This article presents generalizations of SIBTEST and crossing-SIBTEST statistics for differential item functioning (DIF) investigations involving more than two groups. After reviewing the original two-group setup for these statistics, a set of multigroup generalizations that support contrast matrices for joint tests of DIF are presented. To…

The main purpose of this study is to examine the Type I error and statistical power ratios of Differential Item Functioning (DIF) techniques based on different theories under different conditions. For this purpose, a simulation study was conducted by using Mantel-Haenszel (MH), Logistic Regression (LR), Lord's [chi-squared], and Raju's Areas…

Differential item functioning (DIF) is often used to examine validity evidence of alternate form test accommodations. Unfortunately, traditional approaches for evaluating DIF are prone to selection bias. This article proposes a novel DIF framework that capitalizes on regression discontinuity design analysis to control for selection bias. A…

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were…

When there are no personal consequences associated with test performance for examinees, rapid guessing (RG) is a concern and can differ between subgroups. To date, the impact of differential RG on item-level measurement invariance has received minimal attention. To that end, a simulation study was conducted to examine the robustness of the…

In a typical differential item functioning (DIF) analysis, a significance test is conducted for each item. As a test consists of multiple items, such multiple testing may increase the possibility of making a Type I error at least once. The goal of this study was to investigate how to control a Type I error rate and power using adjustment…

When studying differential item functioning (DIF) with students with disabilities (SWD) focal groups typically suffer from small sample size, whereas the reference group population is usually large. This makes it possible for a researcher to select a sample from the reference population to be similar to the focal group on the ability scale. Doing…

In 2009, DeMars stated that when impact exists there will be Type I error inflation, especially with larger sample sizes and larger discrimination parameters for items. One purpose of this study is to present the patterns of Type I error rates using Mantel-Haenszel (MH) and logistic regression (LR) procedures when the mean ability between the…

Background: When studying student performance across different countries or cultures, an important aspect for comparisons is that of score comparability. In other words, it is imperative that the latent variable (i.e., construct of interest) is understood and measured equivalently across all participating groups or countries, if our inferences…

This dissertation comprises three papers that propose, discuss, and illustrate models to make improved inferences about research questions regarding student achievement in education. Addressing the types of questions common in educational research today requires three different "extensions" to traditional educational assessment: (1)…

A nonparametric tree classification procedure is used to detect differential item functioning for items that are dichotomously scored. Classification trees are shown to be an alternative procedure to detect differential item functioning other than the use of traditional Mantel-Haenszel and logistic regression analysis. A nonparametric…

The traditional way of equating the scores on a new test form X to those on an old form Y is equipercentile equating for a population of examinees. Because the population is likely to change between the two administrations, a popular approach is to equate for a "synthetic population." The authors of the articles in this issue of the…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

This article considers models involving a single structural equation with latent explanatory and/or latent dependent variables where discrete items are used to measure the latent variables. Our primary focus is the use of scores as proxies for the latent variables and carrying out ordinary least squares (OLS) regression on such scores to estimate…

In educational tests, subscores are often generated from a portion of the items in a larger test. Guidelines based on mean-squared error are proposed to indicate whether subscores are worth reporting. Alternatives considered are direct reports of subscores, estimates of subscores based on total score, combined estimates based on subscores and…