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Rhodes, Frank; And Others – Math Gaz, 1970
Descriptors: College Mathematics, Geometric Concepts, Geometry, Instruction
Peer reviewed Peer reviewed
Ferligoj, Anuska; Batagelj, Vladimir – Psychometrika, 1982
Using constraints with cluster analysis limits the possible number of clusters. This paper deals with clustering problems where grouping is constrained by a symmetric and reflexive relation. Two approaches, along with illustrations, are presented. (Author/JKS)
Descriptors: Algorithms, Cluster Analysis, Data Analysis, Mathematical Models
Peer reviewed Peer reviewed
Desarbo, Wayne S. – Psychometrika, 1982
A general class of nonhierarchical clustering models and associated algorithms for fitting them are presented. These models generalize the Shepard-Arabie Additive clusters model. Two applications are given and extensions to three-way models, nonmetric analyses, and other model specifications are provided. (Author/JKS)
Descriptors: Algorithms, Cluster Analysis, Data Analysis, Mathematical Models
Peer reviewed Peer reviewed
Cressie, Noel; Holland, Paul W. – Psychometrika, 1983
The problem of characterizing the manifest probabilities of a latent trait model is considered. The approach taken here differs from the standard approach in that a population of examinees is being considered as opposed to a single examinee. Particular attention is given to the Rasch model. (Author/JKS)
Descriptors: Guessing (Tests), Item Analysis, Latent Trait Theory, Mathematical Models
Peer reviewed Peer reviewed
Holling, Heinz – Educational and Psychological Measurement, 1983
Recent theoretical analyses of the concept of suppression are identified and discussed. A generalized definition of suppression is presented and the conditions for suppressor structures in the context of the General Linear Model are derived. (Author)
Descriptors: Mathematical Models, Multiple Regression Analysis, Research Methodology, Statistical Analysis
Peer reviewed Peer reviewed
Gerbing, David W.; Hunter, John E. – Educational and Psychological Measurement, 1982
In a LISREL-IV analysis, a method of specifying a priori the variances of the latent variables for interpretability is demonstrated. The potential confusion of the metric of the latent variables is discussed, since many of the parameter estimates are a function of the metric. (Author/CM)
Descriptors: Computer Programs, Factor Analysis, Mathematical Models, Maximum Likelihood Statistics
Peer reviewed Peer reviewed
Raju, Nambury S. – Educational and Psychological Measurement, 1982
A necessary and sufficient condition for a perfectly homogeneous test in the sense of Loevinger is stated and proved. Using this result, a formula for computing the maximum possible KR-20 when the test variance is assumed fixed is presented. A new index of test homogeneity is also presented and discussed. (Author/BW)
Descriptors: Mathematical Formulas, Mathematical Models, Multiple Choice Tests, Test Reliability
Peer reviewed Peer reviewed
Pruzek, Robert M.; Rabinowitz, Stanley N. – American Educational Research Journal, 1981
Simple modifications of principal component methods are described that have distinct advantages for structural analysis of relations among educational and psychological variables. The methods are contrasted theoretically and empirically with conventional principal component methods and with maximum likelihood factor analysis. (Author/GK)
Descriptors: Factor Analysis, Mathematical Models, Maximum Likelihood Statistics, Multivariate Analysis
Peer reviewed Peer reviewed
Cattell, Raymond B. – Multivariate Behavioral Research, 1982
A data analysis model is proposed for studies concerning attribution theory. The model is based on the author's previous work in the area of trait view theory. (JKS)
Descriptors: Attribution Theory, Data Analysis, Individual Differences, Mathematical Models
Peer reviewed Peer reviewed
Melzer, Charles W.; And Others – Educational and Psychological Measurement, 1981
The magnitude of statistical bias for the phi-coefficient was investigated, using computer simulated examinations in which all the students had equal knowledge. Several modifications of phi were tested, but when applied to real examinations, none succeeded in improving its reproducibility when items are re-used on equivalent student groups.…
Descriptors: Correlation, Item Analysis, Mathematical Models, Multiple Choice Tests
Peer reviewed Peer reviewed
DeSarbo, Wayne S. – Psychometrika, 1981
Canonical correlation and redundancy analysis are two approaches to analyzing the interrelationships between two sets of measurements made on the same variables. A component method is presented which uses aspects of both approaches. An empirical example is also presented. (Author/JKS)
Descriptors: Correlation, Data Analysis, Factor Analysis, Mathematical Models
Peer reviewed Peer reviewed
Perline, Richard; And Others – Applied Psychological Measurement, 1979
Rasch's psychometric model is presented as a special case of additive conjoint measurement. Two data sets, each of which was analyzed using Rasch scaling methods as well as some of the methods of conjoint measurement, are compared. (Author/JKS)
Descriptors: Comparative Analysis, Mathematical Models, Measurement Techniques, Psychometrics
Peer reviewed Peer reviewed
Thomas, Hoben – Psychometrika, 1981
Psychophysicists neglect to consider how error should be characterized in applications of the power law. Failures of the power law to agree with certain theoretical predictions are examined. A power law with lognormal product structure is proposed and approximately unbiased parameter estimates given for several common estimation situations.…
Descriptors: Mathematical Models, Power (Statistics), Psychophysiology, Statistical Bias
Peer reviewed Peer reviewed
Huynh, Huynh – Journal of Educational Statistics, 1981
Simulated data based on five test score distributions indicate that a slight modification of the asymptotic normal theory for the estimation of the p and kappa indices in mastery testing will provide results which are in close agreement with those based on small samples from the beta-binomial distribution. (Author/BW)
Descriptors: Error of Measurement, Mastery Tests, Mathematical Models, Test Reliability
Peer reviewed Peer reviewed
Teece, David J. – Management Science, 1980
Explains the diffusion of an innovative administrative structure (the "M-Form") by using a simple deterministic model commonly employed to represent the diffusion of technological innovations. The performance of the model suggests that additional insights from the study of technological innovation can be applied to the study of…
Descriptors: Administration, Administrative Organization, Adoption (Ideas), Diffusion
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