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…

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…

Small sample sizes pose a severe threat to convergence and accuracy of between-group level parameter estimates in multilevel structural equation modeling (SEM). However, in certain situations, such as pilot studies or when populations are inherently small, increasing samples sizes is not feasible. As a remedy, we propose a two-stage regularized…

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading…

Technological advances have significantly affected education, leading to the creation of online learning platforms such as virtual learning environments and massive open online courses. While these platforms offer a variety of features, none of them incorporates a module that accurately predicts students' academic performance and commitment.…

The standard methodology for many large-scale assessments in education involves regressing latent variables on numerous contextual variables to estimate proficiency distributions. To reduce the number of contextual variables used in the regression and improve estimation, we propose and evaluate principal component analysis on the covariance matrix…

Network models of the WAIS-IV based on regularized partial correlation matrices have been reported to outperform latent variable models based on uncorrected correlation matrices. The present study sought to compare network and latent variable models using both partial and uncorrected correlation matrices with both types of models. The results show…

No matter how strong the theoretical infrastructure of a study is, if the measurement instruments do not have the necessary psychometric qualities, there will be a question of trust in interpreting the findings, and it will be inevitable to make wrong decisions with the results. One of the important steps in scale development/adaptation studies is…

This study aims to apply the model principal component analysis to reduce multicollinearity on variable currency exchange rate in eight countries in Asia against US Dollar including the Yen (Japan), Won (South Korea), Dollar (Hong Kong), Yuan (China), Bath (Thailand), Rupiah (Indonesia), Ringgit (Malaysia), Dollar (Singapore). It looks at yield…

It is well known that a categorical random variable can be represented geometrically by a simplex. Accordingly, several measures of association between categorical variables have been proposed and discussed in the literature. Moreover, the standard definitions of covariance and correlation coefficient for continuous random variables have been…

The Woodcock-Johnson (fourth edition; WJ IV; Schrank, McGrew, & Mather, 2014a) was recently redeveloped and retains its linkage to Cattell-Horn-Carroll theory (CHC). Independent reviews (e.g., Canivez, 2017) and investigations (Dombrowski, McGill, & Canivez, 2017) of the structure of the WJ IV full test battery and WJ IV Cognitive have…

Meta-analytic structural equation modeling (MASEM) involves fitting models to a common population correlation matrix that is estimated on the basis of correlation coefficients that are reported by a number of independent studies. MASEM typically consist of two stages. The method that has been found to perform best in terms of statistical…

The study explored critical factors that explain leadership performance of high-performing principals and examined the relationship between these factors based on the ratings of school constituents in the public school system. The principal component analysis with the use of Varimax Rotation revealed that four components explain 51.1% of the…

The Woodcock-Johnson-III cognitive in the adult time period (age 20 to 90 plus) was analyzed using exploratory bifactor analysis via the Schmid-Leiman orthogonalization procedure. The results of this study suggested possible overfactoring, a different factor structure from that posited in the Technical Manual and a lack of invariance across both…

Rubin and Thayer ("Psychometrika," 47:69-76, 1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one,…