Develops a model of mathematical learning from an exploration of educational research and personal observations. Uses Kolb's model of experiential learning to characterize four mathematical learning styles: (1) allegorizers; (2) integrators; (3) analyzers; and (4) synthesizers. These styles are viewed as corresponding to four stages of…

Presents an overview of Rasch measurement models that begins with a conceptualization of continuous experiences often captured as discrete observations. Discusses the mathematical properties of the Rasch family of models that allow the transformation of discrete deterministic counts into continuous probabilistic abstractions. Also discusses six of…

A method based on homogeneity analysis (multiple correspondence analysis or multiple scaling) is proposed to reduce many categorical variables to one variable with "k" categories. The method is a generalization of the sum of squared distances cluster analysis problem to the case of mixed measurement level variables. (SLD)

This note shows that the formula suggested by N. D. Bryant and S. Gokhale (1972) for correcting indirectly restricted correlations when no information is available on the third (directly restricted) variable is accurate only in one special instance. A more general correction formula is illustrated. (SLD)

Means of identifying sources of rejection of hypotheses regarding linear multivariate statistical models are discussed. Problems with the use of a global test using Roy's largest root criterion and means of solving them are presented, along with a practical application of the techniques. (TJH)

A model which approaches the problem of characterizing distributions of test validity correlation coefficients from the perspective of finite mixture theory is presented. This estimation method offers advantages over validity generalization procedures. Examples are provided to illustrate applications of the method. (SLD)

The structure of information matrices in latent-variable models is explicated, and the degree to which missing information can be recovered by exploring collateral variables for respondents is characterized. Results are illustrated in the context of item-response-theory models, and practical implications are discussed. (SLD)

The power of the likelihood ratio test in multiple group confirmatory factor analysis under partial measurement invariance was studied in a population study with a six-variable, two-factor model where a specification error existed for one group. Results are discussed in terms of strategies of multiple group modeling. (SLD)

With reference to the authors' previous paper (1985), it is proposed that loglinear analysis can be used to detect interactions in a multiway contingency table and explore the form of these interactions with correspondence analysis. Correspondence analysis assists in finding a model with restrictions on the interaction parameters. (TJH)

A summary and a unified treatment of fully general computational solutions for two criteria for transforming two or more matrices to maximal agreement are provided. The two criteria--Maxdiff and Maxbet--have applications in the rotation of factor loading or configuration matrices to maximal agreement and the canonical correlation problem. (SLD)

Proposes a cost/benefit model coupled with a decision tree for determining normal forms, which are used in information systems development processes to group data into well-refined structures. The three primary variables that impact the benefits and costs of normalization (reduced anomalies, storage requirements, and transaction response times)…

Proposes a mathematical model to incorporate the strengths of both the classic approach to agenda-setting research and the time-series technique. Tests the model with data on three issues. Finds both mutual competition and one-way attraction among issues. (SR)

The perturbation theory of the generalized eigenproblem is used to derive influence functions of each squared canonical correlation coefficient and the corresponding canonical vector pair. Three sample versions of these functions are described, and some properties are noted. Two obvious applications, multiple correlation and correspondence…

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)

Discusses information production processes (IPP)--i.e., continuous mathematical models of production processes such as bibliographies, economic production processes, and social usages of words in a text--from the point of view of concentration theory. Gini's index is studied in the dual framework of IPPs. (27 references) (LRW)