Most existing studies on the relationship between factor analysis (FA) and principal component analysis (PCA) focus on approximating the common factors by the first few components via the closeness between their loadings. Based on a setup in Bentler and de Leeuw (Psychometrika 76:461-470, 2011), this study examines the relationship between FA…

Fit indices are descriptive measures that can help evaluate how well a confirmatory factor analysis (CFA) model fits a researcher's data. In multigroup models, before between-group comparisons are made, fit indices may be used to evaluate measurement invariance by assessing the degree to which multiple groups' data are consistent with increasingly…

Data pooling is a powerful strategy in empirical research. However, combining multiple datasets often results in a large amount of missing data, as variables that are not present in some datasets effectively contain missing values for all participants in those datasets. Furthermore, data pooling typically leads to a mix of continuous and…

Exploratory factor analysis (EFA) is one of the standard analytical techniques used in EFL studies. It helps researchers to identify hidden constructs and check whether the survey instruments capture learners' beliefs, feelings and attitudes in EFL classrooms. However, many struggle with the application of EFA due to a lack of clear rationale for…

An application of Bayesian factor analysis for evaluation of scale reliability is discussed, which is developed within the framework of latent variable modeling. The method permits direct point and interval estimation of the reliability coefficient of multiple-component measuring instruments using Bayesian inference. The approach allows also point…

A Bayesian statistics-based approach is discussed that can be used for direct evaluation of the popular Cronbach's coefficient alpha as an internal consistency index for multiple-component measuring instruments, as well as for testing its identity to scale reliability. The method represents an application of confirmatory factor analysis within the…

In this work, we delve into geometric analysis, particularly examining the interplay between lower bounds on Ricci curvature and specific functionals. Our exploration begins with an investigation into the implications of Yamabe invariants for asymptotically Poincare-Einstein manifolds and their conformal boundaries under conditions of…

Most methods for structural equation modeling (SEM) focused on the analysis of covariance matrices. However, "Historically, interesting psychological theories have been phrased in terms of correlation coefficients." This might be because data in social and behavioral sciences typically do not have predefined metrics. While proper methods…

This paper advocates the use of exploratory factor analysis (EFA) for Q-matrix specification in cognitive diagnostic assessment (CDA) of language comprehension. We propose that integrating EFA results into Q-matrix specification improves the psychometric quality of CDA classification results with reference to Q-matrices based solely on human…

Survey responses from 858 undergraduates were examined to determine the key factors affecting students' deep approach to learning at two public institutions. Principal component analysis was adopted to eliminate multicollinearity among factors and extract the key influencing factors. A robust multiple linear regression model was built to explore…

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, interpreting these functional principal components (PCs) can sometimes be challenging due to issues such as roughness and sparsity. In this dissertation,…

Descriptive fit indices that do not require a formal statistical basis and do not specifically depend on a given estimation criterion are useful as auxiliary devices for judging the appropriateness of unrestricted or exploratory factor analytical (UFA) solutions, when the problem is to decide the most appropriate number of common factors. While…

Children's fuzziness leads to increased variance in the data, data loss, and high dropout rates in developmental studies. This study investigated the importance of 20 factors on the person (child, caregiver, experimenter) and situation (task, method, time, and date) level for the data quality as indicated via the number of valid trials in 11…

Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

The Penn Computerized Neurocognitive Battery (CNB) is a collection of tests validated using neuroimaging, genetics, and other criteria. An updated version of the CNB was constructed in which all tests were converted to either computerized adaptive (CAT) or abbreviated forms. In a mixed community/clinical sample (N = 307; mean age = 25.9 years;…