The Mantel-Haenszel estimator is one of the most popular techniques for measuring differential item functioning (DIF). A generalization of this estimator is applied to the context of DIF to compare items by taking the covariance of odds ratio estimators between dependent items into account. Unlike the Item Response Theory, the method does not rely…

This Monte Carlo study assessed Type I error in differential item functioning analyses using Lord's chi-square (LC), Likelihood Ratio Test (LRT), and Mantel-Haenszel (MH) procedure. Two research interests were investigated: item response theory (IRT) model specification in LC and the LRT and continuity correction in the MH procedure. This study…

We derive formulas for the differential item functioning (DIF) measures that two routinely used DIF statistics are designed to estimate. The DIF measures that match on observed scores are compared to DIF measures based on an unobserved ability (theta or true score) for items that are described by either the one-parameter logistic (1PL) or…

Applying single-level statistical models to multilevel data typically produces underestimated standard errors, which may result in misleading conclusions. This study examined the impact of ignoring multilevel data structure on the estimation of item parameters and their standard errors of the Rasch, two-, and three-parameter logistic models in…

M-fluctuation tests are a recently proposed method for detecting differential item functioning in Rasch models. This article discusses a generalization of this method to two additional item response theory models: the two-parametric logistic model and the three-parametric logistic model with a common guessing parameter. The Type I error rate and…

Psychometric measurement models are only valid if measurement invariance holds between test takers of different groups. Global model tests, such as the well-established likelihood ratio (LR) test, are sensitive to violations of measurement invariance, such as differential item functioning and differential step functioning. However, these…

This article offers an approach to examining differential item functioning (DIF) under its item response theory (IRT) treatment in the framework of confirmatory factor analysis (CFA). The approach is based on integrating IRT- and CFA-based testing of DIF and using bias-corrected bootstrap confidence intervals with a syntax code in Mplus.

In this study, we examined the potential impact of item misfit on the reported scores of an admission test from the subpopulation invariance perspective. The target population of the test consisted of 3 major subgroups with different geographic regions. We used the logistic regression function to estimate item parameters of the operational items…

Evaluations of measurement invariance provide essential construct validity evidence--a prerequisite for seeking meaning in psychological and educational research and ensuring fair testing procedures in high-stakes settings. However, the quality of such evidence is partly dependent on the validity of the resulting statistical conclusions. Type I or…

The purpose of the current study was to examine dimensionality and concurrent validity evidence of the EARLI numeracy measures (DiPerna, Morgan, & Lei, 2007), which were developed to assess key skills such as number identification, counting, and basic arithmetic. Two methods (NOHARM with approximate chi-square test and DIMTEST with DETECT…

Minimum sample sizes of about 200 to 250 per group are often recommended for differential item functioning (DIF) analyses. However, there are times when sample sizes for one or both groups of interest are smaller than 200 due to practical constraints. This study attempts to examine the performance of Simultaneous Item Bias Test (SIBTEST),…

Differential item functioning (DIF) occurs when the probability of responding in a particular category to an item differs for members of different groups who are matched on the construct being measured. The identification of DIF is important for valid measurement. This research evaluates an improved version of Lord's X[superscript 2] Wald test for…

This study demonstrates how the stability of Mantel-Haenszel (MH) DIF (differential item functioning) methods can be improved by integrating information across multiple test administrations using Bayesian updating (BU). The authors conducted a simulation that showed that this approach, which is based on earlier work by Zwick, Thayer, and Lewis,…

The models used in this article are secondary dimension mixture models with the potential to explain differential item functioning (DIF) between latent classes, called latent DIF. The focus is on models with a secondary dimension that is at the same time specific to the DIF latent class and linked to an item property. A description of the models…

The Mantel-Haenszel (MH) procedure (Mantel and Haenszel) is a popular method for estimating and testing a common two-factor association parameter in a 2 x 2 x K table. Holland and Holland and Thayer described how to use the procedure to detect differential item functioning (DIF) for tests with dichotomously scored items. Wang, Bradlow, Wainer, and…