Prediction for a number of criteria from a set of predictor variables in a system of regression equations is studied with the possibilities of linear transformations applied to both the criterion and predictor variables. Predictive composites representing a battery of predictor variables provide identical estimates of criterion scores as do the…

Two computer subroutine packages for the analytic rotation of a factor matrix, A(p x m), are described. The first program uses the Flectcher (1970) gradient method, and the second uses the Polak-Ribiere (Polak, 1971) gradient method. The calculations in both programs involve the optimization of a function of free parameters. The result is a…

A general statistical model for the multivariate analysis of mean and covariance structures is described. Matrix calculus is used to develop the statistical aspects of one new special case in detail. This special case separates the confounding of principal components and factor analysis. (DEP)

A procedure for estimating the reliability of a factorially complex composite is considered. An application of its use with Scholastic Aptitude Test data is provided. (Author/JKS)

The Cartesian theory of dimensionality (defined in terms of geometric distances between points in the test space) and Leibnitzian theory (defined in terms of order-generative connected, transitive, and asymmetric relations) are contrasted in terms of the difference between a factor analysis and an order analysis of the same data. (Author/CTM)

Two sets of five items each from the Law School Admission Test were analyzed by two methods of factor analysis, and by the Krus-Bart ordering theoretic method of multidimensional scaling. The results indicated a conceptual gap between latent trait theoretic procedures and order theoretic procedures. (Author/CTM)

Solutions for the indeterminate common factor of a group of variables satisfying the single common factor model are not unique. This paper examines a number of thereoms concerning that problem and draws conclusions from them for factor analysis in general. (Author/JKS)

A method for obtaining teacher ratings from incomplete student ranking data is presented. The procedure involves finding the scores for the teachers on the first principal component of a student intercorrelation matrix, where the missing data are supplied by least squares. (Author)

A reanalysis of the intercorrelation matrix from a principal components analysis of the Life Styles Inventory was conducted using a Canadian sample. Using nonmetric multidimensional scaling, analyses show an almost perfect circumplex pattern. Results illustrate the inadequacy of factor analytic procedures for the analysis and representation of a…

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

Considers a class of estimation procedures for the factor model. The procedures are shown to yield estimates possessing the same asymptotic sampling properties as those from estimation by maximum likelihood or generalized last squares, both special members of the class. General expressions for the derivatives needed for Newton-Raphson…

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)

Beginning with the results of Girschick on the asymptotic distribution of principal component loadings and those of Lawley on the distribution of unrotated maximum likelihood factor loadings, the asymptotic distributions of the corresponding analytically rotated loadings is obtained. The principal difficulty is the fact that the transformation…

Path analyses of two multitrait-multimethod matrices are used as examples of the kind of information afforded by application of the technique. It is concluded that the technique should be of considerable aid to researchers who want to evaluate the convergent and discriminant validity of their measures. (Author/CTM)