Using Partial Residual Plots in Assessing and Improving the Construct Validity of Multiple Regression Models

Advantages of partial residual plots over residual plots in regression analysis are discussed and illustrated by empirical examples. A variation of partial residual equation is introduced and an effective procedure to use this revised form in identifying the proper transformation for achieving linearity and variance stabilization is presented. Essentially, the transformed predictors are identified by partial residual plots and introduced into the regression model to improve the regression fit. Uses, limitations and strengths of partial residual plots are discussed. n formulating the multiple regression model, researchers often feels strongly that an explanatory variable (xj) included in the model influences the response (y). But, they are not sure whether it is the variable (xj), as they happen to measure it, or some function g(xj, that is linearly related to the mean of the response. This is often because the jth regression coefficient is smaller than expected, statistically insignificant, or of the “wrong ” sign. Unfortunately, estimates of partial regression coefficients and summary statistics such as R2, F and t are unable to detect sources of the failure to yield good fit (For a good discussion o