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…

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…

Because research has shown that principals' practices can significantly impact teaching and learning in their schools through multiple avenues, it is critical to understand the validity of tools that measure principal practice. While the field has relied heavily on self-report surveys, little is known about their validity. This study compares…

A fundamental goal of educational research is identifying students' current stage of skill mastery (complete/partial/none). In recent years a number of cognitive diagnosis models have become a popular means of estimating student skill knowledge. However, these models become difficult to estimate as the number of students, items, and skills grows.…

Introduction: The cognitive processes that underpin successful mathematical processing in children have been well researched by experimental psychologists, but are not widely understood among teachers of primary mathematics. This is a shame, as an understanding of these cognitive processes could be highly useful to practitioners. This paper…

An iterative majorization algorithm is proposed for orthogonal congruence rotation that is guaranteed to converge from every starting point. In addition, the algorithm is easier to program than the algorithm proposed by F. B. Brokken, which is not guaranteed to converge. The derivation of the algorithm is traced in detail. (SLD)

Several methodological issues in the multidimensional scaling of coarse dissimilarities were studied, examining whether it was better to scale dissimilarity data directly or to scale a new matrix derived from the original by row comparisons. Findings support an alternative row-comparison measure based on the Jacard coefficient. (SLD)

Rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, is discussed. Rowwise and columnwise indices are particularly suited for evaluating different types of conjectures of a similar pattern of entries across the two matrices. (SLD)

H. F. Kaiser, S. Hunka, and J. Bianchini have presented a method (1971) to compare two matrices of factor loadings based on the same variables, but different groups of individuals. The optimal rotation involved is examined from a mathematical point of view, and the method is shown to be invalid. (SLD)

A method is proposed for comparison of distinct partitions of the same set of n objects through a simple cross-product index defined between corresponding entries from two proximity matrices providing particular a priori codings of the within-class and between-class relationships for the partitions. (SLD)

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…

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…

The common marketing research practice of standardizing the columns of a persons-by-variables data matrix prior to clustering the entities corresponding to the rows was evaluated with 10 large-scale data sets. Results indicate that the column standardization practice may be problematic for some kinds of data that marketing researchers used for…

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)

An equal-level approach is proposed for investigating multitrait-multimethod (MTMM) matrices with respect to other organizational units that contain additional information concerning a MTMM matrix's validity. The approach requires equality in "data level" before coefficients are submitted for evaluation. Disaggregation is central to…