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Okamoto, Masashi; Ihara, Masamori – Psychometrika, 1983
A new algorithm to obtain the least squares solution in common factor analysis is presented. It is based on the up-and-down Marquadt algorithm developed by the present authors. Experiments in the use of the algorithm under various conditions are discussed. (Author/JKS)
Descriptors: Algorithms, Factor Analysis, Least Squares Statistics, Mathematical Models
Peer reviewed Peer reviewed
Kiers, Henk A. L.; ten Berge, Jos M. F. – Psychometrika, 1989
Two alternating least squares algorithms are presented for the simultaneous components analysis method of R. E. Millsap and W. Meredith (1988). These methods, one for small data sets and one for large data sets, can indicate whether or not a global optimum for the problem has been attained. (SLD)
Descriptors: Algorithms, Factor Analysis, Least Squares Statistics, Statistical Analysis
Peer reviewed Peer reviewed
Boik, Robert J. – Psychometrika, 1996
Joint correspondence analysis is a technique for constructing reduced-dimensional representations of pairwise relationships among categorical variables. An alternating least-squares algorithm for conducting joint correspondence analysis is presented that requires fewer iterations than the algorithm previously proposed by M. J. Greenacre. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Factor Analysis, Least Squares Statistics
Peer reviewed Peer reviewed
Nevels, Klaas – Psychometrika, 1989
In FACTALS, an alternating least squares algorithm is used to fit the common factor analysis model to multivariate data. A. Mooijaart (1984) demonstrated that the algorithm is based on an erroneous assumption. This paper gives a proper solution for the loss function used in FACTALS. (Author/TJH)
Descriptors: Algorithms, Factor Analysis, Goodness of Fit, Least Squares Statistics
Peer reviewed Peer reviewed
Goldberger, Arthur S.; Joreskog, Karl G. – Psychometrika, 1972
Descriptors: Algorithms, Factor Analysis, Least Squares Statistics, Mathematical Models
Peer reviewed Peer reviewed
ten Berge, Jos M. F.; Kiers, Henk A. L. – Psychometrika, 1989
The DEDICOM (decomposition into directional components) model provides a framework for analyzing square but asymmetric matrices of directional relationships among "n" objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straightforward computational solution…
Descriptors: Algorithms, Factor Analysis, Goodness of Fit, Least Squares Statistics
Peer reviewed Peer reviewed
Takane, Yoshio; And Others – Psychometrika, 1995
A model is proposed in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks. An algorithm is presented for fitting the model to the data by least squares. Examples demonstrate the method. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Factor Analysis, Least Squares Statistics
Peer reviewed Peer reviewed
DeLeeuw, Jan; Kroonenberg, Peter M. – Psychometrika, 1980
A new method to estimate the parameters of Tucker's three mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. An example is presented. (Author/JKS)
Descriptors: Algorithms, Factor Analysis, Least Squares Statistics, Measurement
Peer reviewed Peer reviewed
ten Berge, Jos M. F.; Kiers, Henk A. L. – Psychometrika, 1993
R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Factor Analysis, Least Squares Statistics
Peer reviewed Peer reviewed
van der Burg, Eeke; de Leeuw, Jan – Psychometrika, 1988
Homogeneity analysis (multiple correspondence analysis), which is usually applied to "k" separate variables, was applied to sets of variables by using sums within sets. The resulting technique, OVERALS, uses optimal scaling. The corresponding OVERALS computer program minimizes a least squares loss function via an alternating least…
Descriptors: Algorithms, Factor Analysis, Least Squares Statistics, Multidimensional Scaling
Peer reviewed Peer reviewed
Cudeck, Robert; Browne, Michael W. – Psychometrika, 1992
A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Estimation (Mathematics), Factor Analysis