Detecting DIF in polytomous items: An empirical comparison of the ordinal logistic regression, logistic discriminant function analysis, Mantel, and Generalized Mantel-Haenszel procedures.

Abstract

This study had four main objectives and two minor objectives: (1) To compare the Type I Error rates of four analytic techniques: the Mantel, Generalized Mantel-Haenszel (GMH), Logistic Discriminant Function Analysis (LDFA), and Ordinal Logistic Regression (OLR) procedures when there was no DIF in items. It was hypothesized that the procedures would differ little in their Type I Error rates, but that the OLR would have relatively the lowest Type I Error rates. (2) To compare the power of the Mantel, GMH, LDFA, and OLR for detecting uniform and nonuniform DIF in polytomous items. It was hypothesized that the Mantel would have the highest power for uniform DIF, but that it would not be useful for detecting nonuniform DIF. The GMH, OLR and LDFA were expected to display high power for nonuniform DIF. (3) To learn whether discrimination of the studied item, reference and focal group ability difference, sample size ratio between reference and focal group, and skewness would affect the performance of the four DIF detection procedures. It was hypothesized that differences in group ability distributions would result in increased Type I Error when item discrimination was high, and that differences in sample size ratio would lower power. (4) To determine whether adding a measure of effect size would reduce Type I Error. It was hypothesized that including effect size in the decision rule would reduce Type I Error for all procedures, and that it would also result in slightly lower power. (5) To compare Type I Error of the LDFA and OLR in classifying DIF as uniform when it was nonuniform and (6) To compare the Type I Error of the LDFA and OLR in classifying DIF as nonuniform when it was uniform. (Abstract shortened by UMI.)