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…

Confirmatory factor analyses (CFA) are often used in psychological research when developing measurement models for psychological constructs. Evaluating CFA model fit can be quite challenging, as tests for exact model fit may focus on negligible deviances, while fit indices cannot be interpreted absolutely without specifying thresholds or cutoffs.…

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…

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…

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…

This dissertation compares the performance of equivalence test (EQT) and null hypothesis test (NHT) procedures for identifying invariant and noninvariant factor loadings under a range of experimental manipulations. EQT is the statistically appropriate approach when the research goal is to find evidence of group similarity rather than group…

Symmetry considerations are important in science, and Group Theory is a theory of symmetry. Classical Measurement Theory is the most used measurement theory in the social and behavioral sciences. In this article, the author uses Matrix Lie (Lee) group theory to formulate a measurement model. Symmetry is defined and illustrated using symmetries of…

A linear model is often used to find the effect of a binary treatment D on a noncontinuous outcome Y with covariates X. Particularly, a binary Y gives the popular "linear probability model (LPM)," but the linear model is untenable if X contains a continuous regressor. This raises the question: what kind of treatment effect does the…

Various areas of educational research are interested in the transitions between different states--or events--in sequential data, with the goal of understanding the significance of these transitions; one notable example is affect dynamics, which aims to identify important transitions between affective states. Unfortunately, several works have…

Factor Score Regression (FSR) is increasingly employed as an alternative to structural equation modeling (SEM) in small samples. Despite its popularity in psychology, the performance of FSR in multigroup models with small samples remains relatively unknown. The goal of this study was to examine the performance of FSR, namely Croon's correction and…

As part of the effort to develop an improved oral reading fluency (ORF) assessment system, Kara et al. (2020) estimated the ORF scores based on a latent variable psychometric model of accuracy and speed for ORF data via a fully Bayesian approach. This study further investigates likelihood-based estimators for the model-derived ORF scores,…