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…

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…

Previous research has individually assessed parallel analysis and minimum average partial for factor retention in exploratory factor analysis using ordinal variables. The current study is a comprehensive simulation study including the manipulation of eight conditions (type of correlation matrix, sample size, number of variables per factor, number…

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…

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…

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,…

The uses and methodology of factor analysis are widely debated and discussed, especially the issues of rotational use, methods of confirmatory factor analysis, and adequate sample size. The variety of perspectives and often conflicting opinions can lead to confusion among researchers about best practices for using factor analysis. The focus of the…

Many researchers recognize that factor analysis can be conducted on both correlation matrices and variance-covariance matrices. Although most researchers extract factors from non-distribution free or parametric methods, researchers can also extract factors from distribution free or non-parametric methods. The nature of the data dictates the method…

In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

Principal Component Analysis is widely used in applied multivariate data analysis, and this article shows how to motivate student interest in this topic using cricket sports data. Here, principal component analysis is successfully used to rank the cricket batsmen and bowlers who played in the 2012 Indian Premier League (IPL) competition. In…

This study investigated personality correlates of early adolescents' tendency to either defend victims of bullying or to avoid involvement in bullying situations. Participants were 591 Dutch fifth- and sixth-grade students (X-bar[subscript age] = 11.42 years). Hierarchical regression models were run to predict these students' peer-reported…