A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decomposed has symmetric slices. We consider the case where two component matrices are randomly sampled…

This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

Least squares methods are sophisticated mathematical curve fitting procedures used in all classical parametric methods. The linear least squares approximation is most often associated with finding the "line of best fit" or the regression line. Since all statistical analyses are correlational and all classical parametric methods are least…

A simulation study was conducted to identify the best hot-deck variation to impute missing values. The three variations included in the study were the hot-deck random, the hot-deck sequential, and the hot-deck distance. The properties of these methods were investigated under three levels of the proportion of incomplete records and four levels…

A discussion of how a tensor theory can be adapted to provide a fully quantitative analysis of a social system. A social tensor is developed from the physical analogue and used to analyze the structure of an education course. (Author/HB)

Univocal varimax is an orthogonal factor rotation strategy aimed at improving upon the simple structure qualities of a preliminary varimax solution. This is accomplished by targetting for patterned rotation the highest element in each row of the varimax factor loading matrix. (Author)

It is shown that common factors are not subject to indeterminancy to the extent that has been claimed (Guttman, 1955), because the measure of indeterminancy that has been adopted is ill-founded. (Author/RC)

Heuristic methods for the construction of term classes are presented and experimental results are obtained to illustrate the usefulness of the method. (Author/PF)

Shows that the Harris factors of R have psychometric properties similar to those discussed by Kaiser and Caffrey (1965) and Bentler (1968). Specifically it is shown that the Harris factors of R maximize a lower-bound to the reliability of a composite measure derived by Guttman (1945). (Author/RC)

Factor structures of student ratings of instruction resulting from total group, between group, and within group analyses were compared. Six factors obtained from responses by students to 31 items were used to approximate the between group covariance matrix based on 437 classroom means and the pooled within classroom covariance matrix. (Author/BJG)

Over the years, a number of rationales have been advanced to solve the problem of "blind" oblique factor transformation. By blind transformation is meant the transformation of orthogonal--and often interpretively ineffectual--factors to a position usually dictated by Thurstone's principles of simple structure, but not influenced by a…

A Monte Carlo investigation of Markov chain matrices was conducted to create empirical distributions for two statistics created from the transition matrices. Curve fitting techniques developed by Karl Pearson were used to deduce if theoretical equations could be fit to the two sets of distributions. The set of distributions which describe the…

Criteria sets are a necessary step in the systematic development of evaluation in education. Evaluation results from the combination of criteria and evidence. There is a need to develop explicit tools for evaluating criteria, similar to those used in evaluating evidence. The formulation of such criteria depends on distinguishing between terms…

Standard errors for maximum likelihood estimates of factor loadings are expressed in terms of the inverse of an augmented information matrix. This formulation arises naturally by viewing the problem as one in constrained maximum likelihood estimation. The constraints correspond to the form of rotation used. Results are given for canonical rotation…