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ten Berge, Jos M. F.; Kiers, Henk A. L. – Psychometrika, 1989
Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution that need not be centered row-wise. The results bear directly on several types of preprocessing methods in Parafac/Candecomp. (Author/TJH)
Descriptors: Correlation, Equations (Mathematics), Mathematical Models, Matrices
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Zegers, Frits E.; ten Berge, Jos M. F. – Psychometrika, 1985
Four types of metric scales are distinguished: absolute, ratio, difference, and interval. A general coefficient of association for two variables of the same scale type is developed which reduces to specific coefficients of association for each scale type. (NSF)
Descriptors: Correlation, Mathematical Models, Scaling, Test Theory
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Fagot, Robert F. – Psychometrika, 1993
A family of coefficients of relational agreement for numerical scales is proposed, generalizing to multiple judges the theory of F. E. Zegers and J. M. F. ten Berge (1985) of association coefficients for two variables, using the premise that choice of coefficient depends on scale type of the variables. (SLD)
Descriptors: Correlation, Equations (Mathematics), Evaluators, Generalizability Theory
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Tzeng, Oliver C. S.; Landis, Dan – Multivariate Behavioral Research, 1978
Two popular models for performing multidimensional scaling, Tucker and Messick's points-of-view model, and Tucker's three mode model, are combined into a single analytic procedure, the 3M-POV model. The procedure is described and its strengths are discussed. Carroll and Chang's INDSCAL model is also mentioned. (JKS)
Descriptors: Correlation, Item Analysis, Mathematical Models, Multidimensional Scaling
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Vooijs, Marcel W.; Van der Kamp, Leo J. T. – Evaluation Review, 1991
A two-step procedure is developed for the analysis of pretest-posttest data. Nonlinear canonical correlation analysis is followed by covariance analysis of optimally scaled pretest and posttest measures. The procedure is available in the computer program CANALS. Advantages of the two-step procedure are discussed. (SLD)
Descriptors: Analysis of Covariance, Comparative Analysis, Computer Software, Correlation
Peer reviewed Peer reviewed
De Ayala, R. J.; Hertzog, Melody A. – Multivariate Behavioral Research, 1991
Multidimensional scaling (MDS) and exploratory and confirmatory factor analyses were compared in the assessment of the dimensionality of data sets, using sets generated to be one-dimensional or two-dimensional and differing in degree of interdimensional correlation and number of items defining a dimension. (SLD)
Descriptors: Comparative Analysis, Correlation, Equations (Mathematics), Factor Structure
Peer reviewed Peer reviewed
Fava, Joseph L.; Velicer, Wayne F. – Multivariate Behavioral Research, 1992
Principal component, image component, three types of factor score estimates, and one scale score method were compared over different levels of variables, saturations, sample sizes, variable to component ratios, and pattern rotations. There were virtually no overall differences among methods, with the average correlation between matched scores…
Descriptors: Comparative Analysis, Correlation, Equations (Mathematics), Estimation (Mathematics)
Baker, Frank B.; Hoyt, Cyril J. – 1972
A scaling technique known as the Method of Reciprocal Averages has been in use since the early 1930's. This technique yields a set of item response weights for a psychological inventory which maximizes the internal consistency of the inventory for a group of subjects. Although the technique has been used for many years, its mathematical…
Descriptors: Analysis of Variance, Correlation, Evaluation Methods, Item Analysis
Peer reviewed Peer reviewed
van Buuren, Stef; van Rijckevorsel, Jan L. A. – Psychometrika, 1992
A technique is presented to transform incomplete categorical data into complete data by imputing appropriate scores into missing cells. A solution of the optimization problem is suggested, and relevant psychometric theory is discussed. The average correlation should be at least 0.50 before the method becomes practical. (SLD)
Descriptors: Classification, Computer Simulation, Correlation, Equations (Mathematics)
Peer reviewed Peer reviewed
Davison, Mark L. – Psychometrika, 1976
Proposes a quadratic programming, least squares solution to Carroll's weighted unfolding model with nonnegativity constraints imposed on weights. It can be used to test various hypotheses about the weighted unfolding model with or without constraints. (RC)
Descriptors: Algorithms, Correlation, Goodness of Fit, Hypothesis Testing
Bart, William M.; Airasian, Peter W. – 1976
The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…
Descriptors: Comparative Analysis, Correlation, Factor Analysis, Factor Structure
Chan, Jason C. – 1991
The following seven statistical procedures are compared in terms of the ability to recover a unidimensional latent trait from Likert-type data: (1) factor analysis based on Pearson correlations (FA-PR); (2) factor analysis based on polychoric correlations (FA-PL); (3) the graded response model in item response theory (IRT-GRM); (4) internal…
Descriptors: Comparative Analysis, Computer Simulation, Correlation, Equations (Mathematics)
Jones, Patricia B.; And Others – 1987
In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…
Descriptors: Cluster Analysis, Correlation, Difficulty Level, Error of Measurement
Zwick, Rebecca – 1986
Although perfectly scalable items rarely occur in practice, Guttman's concept of a scale has proved to be valuable to the development of measurement theory. If the score distribution is uniform and there is an equal number of items at each difficulty level, both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous…
Descriptors: Correlation, Difficulty Level, Item Analysis, Latent Trait Theory
Paulson, James A. – 1985
This paper discusses the use of latent class structure as a modelling framework for tests in which much of the data conforms to a relatively small number of systematic patterns. Application of this framework to the analysis of tests has been limited because available parameter estimation algorithms can only handle a relatively small number of…
Descriptors: Algorithms, Correlation, Estimation (Mathematics), Factor Analysis
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