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)

A distinction is drawn between redundancy measurement and the measurement of multivariate association between two sets of variables. Several measures of multivariate association between two sets of variables are examined. (Author/JKS)

The hypothesis that two variables have a perfect disattenuated correlation and hence measure the same trait, except for errors of measurement, is discussed. Equivalently, the underlying variables, the true scores, are related linearly. It is shown that previously proposed ad hoc tests are, in fact, likelihood ratio tests. (Author/JKS)

The utility of a nonlinear transformation of the criterion variable in multiple regression analysis is established. A well-known law--the Pythagorean Theorem--illustrates the point. (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)

Three different uses of ratio variables in aggregate data analysis are discussed: (1) as measures of theoretical concepts, (2) as a means to control an extraneous factor, and (3) as a correction for heteroscedasticity. Alternatives to ratios for each of these cases are discussed and evaluated. (Author/JKS)

A method is proposed for overcoming the problem of multicollinearity in multiple regression equations where multiplicative independent terms are entered. The method is not a ridge regression solution. (JKS)

Treatments of contextual effects in the social science literature have traditionally focused on statistical phenomena more than on social processes. This article seeks to redress that imbalance by focusing on underlying processes through which social structure and social interaction may impinge upon individuals. (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)

The misleading character of the correlation coefficient was investigated in two studies of intuitive statistical behavior: subjective estimation of partial correlation and subjective estimation of the minimum possible correlation between two variables given their equal correlation with a third. (Author/JKS)

Equations for estimating the value of the multiple correlation coefficient in the population underlying a sample and the value of the population validity coefficient of a sample regression equation were investigated. Results indicated that cross-validation may no longer be necessary for certain purposes. (Author/MH)

The application of multiple linear regression to the identification of appropriate criterion variables and the prediction of enrollment in college courses during a period of major rapid decline (1972-1978) are discussed. An example is presented. (Author/JKS)

A method to provide estimates of parameters of specified nonlinear equations from ordinal data generated from a crossed design is presented. The statistical basis for the method, called NOPE (nonmetric parameter estimation), as well as examples using artifical data, are presented. (Author/JKS)

Repeated measures designs often involve dichotomization of a continuous variable in order to be amenable to the analysis of variance nature of such designs. An alternative to that approach wherein the independent variable is kept continuous is presented. (JKS)

There are a variety of formulas for reducing the positive bias which occurs in estimating R squared in multiple regression or correlation equations. Five different formulas are evaluated in a Monte Carlo study, and recommendations are made. (JKS)