An adapted linear modeling method for interval-valued responses: Golden center and range method

Abstract

Response variables may have replicated measures in experimental studies. The replications of the responses may cause variability due to several reasons, e.g., uncertainty, randomness. It is not proper to define the replicated response measures as a single numerical quantity. In this case, interval-valued response can be used to represent the replicated response values. There have been widely used popular modeling methods for the interval-valued responses in the literature, e.g., Center method, MinMax method and Center and Range (CR) method. This paper introduces an adapted linear modeling method based on CR method. The spread of replicated response measures and golden ratio are used for center point calculation of the CR method. The proposed modeling method is called Golden Center and Range (GCR) method. Three data sets from the literature, polyphenol extraction, wheel cover component and printing ink, were used for application purpose. The performances of the predicted linear regression models were compared by using Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) criteria with 5-fold cross-validation (CV). It is seen from the comparison results that the proposed GCR method has similar prediction performance with the CR method for interval-valued response measured data sets according to nonparametric statistical test.

keywords:

• Replicated response measures
• interval-valued responses
• center and range method
• golden ratio
• cross-validation

Acknowledgements

The authors thank to Dr. Nilüfer Vural (Ankara Y ild ir im Beyaz it University) for helpful suggestions and her valuable contributions about the replicated response measured Polyphenol extraction data set.