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Sara Dhaene; Yves Rosseel – Structural Equation Modeling: A Multidisciplinary Journal, 2024
In confirmatory factor analysis (CFA), model parameters are usually estimated by iteratively minimizing the Maximum Likelihood (ML) fit function. In optimal circumstances, the ML estimator yields the desirable statistical properties of asymptotic unbiasedness, efficiency, normality, and consistency. In practice, however, real-life data tend to be…
Descriptors: Factor Analysis, Factor Structure, Maximum Likelihood Statistics, Computation
Waller, Niels G. – Journal of Educational and Behavioral Statistics, 2023
Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…
Descriptors: Statistics Education, Multivariate Analysis, Factor Analysis, Factor Structure

Jennrich, Robert I. – Psychometrika, 2001
Identifies a general algorithm for orthogonal rotation and shows that when an algorithm parameter alpha is sufficiently large, the algorithm converges monotonically to a stationary point of the rotation criterion from any starting value. Introduces a modification that does not require a large alpha and discusses the use of this modification as a…
Descriptors: Algorithms, Factor Structure, Orthogonal Rotation

Trendafilov, Nickolay T. – Multivariate Behavioral Research, 1996
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)
Descriptors: Algorithms, Factor Analysis, Factor Structure, Matrices

Kiers, Henk A. L. – Psychometrika, 1994
A class of oblique rotation procedures is proposed to rotate a pattern matrix so that it optimally resembles a matrix that has an exact simple pattern. It is demonstrated that the method can recover relatively complex simple structures where other simple structure rotation techniques fail. (SLD)
Descriptors: Algorithms, Factor Analysis, Factor Structure, Matrices

Clarkson, Douglas B.; Jennrich, Robert I. – Psychometrika, 1988
Most of the current analytic rotation criteria for simple structure in factor analysis are summarized and identified as members of a general symmetric family of quartic criteria. A unified development of algorithms for orthogonal and direct oblique rotation using arbitrary criteria from this family is presented. (Author/TJH)
Descriptors: Algorithms, Equations (Mathematics), Evaluation Criteria, Factor Structure

Rozeboom, William W. – Multivariate Behavioral Research, 1992
Enriching factor rotation algorithms with the capacity to conduct repeated searches from random starting points can make the tendency to converge to optima that are merely local a way to catch rotations of the input factors that might otherwise elude discovery. Use of the HYBALL computer program is discussed. (SLD)
Descriptors: Algorithms, Comparative Analysis, Factor Analysis, Factor Structure

Hakstian, A. Ralph; And Others – Multivariate Behavioral Research, 1982
Issues related to the decision of the number of factors to retain in factor analyses are identified. Three widely used decision rules--the Kaiser-Guttman (eigenvalue greater than one), scree, and likelihood ratio tests--are investigated using simulated data. Recommendations for use are made. (Author/JKS)
Descriptors: Algorithms, Data Analysis, Factor Analysis, Factor Structure

Zwick, William R. – Multivariate Behavioral Research, 1982
The performance of four rules for determining the number of components (factors) to retain (Kaiser's eigenvalue greater than one, Cattell's scree, Bartlett's test, and Velicer's Map) was investigated across four systematically varied factors (sample size, number of variables, number of components, and component saturation). (Author/JKS)
Descriptors: Algorithms, Data Analysis, Factor Analysis, Factor Structure

Lohnes, Paul R. – American Educational Research Journal, 1979
Factorial modeling is justified as a method for analyzing correlations in support of causal inference. The method is illustrated and compared to path analysis, LISREL-type analysis, canonical correlation, and commonality analysis. Predictions of impacts of policy manipulations are demonstrated. (Author/CP)
Descriptors: Algorithms, Correlation, Educational Research, Factor Structure

Manatt, Richard P.; Price, Peter P. – Journal of Personnel Evaluation in Education, 1994
Implementation of a career ladder in the Cave Creek Unified School District (Arizona), with a five-factor teacher performance evaluation and accompanying placement algorithm successfully dispersed teachers across plan levels. After three years, there have been no teacher grievances filed, and teachers feel ownership and authority over the career…
Descriptors: Algorithms, Career Ladders, Employment Level, Factor Structure

Birenbaum, Menucha; Tatsuoka, Kikumi – Journal of Educational Measurement, 1982
Empirical results from two studies--a simulation study and an experimental one--indicated that, in achievement data of the problem-solving type where a specific subject matter area is being tested, the greater the variety of the algorithms used, the higher the dimensionality of the test data. (Author/PN)
Descriptors: Achievement Tests, Algorithms, Data Analysis, Factor Structure