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…

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 :…

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…

Exploratory factor analysis involves five key decisions. The second decision, how many factors to retain, is the focus of the current paper. Extracting too many or too few factors often leads to devastating effects on study results. The advantages and disadvantages of the most effective and/or most utilized strategies to determine the number of…

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…

Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

There is a lack of research on the effects of outliers on the decisions about the number of factors to retain in an exploratory factor analysis, especially for outliers arising from unintended and unknowingly included subpopulations. The purpose of the present research was to investigate how outliers from an unintended and unknowingly included…

The purpose of this study was to investigate the application of the parallel analysis (PA) method for choosing the number of factors in component analysis for situations in which data are dichotomous or ordinal. Although polychoric correlations are sometimes used as input for component analyses, the random data matrices generated for use in PA…

A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decomposed has symmetric slices. We consider the case where two component matrices are randomly sampled…

Distributional characteristics of the measure of sampling adequacy (MSA) were investigated in sample correlation matrices generated from multivariate normal populations with covariance matrix equal to the identity. Systematic variation of sample size and number of variables resulted in minimal fluctuation of the overall MSA from .50. (Author/RC)

Formulas are presented in this paper for computing scores associated with factors of G, the image covariance matrix, under three conditions. The subject of the paper is restricted to "pure" image analysis. (Author/NE)