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…

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…

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 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…

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…

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…

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,…

Gives sufficient and necessary conditions for the observability of factors in terms of the parameter matrices and a finite number of variables. Outlines five conditions that rigorously define indeterminacy and shows that (un)observable factors are (in)determinate, and extends L. Guttman's (1955) proof of indeterminacy to Heywood (H. Heywood, 1931)…

Provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally the approach relies on repeated orthomax rotation applied to supermatrices containing the frontal, lateral, or horizontal slabs, respectively. Exemplary analyses illustrate the procedure. (Author/SLD)

A sufficient condition in terms of the unique variances of a common factor model is given for the results of factor analysis to come closer to those of principal components analysis. In general, vectors corresponding to loading matrices can be related to each other by a specific measure of closeness, which is illustrated. (SLD)

A form of Browne's (1967) solution of finding a least squares fit to a specified factor structure is given which does not involve solution of an eigenvalue problem. It suggests the possible existence of a singularity, and a simple modification of Browne's computational procedure is proposed. (Author/RC)

An index of factorial simplicity, employing a quartimax transformational criteria, is developed. This index is both for each row separately and for a factor pattern matrix as a whole. The index varies between zero and one. The problem of calibrating the index is discussed. (Author/RC)

A shortcut formula for the computation of "coefficients of invariance" in the comparison of factor structures is presented. A limitation of the coefficient of invariance is pointed out in the case of comparing two first principal components. (NE)

An iterative process is proposed for obtaining an orthogonal simple structure solution. At each iteration, a target matrix is constructed such that the relative contributions of the target majorize the original ones, factor by factor. The convergence of the procedure is proven, and the algorithm is illustrated. (SLD)