Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time,…

It is known that for trivariate distributions, if two correlations are fixed, the remaining correlation is constrained. If just one is fixed, the remaining two are constrained. Both results are extended to the case of a multivariate distribution. (Author/JKS)

The index of redundancy is a measure of association between a set of independent variables and a set of dependent variables. Properties and interpretations of redundancy variables, in a particular subset of the original variables, are discussed. (JKS)

Commonality components have been defined as a method of partitioning squared multiple correlations. The asymptotic joint distribution of all possible squared multiple correlations is derived. The asymptotic joint distribution of linear combinations of squared multiple correlations is obtained as a corollary. (Author/JKS)

Redundancy analysis is an attempt to provide nonsymmetric measures of the dependence of one set of variables on another set. This paper attempts to clarify the nature of redundancy analysis and its relationships to canonical correlation and multivariate multiple linear regression. (Author/JKS)

A simple roof is presented: that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable. (Author/JKS)

This note proposes an alternative implementation of the regression method which should be slightly faster than the principal components methods for estimating missing data. (RC)

Interpretations regarding the effects of exogenous and endogenous variables on endogenous variables in linear structural equation systems depend upon the convergence of a matrix power series. The test for convergence developed by Joreskog and Sorbom is shown to be only sufficient, not necessary and sufficient. (Author/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)

Many data analysis problems in psychology may be posed conveniently in terms which place the parameters to be estimated on one side of an equation and an expression in these parameters on the other side. A rule for improving the rate of convergence of the iterative solution of such equations is developed and applied to four problems. (Author/RC)