Improving the performance of Model Robust Regression (MRR2) method using new adaptive mixing parameters and a modified penalized error sum of squares

Abstract

The ultimate goal of Response Surface Methodology (RSM) involves the use of regression methods in the prediction of the settings of the explanatory variables that optimize the process or product based on the specified target value. However, current works involving the application of Model Robust Regression 2 (MRR2) method to RSM adopt a fixed mixing parameter which does not allow the estimated curve to capture salient variability inherent in the data as much as locally adaptive mixing parameters. In order to improve on the performance of the MRR2 method, we propose a new function to select locally adaptive mixing parameters and then modify the Penalized Prediction Error Sum of Squares (PRESS**) criterion to incorporates the target value of the process or product. A comparison of the results from the MRR2 method adopting the proposed locally adaptive mixing and those from the existing methods shows that the locally adaptive mixing parameters offer remarkable improvements. Furthermore, we demonstrate that the performance of the MRR2 method is further improved when the target value is accommodated in the criterion for selecting both the locally adaptive bandwidths and the adaptive mixing parameters.