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),…

The recent surge of interests in cognitive assessment has led to developments of novel statistical models for diagnostic classification. Central to many such models is the well-known "Q"-matrix, which specifies the item-attribute relationships. This article proposes a data-driven approach to identification of the "Q"-matrix and…

Polytomous attributes, particularly those defined as part of the test development process, can provide additional diagnostic information. The present research proposes the polytomous generalized deterministic inputs, noisy, "and" gate (pG-DINA) model to accommodate such attributes. The pG-DINA model allows input from substantive experts…

To address the lack of attention to construct shift in item response theory (IRT) vertical scaling, a multigroup, bifactor model was proposed to model the common dimension for all grades and the grade-specific dimensions. Bifactor model estimation accuracy was evaluated through a simulation study with manipulated factors of percentage of common…

Within the framework of item response theory (IRT), there are two recent lines of work on the estimation of classification accuracy (CA) rate. One approach estimates CA when decisions are made based on total sum scores, the other based on latent trait estimates. The former is referred to as the Lee approach, and the latter, the Rudner approach,…

Vertical scaling is necessary to facilitate comparison of scores from test forms of different difficulty levels. It is widely used to enable the tracking of student growth in academic performance over time. Most previous studies on vertical scaling methods assume relatively long tests and large samples. Little is known about their performance when…

The PROC NLMIXED procedure in Statistical Analysis System can be used to estimate parameters of item response theory (IRT) models. The data for this procedure are set up in a particular format called the "long format." The long format takes a substantial amount of time to execute the program. This article describes a format called the "wide…

catcher is a software program designed to compute the [omega] index, a common statistical index for the identification of collusions (cheating) among examinees taking an educational or psychological test. It requires (a) responses and (b) ability estimations of individuals, and (c) item parameters to make computations and outputs the results of…

A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…

This article reviews a new item response theory (IRT) model estimation program, IRTPRO 2.1, for Windows that is capable of unidimensional and multidimensional IRT model estimation for existing and user-specified constrained IRT models for dichotomously and polytomously scored item response data. (Contains 1 figure and 2 notes.)

Local dependence (LD) refers to the violation of the local independence assumption of most item response models. Statistics that indicate LD between a pair of items on a test or questionnaire that is being fitted with an item response model can play a useful diagnostic role in applications of item response theory. In this article, a new score test…

Mixtures of item response theory (IRT) models have been proposed as a technique to explore response patterns in test data related to cognitive strategies, instructional sensitivity, and differential item functioning (DIF). Estimation proves challenging due to difficulties in identification and questions of effect size needed to recover underlying…

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…

Models of modern test theory imply statistical independence among responses, generally referred to as "local independence." One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model,…

The problem of fitting unidimensional item-response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that contains a major dimension of interest but that may also contain minor nuisance dimensions. Because fitting a unidimensional model to multidimensional data results in…