Recent advancements in testing differential item functioning (DIF) have greatly relaxed restrictions made by the conventional multiple group item response theory (IRT) model with respect to the number of grouping variables and the assumption of predefined DIF-free anchor items. The application of the L[subscript 1] penalty in DIF detection has…

Testlets bring several perks in the development and administration of tests, such as 1) the construction of meaningful test items, 2) the avoidance of non-relevant context exposure, 3) the improvement of testing efficiency, and 4) the progression of testlet items requiring higher thinking skills. Thus, the inclusion of testlets in educational…

Measurement invariance is crucial for an effective and valid measure of a construct. Invariance holds when the latent trait varies consistently across subgroups; in other words, the mean differences among subgroups are only due to true latent ability differences. Differential item functioning (DIF) occurs when measurement invariance is violated.…

Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each…

Item response theory (IRT) uses a family of statistical models for estimating stable characteristics of items and examinees and defining how these characteristics interact in describing item and test performance. With a focus on the three-parameter logistic IRT (Birnbaum, 1968; Lord, 1980) model, the current study examines the accuracy and…

In recent years, there has been increasing interest in estimating and improving subscore reliability. In this study, the multidimensional item response theory (MIRT) and the bi-factor model were combined to estimate subscores, to obtain subscores reliability, and subscores classification. Both the compensatory and partially compensatory MIRT…

This study uses a new psychometric model (mixture item response theory-MIMIC model) that simultaneously estimates differential item functioning (DIF) across manifest groups and latent classes. Current DIF detection methods investigate DIF from only one side, either across manifest groups (e.g., gender, ethnicity, etc.), or across latent classes…

The increased use of polytomous item formats has led assessment developers to pay greater attention to the detection of differential item functioning (DIF) in these items. DIF occurs when an item performs differently for two contrasting groups of respondents (e.g., males versus females) after controlling for differences in the abilities of the…