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…

Matrix decomposition structural equation modeling (MDSEM) is introduced as a novel approach in structural equation modeling, contrasting with traditional structural equation modeling (SEM). MDSEM approximates the data matrix using a model generated by the hypothetical model and addresses limitations faced by conventional SEM procedures by…

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…

Simple matrix sampling planned missing (SMS PD) design, introduce missing data patterns that lead to covariances between variables that are not jointly observed, and create difficulties for analyses other than mean and variance estimations. Based on prior research, we adopted a new multigroup confirmatory factor analysis (CFA) approach to handle…

A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their "cols :…

The deviance information criterion (DIC) is widely used to select the parsimonious, well-fitting model. We examined how priors impact model complexity (pD) and the DIC for Bayesian CFA. Study 1 compared the empirical distributions of pD and DIC under multivariate (i.e., inverse Wishart) and separation strategy (SS) priors. The former treats the…

Deciding which random effects to retain is a central decision in mixed effect models. Recent recommendations advise a maximal structure whereby all theoretically relevant random effects are retained. Nonetheless, including many random effects often leads to nonpositive definiteness. A typical remedy is to simplify the random effect structure by…

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…

The purpose of this article is to describe the analytic process of a method of data collection known as Q Methodology. This method is an alternative method in collecting data especially suited to research on "points of views" (Coogan & Herrington, 2011, p. 24). The analytic process of Q methodology involves factor analysis, a…

Data from student learning provide learning curves that, ideally, demonstrate improvement in student performance over time. Existing data mining methods can leverage these data to characterize and improve the domain models that support a learning environment, and these methods have been validated both with already-collected data, and in…

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 measurement error in principal components extracted from a set of fallible measures is discussed and evaluated. It is shown that as long as one or more measures in a given set of observed variables contains error of measurement, so also does any principal component obtained from the set. The error variance in any principal component is shown…

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…