Ordinary least squares (OLS) regression and orthogonal regression (OR) address different questions and make different assumptions about errors. The OLS regression of Y on X yields predictions of a dependent variable (Y) contingent on an independent variable (X) and minimizes the sum of squared errors of prediction. It assumes that the independent…

The present study aims to examine gender differential item functioning (DIF) in the reading comprehension section of a high stakes test using cognitive diagnosis models. Based on the multiple-group generalized deterministic, noisy "and" gate (MG G-DINA) model, the Wald test and likelihood ratio test are used to detect DIF. The flagged…

A latent variable modeling method for studying measurement invariance when evaluating latent constructs with multiple binary or binary scored items with no guessing is outlined. The approach extends the continuous indicator procedure described by Raykov and colleagues, utilizes similarly the false discovery rate approach to multiple testing, 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…

Within polytomous items, differential item functioning (DIF) can take on various forms due to the number of response categories. The lack of invariance at this level is referred to as differential step functioning (DSF). The most common DSF methods in the literature are the adjacent category log odds ratio (AC-LOR) estimator and cumulative…

A number of studies have found multiple indicators multiple causes (MIMIC) models to be an effective tool in detecting uniform differential item functioning (DIF) for individual items and item bundles. A recently developed MIMIC-interaction model is capable of detecting both uniform and nonuniform DIF in the unidimensional item response theory…

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…

We evaluate the item response theory with covariates (IRT-C) procedure for assessing differential item functioning (DIF) without preknowledge of anchor items (Tay, Newman, & Vermunt, 2011). This procedure begins with a fully constrained baseline model, and candidate items are tested for uniform and/or nonuniform DIF using the Wald statistic.…

Methods for detecting differential item functioning (DIF) and item bias are typically used in the process of item analysis when developing new measures; adapting existing measures for different populations, languages, or cultures; or more generally validating test score inferences. In 2007 in "Language Assessment Quarterly," Zumbo…

These authors congratulate Albert Maydeu-Olivares on his lucid and timely overview of goodness-of-fit assessment in IRT models, a field to which he himself has contributed considerably in the form of limited information statistics. In this commentary, Oberski and Vermunt focus on two aspects of model fit: (1) what causes there may be of misfit;…

An odds ratio approach (ORA) under the framework of a nested logit model was proposed for evaluating differential distractor functioning (DDF) in multiple-choice items and was compared with an existing ORA developed under the nominal response model. The performances of the two ORAs for detecting DDF were investigated through an extensive…

Model specification issues on the cross-level two-way differential item functioning model were previously investigated by Patarapichayatham et al. (2009). Their study clarified that an incorrect model specification can easily lead to biased estimates of key parameters. The objective of this article is to provide further insights on the issue by…

There has been growing use of ideal point models to develop scales measuring important psychological constructs. For meaningful comparisons across groups, it is important to identify items on such scales that exhibit differential item functioning (DIF). In this study, the authors examined several methods for assessing DIF on polytomous items…

This note is concerned with a latent variable modeling approach for the study of differential item functioning in a multigroup setting. A multiple-testing procedure that can be used to evaluate group differences in response probabilities on individual items is discussed. The method is readily employed when the aim is also to locate possible…

Previous research has demonstrated that DIF methods that do not account for multilevel data structure could result in too frequent rejection of the null hypothesis (i.e., no DIF) when the intraclass correlation coefficient (?) of the studied item was the same as ? of the total score. The current study extended previous research by comparing the…