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Borg, Ingwer – Psychometrika, 1978
Procrustean analysis is a form of factor analysis where a target matrix of results is specified and then approximated. Procrustean analysis is extended here to the case where matrices have different row order. (Author/JKS)
Descriptors: Correlation, Factor Analysis, Mathematical Models, Matrices
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Halperin, Silas – Educational and Psychological Measurement, 1976
Component analysis provides an attractive alternative to factor analysis, since component scores are easily determined while factor scores can only be estimated. The correct method of determining component scores is presented as well as several illustrations of how commonly used incorrect methods distort the meaning of the component solution. (RC)
Descriptors: Factor Analysis, Mathematical Models, Matrices, Scores
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MacCallum, Robert C. – Psychometrika, 1977
The role of conditionality in the INDSCAL and ALSCAL multidimensional scaling procedures is explained. The effects of conditionality on subject weights produced by these procedures is illustrated via a single set of simulated data. Results emphasize the need for caution in interpreting subject weights provided by these techniques. (Author/JKS)
Descriptors: Individual Differences, Mathematical Models, Multidimensional Scaling, Statistical Analysis
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Burrell, Quentin L. – Journal of Documentation, 1988
Proposes a probabilistic mechanism to describe various forms of the Bradford phenomenon reported in bibliographic research. The inclusion of a time parameter in the model to allow predictions of dynamic systems is explained. (58 references) (CLB)
Descriptors: Bibliometrics, Mathematical Models, Prediction, Probability
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Bozdogan, Hamparsum – Psychometrika, 1987
This paper studies the general theory of Akaike's Information Criterion (AIC) and provides two analytical extensions. The extensions make AIC asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the two models. The criteria are applied in two Monte Carlo experiments. (Author/GDC)
Descriptors: Evaluation Criteria, Mathematical Models, Monte Carlo Methods, Selection
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Tate, Richard L.; Bryant, John L. – Multivariate Behavioral Research, 1986
The shape of the response surface associated with a discriminant analysis provides insight into the value of the derived optimal discriminant variates. A procedure for the determination of "indifference regions," presented in this article, allows the assessment of the degree of flatness of the response surface for any analysis.…
Descriptors: Discriminant Analysis, Mathematical Models, Multivariate Analysis, Statistical Studies
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Everitt, B. S. – Multivariate Behavioral Research, 1984
Latent class analysis is formulated as a problem of estimating parameters in a finite mixture distribution. The EM algorithm is used to find the maximum likelihood estimates, and the case of categorical variables with more than two categories is considered. (Author)
Descriptors: Algorithms, Estimation (Mathematics), Mathematical Models, Maximum Likelihood Statistics
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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
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Van de Geer, John P. – Psychometrika, 1984
A family of solutions for linear relations among k sets of variables is proposed. Solutions are compared with respect to their optimality properties. For each solution the appropriate stationary equations are given. For one example it is shown how the determinantal equation of the stationary equations can be interpreted. (Author/BW)
Descriptors: Correlation, Mathematical Models, Multiple Regression Analysis, Orthogonal Rotation
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Kelderman, Hendrikus – Psychometrika, 1984
The assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. Using ordinary contingency table methods, the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions. (Author/BW)
Descriptors: Goodness of Fit, Latent Trait Theory, Mathematical Models
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Otter, Pieter W. – Psychometrika, 1986
In this paper the parameter identifiability and estimation of a general dynamic structural model under indirect observation is considered from a system theoretic perspective. (Author/LMO)
Descriptors: Estimation (Mathematics), Factor Analysis, Mathematical Models, Statistical Studies
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Rae, Gordon – Educational and Psychological Measurement, 1984
Various indices for measuring agreement among several raters on the presence or absence of a trait can be interpreted as intraclass correlation coefficients. Such a reformulation clarifies the relationships among the measures, simplifies the computations involved, and permits simple significance tests to be carried out. An illustrative example is…
Descriptors: Correlation, Mathematical Models, Observation, Research Methodology
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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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Marascuilo, Leonard A.; Levin, Joel R. – American Educational Research Journal, 1976
An alternative is proposed to the usual Interaction and Nested Analysis of Variance (ANOVA) models by which a researcher will be able to investigate both interaction and nested questions in the same experiment without committing Type IV errors. (RC)
Descriptors: Analysis of Variance, Hypothesis Testing, Interaction, Mathematical Models
McCamey, Randy – 2002
The Rasch measurement model improves on traditional test construction by creating tests in which the person's ability is independent of the sample of items used and the norm group used to calibrate the test. This paper reviews the Rasch model by describing properties of the item characteristic curve (ICC) and discussing the utility of having…
Descriptors: Ability, Item Response Theory, Mathematical Models, Test Construction
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