A method is proposed for comparison of distinct partitions of the same set of n objects through a simple cross-product index defined between corresponding entries from two proximity matrices providing particular a priori codings of the within-class and between-class relationships for the partitions. (SLD)

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…

Described herein are formulas and computational procedures for estimating the mean and second through fourth central moments of universe scores through multiple matrix sampling. Additionally, procedures are given for approximating the standard error associated with each estimate. All procedures are applicable when items are scored either…

ORDMET is applicable to structures obtained from additive conjoint measurement designs, unfolding theory, general Fechnerian scaling, types of multidimensional scaling, and ordinal multiple regression. A description is obtained of the space containing all possible numerical representations which can satisfy the structure, size, and shape of which…

Although the issue of dimensionality of the data obtained from educational and psychological tests has received considerable attention, the terms "unidimensional" and "multidimensional" have not been used very precisely. One use of the term dimensionality is to refer to the number of hypothesized psychological constructs…

Standard errors of pooled mean estimate in multiple matrix sampling were compared for two procedures. The data were from tests involving items with and without replacement. The two procedures involve the formulations of Madow and Lord, and Novick; the former permits sampling of item, with or without replacement, whereas the latter is to be used…

Extending the definitions of part and bipartial correlation to sets of variates, the notion of part and bipartial canonical correlation analysis are developed and illustrated. (Author)

Presents an exposition of two data reduction methods--single-link and complete-link hierarchical clustering. Emphasis is on statistical techniques for evaluating the adequacy of a completed partition hierarchy and the individual partitions within the sequence. A numerical reanalysis of data illustrates the methodology. (RC)

Two applications of Kristof's theorem on traces of matrix products are presented in order to highlight their utility for psychometric theory and studies. (Author/JKS)

Estimates of the internal consistency and reliability of the first principal component are provided through the use of the largest characteristic root and associated vector of the equicorrelation matrix. The estimate of the internal consistency is also shown to be a lower bound for the measure provided by Horn (1969). (Author)

The fundamental problems that ipsative measures impose for factor analysis are shown analytically. Normative and ipsative correlation matrices are used to show that the factor pattern induced by ipsativity will overwhelm any factor structure seen with normative factor analysis, making factor analysis not interpretable. (SLD)

A "doubly-centered" raw data matrix is one for which both columns and rows have both unit variance and means equal to zero. The factor scores from one analysis are the same as factor pattern coefficients from the other analysis except for a variance adjustment. This study explored an extension of the reciprocity principle which may have…