Methods of examining parameter sensitivity can be understood as relaxing the degree of certainty about the model’s accuracy (rather than relaxing the degree of certainty about precision, as with standard errors and confidence intervals) and as an acknowledgment that all models are wrong and almost necessarily biased (Box, 1976 Edwards, 2013), due to, for instance, missing variables, incorrect error terms, or missing (interaction) terms, or because measurement error is ignored (Jaccard & Wan, 1995). Although the two types of uncertainty are related (Pek et al., 2016), tests for one cannot serve as tests for the other. The uncertainty of parameter estimates we focus on here is not the uncertainty that stems from sampling variation, but uncertainty stemming from possible model inaccuracies, which are rarely known in practice. In those cases, the weights are considered sensitive and provide a poor basis for scientific conclusions (Green, 1977), and it is therefore prudent to ensure that the weights obtained in a study are not too sensitive. Under some conditions, even very small decrements in R 2 can be associated with substantially different regression weights for the predictor variables. The degree of discrepancy between sets of fungible weights and the OLS weights is independent of sample size, and their behavior is determined by factors other than those that determine the confidence interval for regression weights (Jones, 2013 Pek, Chalmers, & Monette, 2016). Each set of weights yields the same value of R 2, as well as the same correlation between the ordinary least squares (OLS) and alternative predicted values (Waller, 2008). We close with a discussion of some important implications of our results regarding parameter sensitivity and the trustworthiness of effect estimates.įungible weights are sets of alternative, suboptimal weights that may be used to examine parameter sensitivity in multiple linear regression models by way of a minor decrement in R 2. An R function is provided to calculate the range of fungible weights for a given covariance matrix. 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. 839, and including the predictor’s VIF and its interactions yields R 2 =. ![]() In the more complicated three-predictor case, the effects of the other two correlations yield R 2 =. 990) an interaction with the variance inflation factor ( VIF) yields R 2 = 1. 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 ( R 2 =. 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 R 2, differ from the optimal OLS weights. Sensitive parameters serve as a weak foundation for scientific inferences, because they provide less certainty about the accuracy and trustworthiness of the estimated model.
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