Presents a mathematical model utilizing three-letter codes of personality patterns determined from the Self Directed Search. This model compares personality types over time or determines relationships between personality types and person-environment interactions. This approach is consistent with Holland's theory yet more comprehensive than one- or…

Path analysis is defined for explicitly formulating theory, and for attaching quantitative estimates to causal effects thought to exist on a priori grounds. The four basic kinds of path models are illustrated: (1) recursive; (2) block; (3) block-recursive and (4) nonrecursive. (Author/GDC)

A discussion is presented concerning variables associated with children's representation of certain addition and subtraction problems. Problem components are classified as physical, pictorial, sensual, verbal-spoken, verbal-written, symbolic, or internal. Problems are discussed as abstract (symbolic) or nonsymbolic. Three problem components are…

A maximum likelihood method of estimating the parameters of the multiple factor model when data are missing from the sample is presented. A Monte Carlo study compares the method with five heuristic methods of dealing with the problem. The present method shows some advantage in accuracy of estimation. (Author/CTM)

Presents the bivariate normal probability distribution as a method for estimating the prevalence of giftedness. The bivariate model requires the specification of two cutoff values for two selection variables and information regarding the size of the correlations between variables. The use and interpretation of bivariate estimates is discussed.…

A three-dimensional theory of frustration-aggression is presented. It is proposed that aggressiveness can be measured by computing the kinetic energy of a response. Aggressiveness is equated with energy state. Experimental and laboratory procedures are outlined. (Author/BEF)

Explains the phenomenon of Brownian motion, which serves as a mathematical model for random processes. Topics addressed include kinetic theory, Einstein's theory, particle displacement, and others. Points out that observations of the random course of a particle suspended in fluid led to the first accurate measurement of atomic mass. (DH)

A modified beta binomial model is presented for use in analyzing random guessing multiple choice tests and taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented.…

Review of recent developments in statistical theories for social sciences highlights Haitun's statistical distributions, Laplace's "Law of Succession" and distribution, Laplace and Bradford analysis of book-index data, inefficiency of frequency distribution analysis, Laws of Bradford and Zipf, natural categorization, and Bradford Law and…

A model which gives maximum likelihood estimates of measurement error within the context of a simplex model for practice effects is presented. The appropriateness of the model is tested for five traits, and error estimates are compared to the classical formula estimates. (Author/JKS)

This paper demonstrates how the problem of calibrating measures can be formulated in terms of confirmatory factor analysis. The relationships between traditional approaches and a confirmatory factor approach are specified. (Author/CTM)

Discusses the use of computer programs in science and mathematics. Provides examples of how computation offers a new means of describing and investigating scientific and mathematical systems and how computer simulation can be used to examine new kinds of models for natural phenomena. (JN)

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. (Author/CTM)

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)

Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…