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…

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…

Sharing user information between systems is an area of interest for every field involving personalization. Recommender Systems are more advanced in this aspect than Intelligent Tutoring Systems (ITSs) and Intelligent Learning Environments (ILEs). A reason for this is that the user models of Intelligent Tutoring Systems and Intelligent Learning…

CEFA 3.02(Browne, Cudeck, Tateneni, & Mels, 2008) is a factor analysis computer program designed to perform exploratory factor analysis. It provides the main properties that are needed for exploratory factor analysis, namely a variety of factoring methods employing eight different discrepancy functions to be minimized to yield initial…

A computer program to compare factor matrices which have at least some variables in common is described. The program calculates both the salient variable similarity index and the congruence coefficient. There are no limits for the number of variables or factors in either matrix. (Author/JKS)

In matrix comparison, the performance of four vector matching indices (the coefficient of congruence, the Pearson product moment correlation, the "s"-statistic, and kappa) was evaluated. Advantages and disadvantages of each index are discussed, and the performance of each was assessed within the framework of principal components…

Various analytic choices in principal components and common factor analysis are discussed. Differences and similarities among these extraction methods are explained, and aids in interpreting the origin of detected effects are explored. Specifically, the nature and use of structure and pattern coefficients are examined. Communalities and methods…

A relatively simple technique for assessing the convergence of sets of variables across method domains is presented. The technique, two-step principal components analysis, empirically orthogonalizes each method domain into sets of components, and then analyzes convergence among components across domains. (Author)

Results of empirical comparisons of an inferential model of order analysis with factor analytic models were reported for two sets of data. On the prestructured data set both order and factor analytic models returned its dimensions of length, width and height, but on the random data set the factor analytic models indicated the presence of…

Rasch measurement is preferable to factor analysis for reducing complex data matrices to unidimensional variables because factor analysis can mistake ordinally labeled stochastic observations for linear measures, and it does not construct linear measurement. Guidelines and instructions on how to use Rasch measurement to replace factor analysis are…

Five techniques that combine the ideals of rotation of matrices of factor loadings to optimal agreement and rotation to simple structure are compared on the basis of empirical and contrived data. Combining a generalized Procrustes analysis with Varimax on the main of the matched loading matrices performed well on all criteria. (SLD)

Nonlinear factor analysis is a tool commonly used by measurement specialists to identify both the presence and nature of multidimensionality in a set of test items, an important issue given that standard Item Response Theory models assume a unidimensional latent structure. Results from most factor-analytic algorithms include loading matrices,…

Two proposed methods of factor analyzing a correlation matrix using only the off-diagonal elements are compared. The purpose of these methods is to avoid using the diagonal communality elements which are generally unknown and must be estimated. (Author/JKS)