Linear functional relationships are intended to be symmetric and therefore cannot generally be accurately estimated using ordinary least squares regression equations. Orthogonal regression (OR) models allow for errors in both "Y" and "X" and therefore can provide symmetric estimates of these relationships. The most…

We study flexible Bayesian methods that are amenable to a wide range of learning problems involving complex high dimensional data structures, with minimal tuning. We consider parametric and semiparametric Bayesian models, that are applicable to both static and dynamic data, arising from a multitude of areas such as economics, finance and…

Educational reform is most likely to be successful when teachers are knowledgeable about the intended reform, and when their concerns about the reform are understood and addressed. The Common Core State Standards (CCSS) is an effort to establish a set of nationwide expectations for students and teachers. This study examined teacher understanding…

The extension of regression estimation and poststratification to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISTREL framework. (Author/LMO)

The usefulness of path analysis as a means of better understanding various linear models is demonstrated. First, two linear models are presented in matrix form using linear structural relations (LISREL) notation. The two models, regression and factor analysis, are shown to be identical although the research question and data matrix to which these…

A response to comments on internal correlation for statistical analysis, as proposed by the present authors (1989), is provided. Focus is on issues raised by W. W. Rozeboom (1989). Comments by J. H. Schuenemeyer (1989) and R. Bargmann (1989) are briefly considered. (TJH)

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)

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

Canonical weights and structure correlations are used to construct low dimensional views of the relationships between two sets of variables. These views, in the form of biplots, display familiar statistics: correlations between pairs of variables, and regression coefficients. (SLD)

A simple procedure for establishing convergent and discriminant validity is presented, as an alternative to the LISREL-based nested model used by R. P. Bagozzi (1978) and K. F. Widaman (1985). Ordinary least-squares regression is used, with the correlation between measures as the dependent variable. (SLD)

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of diagonal elements. This paper reviews both fields; points out various small errors; and presents a methodological comparision of factor analysis and…

The applicability of a new multiple-group factor analysis of dichotomous variables is shown and contrasted with the item response theory approach to item bias analysis. Situations are considered where the same set of test items has been administered to more than one group of examinees. (Author/BS).

The internal correlation--a measure of dependency in a set of variables--is discussed and generalized. Applications of the internal correlation coefficient and its generalizations are given for several data-analytic situations. The internal correlation is illustrated and the concept is expanded to a series of additional indices. (TJH)

Use of internal correlation for statistical analysis--proposed by G. W. Joe and J. L. Mendoza (1989)--is discussed. Focus is on the "content" question (what this application can do with the information that statistics contain) and the "eloquence" question (the advantages of this means of encoding information over other means). (TJH)

Multivariate distributions are studied in which all bivariate regressions can be linearized by separate transformation of each of the variables. A two-stage procedure, first scaling the variables optimally and then fitting a simultaneous equations model, is studied in detail. (SLD)