Weighted Structural Regression: A Broad Class Of Adaptive Methods For Improving Linear Prediction

Abstract

Given a criterion variable and two or more predictors, applied linear prediction usually entails some form of OLS regression. But when there are several predictors, and especially when these are subject to non-ignorable errors of measurement, applications of OLS methods are often fraught with problems. Weighted structural regression (WSR) methods can mitigate many difficulties through the incorporation of prior structural models into analyses. WSR methods are sufficiently general to include OLS, ridge, reduced rank regression, as well as most covariance structural regression models, as special cases; many other regression methods, heretofore not available, are also included. In this article adaptive forms of WSR are developed and discussed. According to our bootstrapping studies the new methods have potential to recover known population regression weights and predict criterion score values routinely better than OLS with which they are compared. These new methods are scale free as well as simple to compute; they seem well suited to many prediction applications in behavioral research.

Meta-Analysis of Adolescent Drug Prevention Programs: Results of the 1993 Meta-Analysis

“…However, this was offset by verifying the results using a second regression procedure, weighted structural regression (WSR). WSR was developed to alleviate problems of numerous, correlated predictors and limited sample sizes faced by social scientists (Pruzek and Lepak 1992).…”

Attachment and interpersonal characteristics of college students with and without disabilities.

“…As recommended by Pruzek and Lepak (1992) for exploratory studies with multiple variables in which prior knowledge of potential results is limited, a factor analysis was conducted on the 17 scores produced by the FIRO-B, ISQ, Frequency of Insecure Memories (FISM), and BIC. The purpose of the factor analysis was to achieve parsimony by reducing the 17 scores to a smaller number of scores, representing the explanatory concepts among the original scores (Tinsley & Tinsley, 1987).…”

How are Developmentally Appropriate or Traditional Teaching Practices Related to the Mathematics Achievement of General and Special Education Students?

“…(Pruzek, 1988;Pruzek & Lepak, 1992). Further strengthening our confidence in this method, Guadagnoli and Velicer (1988) reported that components with four or more loadings above .60, or three or more above .80, can be considered to be reliable and generalizable for a wide range of sample sizes.…”