Formulating the Rasch Differential Item Functioning Model Under the Marginal Maximum Likelihood Estimation Context and Its Comparison With Mantel– Haenszel Procedure in Short Test and Small Sample Conditions

This study elaborates the Rasch differential item functioning (DIF) model formulation under the marginal maximum likelihood estimation context. Also, the Rasch DIF model performance was examined and compared with the Mantel–Haenszel (MH) procedure in small sample and short test length conditions through simulations. The theoretically known relationship of the DIF estimators between the Rasch DIF model and the MH procedure was confirmed. In general, the MH method showed a conservative tendency for DIF detection rates compared with the Rasch DIF model approach. When there is DIF, the z test (when the standard error of the DIF estimator is estimated properly) and the likelihood ratio test in the Rasch DIF model approach showed higher DIF detection rates than the MH chi-square test for sample sizes of 100 to 300 per group and test lengths ranging from 4 to 39. In addition, this study discusses proposed Rasch DIF classification rules that accommodate statistical inference on the direction of DIF. Florida State University, Tallahassee, FL, USA University of California, Berkeley, Berkeley, CA, USA Corresponding Author: Insu Paek, Educational Psychology and Learning Systems, Florida State University, 3204D Stone Building, 1114 W. Call Street, Tallahassee, FL 32306-4453, USA Email: [email protected] Educational and Psychological Measurement 71(6) 1023–1046 a The Author(s) 2011 Reprints and permission: sagepub.com/journalsPermissions.nav DOI: 10.1177/0013164411400734 http://epm.sagepub.com