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…

In component analysis solutions, post-multiplying a component score matrix by a nonsingular matrix can be compensated by applying its inverse to the corresponding loading matrix. To eliminate this indeterminacy on nonsingular transformation, we propose Joint Procrustes Analysis (JPA) in which component score and loading matrices are simultaneously…

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…

The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of "R" factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing…

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

This article presents a state-space modeling (SSM) technique for fitting process factor analysis models directly to raw data. The Kalman smoother via the expectation-maximization algorithm to obtain maximum likelihood parameter estimates is used. To examine the finite sample properties of the estimates in SSM when common factors are involved, a…

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…

Numerous procedures have been suggested for determining the number of factors to retain in factor analysis. However, previous studies have focused on comparing methods using normal data sets. This study had two phases. The first phase explored the Kaiser method, Scree test, Bartlett's chi-square test, Minimum Average Partial (1976&2000),…

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

Normal theory maximum likelihood (ML) is by far the most popular estimation and testing method used in structural equation modeling (SEM), and it is the default in most SEM programs. Even though this approach assumes multivariate normality of the data, its use can be justified on the grounds that it is fairly robust to the violations of the…

Kaiser's measure of sampling adequacy is applied to a special Spearman matrix and a special q cluster generalization. The result supports the contention that the measure should be no less than five tenths for data to be appropriate for factor analysis. A table is presented. (Author/JKS)

Studies concerning the relation of sample size to the number of variables in factor analysis are reviewed. It is noted that constraints imposed on the dimensionality of the variables by having fewer observations than variables are not mentioned in the literature. Suggestions for resolution of the problem are made. (Author/JKS)

Matching by Procrustes methods involves the transformation of one matrix to match with another. A special least squares criterion, the congruence coefficient, has advantages as a criterion for some factor analytic interpretations. A Procrustes method maximizing the congruence coefficient is given. (Author/JKS)

A principal components analysis of matrices of Spearman's rho statistic for inter-rater reliability is proposed as an alternative to Kendall's coefficient of concordance. Advantages and possible uses of the proposed method are presented. (JKS)

A method is presented for determining the number of components to retain in a principal components or image components analysis which utilizes a matrix of partial correlations. Advantages and uses of the method are discussed and a comparison of the proposed method with existing methods is presented. (JKS)