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Voskoglou, Michael Gr. – International Journal of Mathematical Education in Science and Technology, 2010
We represent the main stages of the process of mathematical modelling as fuzzy sets in the set of the linguistic labels of negligible, low intermediate, high and complete success by students in each of these stages and we use the total possibilistic uncertainty as a measure of students' modelling capacities. A classroom experiment is also…
Descriptors: Mathematical Models, Experiments, Markov Processes, Matrices
Rozeboom, William W. – Multivariate Behavioral Research, 2009
The topic of this article is the interpretation of structural equation modeling (SEM) solutions. Its purpose is to augment structural modeling's metatheoretic resources while enhancing awareness of how problematic is the causal significance of SEM-parameter solutions. Part I focuses on the nonuniqueness and consequent dubious interpretability of…
Descriptors: Structural Equation Models, Equations (Mathematics), Matrices, Probability
Bonacich, Phillip; Bienenstock, Elisa Jayne – Social Psychology Quarterly, 2009
This paper presents and tests a general model to predict emergent exchange patterns and power differences in reciprocal exchange networks when individual actors follow the norm of reciprocity. With an interesting qualification, the experimental results reported here support the power-dependence approach (Emerson 1972a, b): those who acquire the…
Descriptors: Interpersonal Communication, Power Structure, Prediction, Interpersonal Relationship

ten Berge, Jos M. F. – Psychometrika, 1991
The phenomenon of 2 x 2 x 2 arrays having nonmaximal rank with positive probability, pointed out by J. Kruskal (1989), is generalized to 2 x "n" x "n" arrays. It is concluded that a pair of asymmetric square matrices can be diagonalized simultaneously with positive probability. (SLD)
Descriptors: Equations (Mathematics), Generalization, Mathematical Models, Matrices

Eaves, David – Journal of Multivariate Analysis, 1976
Vector sum of a white noise in an unknown hyperspace and an Ornstein-Uhlenbeck process in an unknown line is observed through sharp linear test functions over a finite time span. Parameters associated with white noise are determinable and index measure-equivalence classes in relevant sample space. Intraclass relative density provides a basis for…
Descriptors: Analysis of Covariance, Bayesian Statistics, Diffusion, Mathematical Models

Snijders, Tom A. B. – Psychometrika, 1991
A complete enumeration method and a Monte Carlo method are presented to calculate the probability distribution of arbitrary statistics of adjacency matrices when these matrices have the uniform distribution conditional on given row and column sums, and possibly on a given set of structural zeros. (SLD)
Descriptors: Computer Simulation, Equations (Mathematics), Mathematical Models, Matrices

Rennie, Robert R.; Villegas, C. – Journal of Multivariate Analysis, 1976
An asymptotic theory is developed for a new time series model introduced in TM 502 289. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in that they have the same asymptotic distribution as the maximum likelihood estimators. (Author/RC)
Descriptors: Algorithms, Analysis of Covariance, Mathematical Models, Matrices

van der Linden, Wim J. – Applied Psychological Measurement, 1979
The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)
Descriptors: Difficulty Level, Item Sampling, Latent Trait Theory, Mathematical Models
Dinero, Thomas E.; Haertel, Edward – 1976
This paper will discuss the results of a series of computer simulations comparing the Rasch logistic model to a series of models departing to various degrees from its assumption of equal discrimination power for all items. The results have implications for test construction and test scoring, indicating how closely the conventional raw score…
Descriptors: Comparative Analysis, Computer Programs, Goodness of Fit, Individual Differences
Brigman, S. Leellen; Bashaw, W. L. – 1976
Procedures are presented for equating simultaneously several tests which have been calibrated by the Rasch Model. Three multiple test equating designs are described. A Full Matrix Design equates each test to all others. A Chain Design links tests sequentially. A Vector Design equates one test to each of the other tests. For each design, the Rasch…
Descriptors: Ability, Achievement Tests, Computer Programs, Equated Scores

Gardner, William – Psychometrika, 1990
This paper provides a method for analyzing data consisting of event sequences and covariate observations associated with Markov chains. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. (TJH)
Descriptors: Cognitive Development, Equations (Mathematics), Estimation (Mathematics), Individual Differences
Moonan, William J. – 1974
The purpose of this paper is to lay a basis for and discuss the components of a system, called COMET, designed to objectively measure and evaluate the competency of trainees in military training enterprises. COMET is an acronym for "Computerized Objective Measurement and Evaluation of Trainees." These goals will be accomplished by: (a)…
Descriptors: Computer Programs, Goodness of Fit, Item Analysis, Mathematical Models
Aims, Doug – 1971
A Markov model for predicting performance on criterion-referenced tests is presented,. The model is expressed mathematically as a function of transition matrix, a current state vector, and a future state vector. The matrix is defined in terms of conditional probabilities, i.e., the probability of making a transition to a specific future…
Descriptors: Bayesian Statistics, Criterion Referenced Tests, Decision Making, Mastery Tests
Besel, Ronald – 1971
The Mastery-Learning test model is extended. Methods for estimating prior probabilities are described. The use of an adjustment matrix to transform a probability of mastery measure and empirical methods for estimating adjustment matrix parameters are derived. Adjustment matrices are interpreted as indicators of instructional effectiveness and as…
Descriptors: Criterion Referenced Tests, Decision Making, Groups, Individual Testing