This study implements a scale purification procedure onto the standard MIMIC method for differential item functioning (DIF) detection and assesses its performance through a series of simulations. It is found that the MIMIC method with scale purification (denoted as M-SP) outperforms the standard MIMIC method (denoted as M-ST) in controlling false-positive rates and yielding higher true-positive rates. Only when the DIF pattern is balanced between groups or when there is a small percentage of DIF items in the test does M-ST perform as appropriately as M-SP. Moreover, both methods yield a higher true-positive rate under the two-parameter logistic model than under the three-parameter model. M-SP is preferable to M-ST, because DIF patterns in real tests are unlikely to be perfectly balanced and the percentages of DIF items may not be small.
Ackerman, T.A. ( 1992). A didactic explanation of item bias, item impact, and item validity from a multidimensional perspective. Journal of Educational Measurement, 29, 67-91.
2.
Birnbaum, A. ( 1968). Some latent trait models and their use in inferring an examinee’s ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 397-424). Reading MA : Addison-Wesley.
3.
Candell, G.L., & Drasgow, F. ( 1988). An iterative procedure for linking metrics and assessing item bias in item response theory. Applied Psychological Measurement , 12, 253-260.
4.
Clauser, B., Mazor, K., & Hambleton, R.K. (1993). The effects of purification of the matching criterion on the identification of DIF using the Mantel-Haenszel procedure. Applied Measurement in Education, 6, 269-279.
5.
Cohen, A.S., Kim, S.H., & Wollack, J.A. ( 1996). An investigation of the likelihood ratio test for detection of differential item functioning. Applied Psychological Measurement , 20, 15-26.
6.
Finch, H. ( 2005). The MIMIC model as a method for detecting DIF: Comparison with Mantel-Haenszel, SIBTEST, and the IRT likelihood ratio. Applied Psychological Measurement, 29, 278-295.
7.
Fleishman, J.A., Spector, W.D., & Altman, B.M. ( 2002). Impact of differential item functioning on age and gender differences in functional disability. Journal of Gerontology: Social Sciences, 57B(5), S275-S283.
8.
French, B.F., & Maller, S.J. ( 2007). Iterative purification and effect size use with logistic regression for differential item functioning detection. Educational and Psychological Measurement, 67, 373-393.
9.
Glöckner-Rist, A., & Hoitjink, H. ( 2003). The best of both worlds: Factor analysis of dichotomous data using item response theory and structural equation modeling. Structural Equation Modeling, 10, 544-565.
10.
González-Romá, V. , Hernández , A., & Gómez-Benito, J. ( 2006). Power and Type I error of the mean and covariance structure analysis model for detecting differential item functioning in graded response items. Multivariate Behavioral Research, 41, 29-53.
11.
Hidalgo-Montesinos, M.D., & Gómez-Benito, J. (2003). Test purification and the evaluation of differential item functioning with multinomial logistic regression. European Journal of Psychological Assessment, 19, 1-11.
12.
Holland, W.P., & Thayer, D.T. ( 1988). Differential item performance and the Mantel-Haenszel procedure. In H. Wainer & H. I. Braun (Eds.), Test validity (pp. 129-145). Hillsdale, NJ: Lawrence Erlbaum.
13.
Lautenschlager, G.J., Flaherty, V.L., & Park, D. ( 1994). IRT differential item functioning: An examination of ability scale purifications. Educational and Psychological Measurement, 54, 21-31.
Lord, F.M. ( 1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
16.
MacIntosh, R., & Hashim, S. ( 2003). Variance estimation for converting MIMIC model parameters to IRT parameters in DIF analysis. Applied Psychological Measurement , 27, 372-379.
Miller, M.D., & Oshima, T.C. ( 1992). Effect of sample size, number of biased items and magnitude of bias on a two-stage item bias estimation method. Applied Psychological Measurement, 16, 381-388.
19.
Muthén, B.O. ( 1985). A method for studying the homogeneity of test items with respect to other relevant variables. Journal of Educational Statistics, 10, 121-132.
20.
Muthén, B.O. ( 1988). Some uses of structural equation modeling in validity studies: Extending IRT to external variables. In H. Wainer & H. Braun (Eds.), Test validity (pp. 213-238). Hillsdale, NJ: Lawrence Erlbaum.
21.
Muthén, B.O., Kao, C.-F., & Burstein, L. ( 1991). Instructionally sensitive psychometrics: Application of a new IRT-based detection technique to mathematics achievement test items . Journal of Educational Measurement, 28, 1-22.
Navas-Ara, M.J., & Gómez-Benito, J. (2002). Effects of ability scale purification on identification of DIF. European Journal of Psychological Assessment, 18, 9-15.
24.
Oort, F.J. ( 1998). Simulation study of item bias detection with restricted factor analysis. Structural Equation Modeling, 5, 107-124.
25.
Park, D.G., & Lautenschlager, G.J. (1990). Improving IRT item bias detection with iterative linking and ability scale purification. Applied Psychological Measurement, 14, 163-173.
26.
Raju, N.S. ( 1988). The area between two item characteristic curves . Psychometrika, 53, 495-502.
27.
Shealy, R.T., & Stout, W.F. ( 1993). A model-biased standardization approach that separates true bias/ DIF from group ability differences and detects test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159-194.
Takane, Y., & de Leeuw, J. ( 1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika , 52, 393-408.
30.
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. Braun (Eds.), Test validity (pp. 147-169). Hillsdale, NJ: Lawrence Erlbaum.
31.
Wang, W.-C. ( 2004). Effects of anchor item methods on the detection of differential item functioning within the family of Rasch models. Journal of Experimental Education, 72, 221-261.
32.
Wang, W.-C., & Su, Y.-H. ( 2004a). Effects of average signed area between two item characteristic curves and test purification procedures on the DIF detection via the Mantel-Haenszel method. Applied Measurement in Education , 17, 113-144.
33.
Wang, W.-C., & Su, Y.-H. ( 2004b). Factors influencing the Mantel and generalized Mantel-Haenszel methods for the assessment of differential item functioning in polytomous items. Applied Psychological Measurement, 28, 450-480.
34.
Wang, W.-C., & Yeh, Y.-L. (2003). Effects of anchor item methods on differential item functioning detection with the likelihood ratio test. Applied Psychological Measurement, 27, 479-498.
35.
Wright, B.D., & Stone, M.H. ( 1979). Best test design. Chicago: MESA Press.
