An empirical assesssment of the space distortion properties of two prototypic hierarchical clustering procedures is given in terms of an occupancy model developed from combinatorics. Using one simple example, the single-link and complete-link clustering strategies now in common use in the behavioral sciences are empirically shown to be space…

A study was made of the problem of representing the expectations of mean squares associated with analysis of variance sources of variation for experimental designs. These designs have a factorial structure over repeated measures or, for some other reason, have variates within a factorial design not all of which are mutually independent. A simple…

The relationship of sample size to number of variables in the use of factor analysis has been treated by many investigators. In attempting to explore what the minimum sample size should be, none of these investigators pointed out the constraints imposed on the dimensionality of the variables by using a sample size smaller than the number of…

Multivariate models are demonstrated to analyze repeated measures profile and growth curve data when univariate or multivariate mixed model assumptions are not tenable. Standard mixed model tests are recovered from certain multivariate hypotheses. The procedures are illustrated using numerical examples. (Author/RC)

Investigated empirically through post mortem item-examinee sampling were the relative merits of two alternative procedures for allocating items to subtests in multiple matrix sampling and the feasibility of using the jackknife in approximating standard errors of estimate. The results indicate clearly that a partially balanced incomplete block…

A rigorous definition for a factor analysis model and a complete solution of the factor score indeterminacy problem are presented in this technical paper. The meaning and application of these results are discussed. (Author/JKS)

Two statements concerning magic squares, considered as 3x3 matrices, are discussed and their proofs given using only high school level techniques. (MP)

The use of matrix sampling to overcome the impracticality of the pair comparison method for obtaining scale values is empirically tested. Results indicate that matrix sampling is useful in such applications. (Author/JKS)

Principal components analysis is generalized to the case where any of the variables under consideration can be nominal, ordinal or interval. Hotelling's original formulation is seen to be a special case of this generalization. (JKS)

A group of factor analytic rotation procedures are developed which yield both hyperplane fittings and oblique Procrustean analyses as special cases. It is generally supposed that these techniques are rather different in approach. Illustrations are presented and discussed. (Author/JKS)

Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.…

An algorithm for assessing the correspondence of one or more attribute rating variables to a symmetric matrix of dissimilarities is presented. It is useful as an alternative to fitting property variables into a multidimensional scaling space. The relation between the matrix and the variables is determined by evaluating pairs of pairs relations.…

This study formulates a property of a quantification method, the principle of equivalent partitioning. When used with Guttman's principle of internal consistency, the combination allows the analysis of correlational data in terms of the variate(s) chosen by the investigator. Applications to multiple-choice, rank-order, and paired comparison data…

The extension of regression estimation and poststratification to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISTREL framework. (Author/LMO)

This paper focuses on making specific connections between basic social and psychological needs of campus residents and the principles of architectural design that can be applied to the design and renovation of educational facilities. Various research was used to select six "principles of social ecology" that were cross-referenced with…