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Moonan, William J. – 1975
The purposes of the paper were to develop a structure by which assessment models could be uniquely characterized and to develop assessment models and their associated computer programs which could be used for personnel research purposes. To these ends two aspects of assessment, measurement and evaluation, were identified. Their distinction was…
Descriptors: Computer Programs, Mathematical Models, Measurement Techniques, Personnel Evaluation

Levy, Kenneth J. – Educational and Psychological Measurement, 1976
Marascuilo (1966) proposes a chi square analog of Scheffe's multiple comparisons procedure. With respect to pairwise comparisons among k independent correlation coefficients, a multiple range procedure will produce lower critical values than the corresponding chi square values, thereby increasing the power of the resulting tests. Basis of the…
Descriptors: Analysis of Variance, Correlation, Mathematical Models, Statistical Significance

Epstein, D. J.; Smith, A. C. – American Journal of Physics, 1979
Discusses the paradoxes that can result when physical examples lead to infinite series. Two examples are presented: the Madelung energy of a one-dimensional array of alternating positive and negative charges, and a point charge between infinite parallel plates. (BB)
Descriptors: Mathematical Models, Mathematics, Physics, Science Education

Walton, Joseph M.; And Others – Multiple Linear Regression Viewpoints, 1978
Ridge regression is an approach to the problem of large standard errors of regression estimates of intercorrelated regressors. The effect of ridge regression on the estimated squared multiple correlation coefficient is discussed and illustrated. (JKS)
Descriptors: Correlation, Mathematical Models, Multiple Regression Analysis, Predictor Variables

Brookes, Bertram C.; Griffiths, Jose M. – Journal of the American Society for Information Science, 1978
Frequency, rank, and frequency rank distributions are defined. Extensive discussion on several aspects of frequency rank distributions includes the Poisson process as a means of exploring the stability of ranks; the correlation of frequency rank distributions; and the transfer coefficient, a new measure in frequency rank distribution. (MBR)
Descriptors: Comparative Analysis, Correlation, Definitions, Laws

Cicchetti, Domenic V.; Fleiss, Joseph L. – Applied Psychological Measurement, 1977
The weighted kappa coefficient is a measure of interrater agreement when the relative seriousness of each possible disagreement can be quantified. This monte carlo study demonstrates the utility of the kappa coefficient for ordinal data. Sample size is also briefly discussed. (Author/JKS)
Descriptors: Mathematical Models, Rating Scales, Reliability, Sampling

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

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

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

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

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

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

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

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

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