The purpose of this study was to investigate multidimensional DIF with a simple and nonsimple structure in the context of multidimensional Graded Response Model (MGRM). This study examined and compared the performance of the IRT-LR and Wald test using MML-EM and MHRM estimation approaches with different test factors and test structures in…

Coefficient omega indices are model-based composite reliability estimates that have become increasingly popular. A coefficient omega index estimates how reliably an observed composite score measures a target construct as represented by a factor in a factor-analysis model; as such, the accuracy of omega estimates is likely to depend on correct…

David Thissen, a professor in the Department of Psychology and Neuroscience, Quantitative Program at the University of North Carolina, has consulted and served on technical advisory committees for assessment programs that use item response theory (IRT) over the past couple decades. He has come to the conclusion that there are usually two purposes…

Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores,…

In educational measurement, the construction of parallel test forms is often a combinatorial optimization problem that involves the time-consuming selection of items to construct tests having approximately the same test information functions (TIFs) and constraints. This article proposes a novel method, genetic algorithm (GA), to construct parallel…

Student responses to a large number of constructed response items in three Math and three Reading tests were scored on two occasions using three ways of assigning raters: single reader scoring, a different reader for each response (item-specific), and three readers each scoring a rater item block (RIB) containing approximately one-third of a…

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…

The Bologna Declaration brought reforms into higher education that imply changes in teaching methods, didactic materials and textbooks, infrastructures and laboratories, etc. Statistics and mathematics are disciplines that traditionally have the worst success rates, particularly in non-mathematics core curricula courses. This research project,…

In many practical applications of item response theory, the parameters of overlapping subsets of test items are estimated from different samples of examinees. A linking procedure is then employed to place the resulting item parameter estimates onto a common scale. It is standard practice to ignore the uncertainty associated with the linking step…

A statistical test for detecting answer copying on multiple-choice tests based on Cohen's kappa is proposed. The test is free of any assumptions on the response processes of the examinees suspected of copying and having served as the source, except for the usual assumption that these processes are probabilistic. Because the asymptotic null and…

A method for incorporating maximum likelihood (ML) estimation into reliability analyses with item-level missing data is outlined. An ML estimate of the covariance matrix is first obtained using the expectation maximization (EM) algorithm, and coefficient alpha is subsequently computed using standard formulae. A simulation study demonstrated that…

A method of estimating the operating characteristics of a new test item added to an established test without assuming a prior model has been proposed by the author. In this paper, the author extends this logic by proposing a different hypothesized distribution of the resulting estimate. The former method used a normal approximation; the present…

Different item response theory (IRT) models may be employed for item calibration. Change of testing vendors, for example, may result in the adoption of a different model than that previously used with a testing program. To provide scale continuity and preserve cut score integrity, item parameter estimates from the new model must be linked to the…

If a loss function is available specifying the social cost of an error of measurement in the score on a unidimensional test, an asymptotic method, based on item response theory, is developed for optimal test design for a specified target population of examinees. Since in the real world such loss functions are not available, it is more useful to…

The advantages of applying confirmatory factor analysis (CFA) to multitrait-multimethod (MTMM) data are widely recognized. However, because CFA as traditionally applied to MTMM data incorporates single indicators of each scale (i.e., each trait/method combination), important weaknesses are the failure to: (1) correct appropriately for measurement…