Differential item functioning (DIF) often arises from multiple sources. Within the context of multidimensional item response theory, this study examined DIF items with varying secondary dimensions using the three DIF methods: SIBTEST, Mantel-Haenszel, and logistic regression. The effect of the number of secondary dimensions on DIF detection rates…

Accurate item parameters and standard errors (SEs) are crucial for many multidimensional item response theory (MIRT) applications. A recent study proposed the Gaussian Variational Expectation Maximization (GVEM) algorithm to improve computational efficiency and estimation accuracy (Cho et al., 2021). However, the SE estimation procedure has yet to…

A standard assumption of latent class (LC) analysis is conditional independence, that is the items of the LC are independent of the covariates given the LCs. Several approaches have been proposed for identifying violations of this assumption. The recently proposed likelihood ratio approach is compared to residual statistics (bivariate residuals…

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…

We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter…

Much research has been devoted to identification of differential item functioning (DIF), which occurs when the item responses for individuals from two groups differ after they are conditioned on the latent trait being measured by the scale. There has been less work examining differential step functioning (DSF), which is present for polytomous…

This article presents the performance of item response theory (IRT) models when double ratings are used as item scores over single ratings when rater effects are present. Study 1 examined the influence of the number of ratings on the accuracy of proficiency estimation in the generalized partial credit model (GPCM). Study 2 compared the accuracy of…

Testing item fit is central in item response theory (IRT) modeling, since a good fit is necessary to draw valid inferences from estimated model parameters. "Infit" and "outfit" fit statistics, widespread indices for detecting deviations from the Rasch model, are affected by data factors, such as sample size. Consequently, the…

Previous work showing that revised parallel analysis can be effective with dichotomous items has used a two-parameter model and normally distributed abilities. In this study, both two- and three-parameter models were used with normally distributed and skewed ability distributions. Relatively minor skew and kurtosis in the underlying ability…

In real-world situations, multidimensional data may appear on large-scale tests or attitudinal surveys. A simple structure, multidimensional model may be used to evaluate the items, ignoring the cross-loading of some items on the secondary dimension. The purpose of this study was to investigate the influence of structure complexity magnitude of…

In dichotomous item response theory (IRT) framework, the asymptotic standard error (ASE) is the most common statistic to evaluate the precision of various ability estimators. Easy-to-use ASE formulas are readily available; however, the accuracy of some of these formulas was recently questioned and new ASE formulas were derived from a general…

Research has shown that cross-sectional mediation analysis cannot accurately reflect a true longitudinal mediated effect. To investigate longitudinal mediated effects, different longitudinal mediation models have been proposed and these models focus on different research questions related to longitudinal mediation. When fitting mediation models to…

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…

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap,…

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…