Use of the linear regression method to evaluate population accuracy of predictions from non-linear models

To address the limitations of commonly used cross-validation methods, the linear regression method (LR) was proposed to estimate population accuracy of predictions based on the implicit assumption that the fitted model is correct. This method also provides two statistics to determine the adequacy of the fitted model. The validity and behavior of the LR method have been provided and studied for linear predictions but not for nonlinear predictions. The objectives of this study were to 1) provide a mathematical proof for the validity of the LR method when predictions are based on conditional means, regardless of whether the predictions are linear or non-linear 2) investigate the ability of the LR method to detect whether the fitted model is adequate or inadequate, and 3) provide guidelines on how to appropriately partition the data into training and validation such that the LR method can identify an inadequate model.