This study offers an approach to testing for differential item functioning (DIF) in a recently developed measurement framework, referred to as "D"-scoring method (DSM). Under the proposed approach, called "P-Z" method of testing for DIF, the item response functions of two groups (reference and focal) are compared by…

Psychometricians have devoted much research and attention to categorical item responses, leading to the development and widespread use of item response theory for the estimation of model parameters and identification of items that do not perform in the same way for examinees from different population subgroups (e.g., differential item functioning…

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational…

The estimation of test score "gaps" and gap trends plays an important role in monitoring educational inequality. Researchers decompose gaps and gap changes into within- and between-school portions to generate evidence on the role schools play in shaping these inequalities. However, existing decomposition methods assume an equal-interval…

Clinical, medical, and health psychologists use difference scores obtained from pretest--posttest designs employing the same test to assess intraindividual change possibly caused by an intervention addressing, for example, anxiety, depression, eating disorder, or addiction. Reliability of difference scores is important for interpreting observed…

Ramsay and Wiberg used a new version of item response theory that represents test performance over nonnegative closed intervals such as [0, 100] or [0, n] and demonstrated that optimal scoring of binary test data yielded substantial improvements in point-wise root-mean-squared error and bias over number right or sum scoring. We extend these…

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…

Mechanisms causing item nonresponses in large-scale assessments are often said to be nonignorable. Parameter estimates can be biased if nonignorable missing data mechanisms are not adequately modeled. In trend analyses, it is plausible for the missing data mechanism and the percentage of missing values to change over time. In this article, we…

Standard errors computed according to the operational practices of international large-scale assessment studies such as the Programme for International Student Assessment's (PISA) or the Trends in International Mathematics and Science Study (TIMSS) may be biased when cross-national differential item functioning (DIF) and item parameter drift are…

The purpose of this ITEMS module is to provide an introduction to differential item functioning (DIF) analysis using mixture item response models. The mixture item response models for DIF analysis involve comparing item profiles across latent groups, instead of manifest groups. First, an overview of DIF analysis based on latent groups, called…