Factors associated with sensitive regression weights: A fungible parameter approach

Abstract

Sensitive parameters serve as a weak foundation for scientific inferences, because they provide less certainty about the accuracy and trustworthiness of the estimated model. Fungible weights may be used to examine parameter sensitivity by looking at how much sets of interchangeable, slightly suboptimal linear regression weights, all of which yield an identical, slightly reduced value of R2, differ from the optimal OLS weights. We find that in the two-predictor case, the range of a predictor’s fungible weights is almost completely explained by the absolute value of the correlation of the other predictor with the criterion variable (R2 =.990); an interaction with the variance inflation factor (VIF) yields R2 = 1. In the more complicated three-predictor case, the effects of the other two correlations yield R2 =.839, and including the predictor’s VIF and its interactions yields R2 =.910. The effects observed occur because alternative predictors with a high correlation with the criterion, or with each other, can compensate for the changes to a predictor’s weight while still yielding similar predicted values. An R function is provided to calculate the range of fungible weights for a given covariance matrix. We close with a discussion of some important implications of our results regarding parameter sensitivity and the trustworthiness of effect estimates.