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

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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.