Results of empirical comparisons of an inferential model of order analysis with factor analytic models were reported for two sets of data. On the prestructured data set both order and factor analytic models returned its dimensions of length, width and height, but on the random data set the factor analytic models indicated the presence of…

The application of component analysis to phenotypic, genetic, and environmental correlation matrices is discussed. Formulas for computation of component scores and the interpretation of factors is discussed. An example is presented. (Author/JKS)

In order to make parallel analysis more accessible to researchers employing principal component techniques, regression equations are presented for the logarithms of the latent roots of random data correlation matrices with unities on the diagonal. (Author/LMO)

Discusses Guttman's index of indeterminacy in light of alternative solutions which are equally likely to be correct and alternative solutions for the factor which are not equally likely to be chosen. Offers index which measures a different aspect of the same indeterminacy problem. (ROF)

Examples are presented in which it is either necessary or desirable to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is outlined which represents a two-matrix extension of the general "orthomax" orthogonal rotation criterion. (Author/RC)

In order to make the parallel analysis criterion for determining the number of factors in factor analysis easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. (Author/JKS)

Tucker's method of oblique congruence rotation is shown to be equivalent to a procedure by Meredith. This implies that Monte Carlo studies on congruence by Nesselroade, Baltes, and Labouvie and by Korth and Tucker are highly comparable. The problem of rotating two matrices orthogonally to maximal congruence is considered. (Author/CTM)

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)

Rasch measurement is preferable to factor analysis for reducing complex data matrices to unidimensional variables because factor analysis can mistake ordinally labeled stochastic observations for linear measures, and it does not construct linear measurement. Guidelines and instructions on how to use Rasch measurement to replace factor analysis are…

The DEDICOM (decomposition into directional components) model provides a framework for analyzing square but asymmetric matrices of directional relationships among "n" objects or persons in terms of a small number of components. One version of DEDICOM ignores the diagonal entries of the matrices. A straightforward computational solution…

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)

Five techniques that combine the ideals of rotation of matrices of factor loadings to optimal agreement and rotation to simple structure are compared on the basis of empirical and contrived data. Combining a generalized Procrustes analysis with Varimax on the main of the matched loading matrices performed well on all criteria. (SLD)

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…

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…