Problems in avoiding the singularity problem in analyzing matrices for optimal scaling are addressed. Conditions are given under which the stationary points and values of a ratio of quadratic forms in two singular matrices can be obtained by a series of simple matrix operations. (Author/JKS)

Issues in the application of multiple regression analysis as a data analytic tool are discussed at some length. Included are discussions on component regression, factor regression, ridge regression, and systems of equations. (JKS)

A theorem which gives the range of possible correlations between a common factor and an external variable (not contained in the factor analysis) is presented. Analogous expressions for component theory are also derived. (Author/JKS)

Factor scale scores are sometimes used as weights to create composite variables representing the variables included in a factor analysis. If these composite variables are then used to predict some dependent variable, serious theoretical and methodological problems arise. This paper explores these problems and suggests strategies for circumventing…

It is shown how partial covariance, part and partial correlation, and regression weights can be estimated and tested for significance by means of a factor analytic model. Comparable partial covariance, correlations, and regression weights have identical significance tests. (Author)

An example demonstrates that Joreskog's suggested sufficient conditions for identifying unknown parameters in a confirmatory factor analytic model with correlated factors are not sufficient. Sufficient conditions are presented. (Author/JKS)

A variety of algorithms for analyzing covariance structures are considered. Additionally, two methods of estimation, maximum likelihood, and weighted least squares are considered. Comparisons are made between these algorithms and factor analysis. (Author/JKS)

A general approach to analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.…

Computer-based Monte Carlo methods compared the predictive accuracy upon replication of regression of five complete and four incomplete factor score estimation methods. Prediction on incomplete factor scores showed better double cross-validated prediction accuracy than on complete scores. The unique unit-weighted factor score was superior among…