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Hafner, Robert – Psychometrika, 1981
The method proposed by Harman and Fukuda to treat the so-called Heywood case in the minres method in factor analysis (i.e., the case where the resulting communalities are greater than one) involves the frequent solution of eigenvalue problems. A simple method to treat this problem is presented. (Author/JKS)
Descriptors: Algorithms, Data Analysis, Factor Analysis

Klauer, Karl Christoph – Psychometrika, 1989
Concepts of ordinal network representation are discussed. Notation (the type of data that can be represented) and the type of representation given are reviewed. The idea of reduced ordinal networks is explored; and the algorithm, uniqueness results, and error handling problems are presented. Examples of data analysis are included. (SLD)
Descriptors: Algorithms, Data Analysis, Data Interpretation, Graphs

Kiers, Henk A. L.; And Others – Psychometrika, 1990
An algorithm is described for fitting the DEDICOM model (proposed by R. A. Harshman in 1978) for the analysis of asymmetric data matrices. The method modifies a procedure proposed by Y. Takane (1985) to provide guaranteed monotonic convergence. The algorithm is based on a technique known as majorization. (SLD)
Descriptors: Algorithms, Data Analysis, Generalizability Theory, Matrices

Kiers, Henk A. L. – Psychometrika, 1995
Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Matrices, Multivariate Analysis

Kiers, Henk A. L.; Groenen, Patrick – Psychometrika, 1996
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)
Descriptors: Algorithms, Comparative Analysis, Matrices, Orthogonal Rotation

Kiers, Henk A. – Psychometrika, 1990
General algorithms are presented that can be used for optimizing matrix trace functions subject to certain constraints on the parameters. The parameter set that minimizes the majorizing function also decreases the matrix trace function, providing a monotonically convergent algorithm for minimizing the matrix trace function iteratively. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Least Squares Statistics, Matrices

Mooijaart, Ab; van der Heijden, Peter G. M. – Psychometrika, 1992
It is shown that it is not easy to apply the EM algorithm to latent class models in the general case with equality constraints because a nonlinear equation has to be solved. A simpler condition is given in which the EM algorithm can be easily applied. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Estimation (Mathematics), Mathematical Models

Ponocny, Ivo – Psychometrika, 2000
Introduces a new algorithm for obtaining exact person fit indexes for the Rasch model. The algorithm realizes most tests for a general family of alternative hypotheses, including tests concerning differential item functioning. The method is also used as a goodness-of-fit test in some circumstances. Simulated examples and an empirical investigation…
Descriptors: Algorithms, Goodness of Fit, Item Bias, Simulation

Waller, Niels G.; Kaiser, Heather A.; Illian, Janine B.; Manry, Mike – Psychometrika, 1998
The classification capabilities of the one-dimensional Kohonen neural network (T. Kohonen, 1995) were compared with those of two partitioning and three hierarchical cluster methods in 2,580 data sets with known cluster structure. Overall, the performance of the Kohonen networks was similar to, or better than, that of the others. Implications for…
Descriptors: Algorithms, Classification, Cluster Analysis, Comparative Analysis

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

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

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

Winsberg, Suzanne; Carroll, J. Douglas – Psychometrika, 1989
An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model that assumes both common and specific dimensions is described and contrasted with the "standard" (Two-Way) MDS model. Illustrations with both artificial and real data on the judged similarity of nations are provided. (TJH)
Descriptors: Algorithms, Chi Square, Maximum Likelihood Statistics, Multidimensional Scaling

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

Rindskopf, David – Psychometrika, 1992
A general approach is described for the analysis of categorical data when there are missing values on one or more observed variables. The method is based on generalized linear models with composite links. Situations in which the model can be used are described. (SLD)
Descriptors: Algorithms, Classification, Data Analysis, Estimation (Mathematics)