Hierarchial causal models are described as pictorial representations of multiple regression equations. These models are particularly helpful for three reasons: (1) the formulation of problems in a path analytic framework forces a degree of explicitness that is often not present in research reports that rely solely on regression; (2) they provide a…

Recent theoretical analyses of the concept of suppression are identified and discussed. A generalized definition of suppression is presented and the conditions for suppressor structures in the context of the General Linear Model are derived. (Author)

This paper introduces a model for describing outliers (observations which are extreme in some sense or violate the apparent pattern of other observations) in linear regression which can be viewed as a mixture of a quadratic and a linear regression. The maximum likelihood estimators of the parameters in the model are derived and their asymptotic…

Several themes which are common to both econometrics and psychometrics are surveyed. The themes are illustrated by reference to permanent income hypotheses, simultaneous equation models, adaptive expectations and partial adjustment schemes, and by reference to test score theory, factor analysis, and time-series models. (Author)

A set of mathematical consistencies that forms conditions of inequality in a theorem is summarized, and a strategy for its application with real data is presented. The theorem and strategy are suggested for immediate use by the practitioner seeking cause-effect relationships in a system of variables to cut down guess work and time in analysis and…

A method is developed for testing a priori multiple regression models. The method allows one to specify in advance as many unstandardized or standardized coefficients as one wants to and allows the remaining slopes to be free to vary. (Author/PN)

Quantitative methods for research synthesis usually involve calculation of an estimate of effect size for each of a series of studies. Some problems associated with ad hoc methods of analysis, such as ordinary least squares regression analysis using estimates of effect size, are described. (Author/JKS)

A review of cross-validation shrinkage formulas is presented which focuses on the theoretical and practical problems in the use of various formulas. Practical guidelines for use of both formulas and empirical cross-validation are provided. A comparison of results using these formulas in a range of situations is then presented. The result of these…

One aspect of multiple regression--the shrinkage of the multiple correlation coefficient on cross-validation is reviewed. The paper consists of four sections. In section one, the distinction between a fixed and a random multiple regression model is made explicit. In section two, the cross-validation paradigm and an explanation for the occurrence…

The purpose of this paper is to demonstrate how multiple linear regression provides a viable statistical methodology for dealing with meta-analysis in general, and specifically with the issues of nonindependence and design complexity, such as multiple treatments. Since the F-test and t-test are special cases of the general linear model,…

Path analysis is presented as a technique that can be used to test on a priori model based on a theoretical conceptualization involving a network of selected variables. This being an introductory source, no previous knowledge of path analysis is assumed, although some understanding of the fundamentals of multiple regression analysis might be…

The applicability of a mathematical theorem designed to trace causality of a three-variable path that consists of an initial cause variable, an intermediate variable, and a final-effect variable with control over other system variables is evaluated. The formula was used with a horizontal rather than a normal distribution, as had been done in an…

Similarities between regression analysis and analysis of variance are noted and it is argued that the former has advantages over the latter. It is also argued that canonical correlation analysis is more suitable than factor analysis in certain cases. The argument is illustrated with four recent pieces of educational research. (DG)

The use of a path analysis model to obtain unique, substantively meaningful decomposition of variance among endogenous (independent) variables in the model is argued. This reasoning runs counter to more traditional path analytic work. An example is provided. (Author/JKS)