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…

Cluster randomized control trials often incorporate a longitudinal component where, for example, students are followed over time and student outcomes are measured repeatedly. Besides examining how intervention effects induce changes in outcomes, researchers are sometimes also interested in exploring whether intervention effects on outcomes are…

Multidimensionality and hierarchical data structure are common in assessment data. These design features, if not accounted for, can threaten the validity of the results and inferences generated from factor analysis, a method frequently employed to assess test dimensionality. In this article, we describe and demonstrate the application of the…

We examined the performance of coefficient alpha and its potential competitors (ordinal alpha, omega total, Revelle's omega total [omega RT], omega hierarchical [omega h], greatest lower bound [GLB], and coefficient "H") with continuous and discrete data having different types of non-normality. Results showed the estimation bias was…

A study was conducted to implement the use of a standardized effect size and corresponding classification guidelines for polytomous data with the POLYSIBTEST procedure and compare those guidelines with prior recommendations. Two simulation studies were included. The first identifies new unstandardized test heuristics for classifying moderate and…

For large-scale assessments, data are often collected with missing responses. Despite the wide use of item response theory (IRT) in many testing programs, however, the existing literature offers little insight into the effectiveness of various approaches to handling missing responses in the context of scale linking. Scale linking is commonly used…

Determining the number of factors in exploratory factor analysis is arguably the most crucial decision a researcher faces when conducting the analysis. While several simulation studies exist that compare various so-called factor retention criteria under different data conditions, little is known about the impact of missing data on this process.…

A simulation study was conducted to investigate the heuristics of the SIBTEST procedure and how it compares with ETS classification guidelines used with the Mantel-Haenszel procedure. Prior heuristics have been used for nearly 25 years, but they are based on a simulation study that was restricted due to computer limitations and that modeled item…

This article studies the Type I error, false positive rates, and power of four versions of the Lagrange multiplier test to detect measurement noninvariance in item response theory (IRT) models for binary data under model misspecification. The tests considered are the Lagrange multiplier test computed with the Hessian and cross-product approach,…

While hierarchical linear modeling is often used in social science research, the assumption of normally distributed residuals at the individual and cluster levels can be violated in empirical data. Previous studies have focused on the effects of nonnormality at either lower or higher level(s) separately. However, the violation of the normality…

Mediation models have been widely used in many disciplines to better understand the underlying processes between independent and dependent variables. Despite their popularity and importance, the appropriate sample sizes for estimating those models are not well known. Although several approaches (such as Monte Carlo methods) exist, applied…

Careless responding is a bias in survey responses that disregards the actual item content, constituting a threat to the factor structure, reliability, and validity of psychological measurements. Different approaches have been proposed to detect aberrant responses such as probing questions that directly assess test-taking behavior (e.g., bogus…

Wollack et al. (2015) suggested the erasure detection index (EDI) for detecting fraudulent erasures for individual examinees. Wollack and Eckerly (2017) and Sinharay (2018) extended the index of Wollack et al. (2015) to suggest three EDIs for detecting fraudulent erasures at the aggregate or group level. This article follows up on the research of…

Latent profile analysis (LPA) identifies heterogeneous subgroups based on continuous indicators that represent different dimensions. It is a common practice to measure each dimension using items, create composite or factor scores for each dimension, and use these scores as indicators of profiles in LPA. In this case, measurement models for…

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading…