Mokken Scale Analysis (MSA) is a nonparametric approach that offers exploratory tools for understanding the nature of item responses while emphasizing invariance requirements. MSA is often discussed as it relates to Rasch measurement theory, which also emphasizes invariance, but uses parametric models. Researchers who have compared and combined…

Longitudinal item response data often exhibit two types of measurement noninvariance: the noninvariance of item parameters between subject groups and that of item parameters across multiple time points. This study proposes a comprehensive approach to the simultaneous modeling of both types of measurement noninvariance in terms of longitudinal item…

Testing for differential item functioning (DIF) has undergone rapid statistical developments recently. Moderated nonlinear factor analysis (MNLFA) allows for simultaneous testing of DIF among multiple categorical and continuous covariates (e.g., sex, age, ethnicity, etc.), and regularization has shown promising results for identifying DIF among…

This study aims to compare item and student parameters of dichotomously scored multidimensional constructs estimated based on unidimensional and multidimensional Item Response Theory (IRT) under different conditions of sample size, interdimensional correlation and number of dimensions. This research, conducted with simulations, is of a basic…

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…

This study presents a generalized version of the residual differential item functioning (RDIF) detection framework in item response theory, named GRDIF, to analyze differential item functioning (DIF) in multiple groups. The GRDIF framework retains the advantages of the original RDIF framework, such as computational efficiency and ease of…

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…

When measuring latent constructs, for example, language ability, we use statistical models to specify appropriate relationships between the latent construct and observe responses to test items. These models rely on theoretical assumptions to ensure accurate parameter estimates for valid inferences based on the test results. This dissertation…

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…

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…

Marginal maximum likelihood, a common estimation method for item response theory models, is not inherently a Bayesian procedure. However, due to estimation difficulties, Bayesian priors are often applied to the likelihood when estimating 3PL models, especially with small samples. Little focus has been placed on choosing the priors for marginal…

The use of discrete categorical formats to assess psychological traits has a long-standing tradition that is deeply embedded in item response theory models. The increasing prevalence and endorsement of computer- or web-based testing has led to greater focus on continuous response formats, which offer numerous advantages in both respondent…

While significant attention has been given to test equating to ensure score comparability, limited research has explored equating methods for rater-mediated assessments, where human raters inherently introduce error. If not properly addressed, these errors can undermine score interchangeability and test validity. This study proposes an equating…

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…

Test score comparability in international large-scale assessments (LSA) is of utmost importance in measuring the effectiveness of education systems and understanding the impact of education on economic growth. To effectively compare test scores on an international scale, score linking is widely used to convert raw scores from different linguistic…