curves . Psychometrika, 53, 495-502.
19.
Raju, N.S. (1990). Determining the significance of estimated signed and unsigned areas between two item response functions. Applied Psychological Measurement, 14, 197-207.
20.
Raju, N.S., Oshima, T.C., Fortmann, K., Nering, M., & Kim, W. (2006, February). The new significance test for Raju's polytomous DFIT. Poster session presented at the Georgia Institute of Technology New Directions in Psychological Measurement with Model-Based Approaches conference, Atlanta, GA.
21.
Raju, N.S., Oshima, T.C., & Wolach, A. (2005). Differential functioning of items and tests (DFIT): Dichotomous and polytomous [Computer program]. Chicago : Illinois Institute of Technology.
22.
Raju, N.S., van der Linden, W.J., & Fleer, P.F. (1995). An IRT-based internal measure of test bias with applications for differential item functioning. Applied Psychological Measurement, 19, 353-368.
23.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores (Psychometric Monograph No. 17). Iowa City, IA: Psychometric Society.
24.
Thissen, D., Steinberg, L., & Wainer, H. (1988). Use of item response theory in the study of group differences in trace lines. In H. Wainer & H. I. Braun (Eds.), Test validity (pp. 147-169). Hillsdale, NJ: Erlbaum.
25.
Zickar, M.J. (2002). Modeling data with polytomous item response theory . In F. Drasgow & N. Schmitt (Eds.), Measuring and analyzing behavior in organizations: Advances in measurement and data analysis (pp. 123-155). San Francisco: Jossey-Bass.
