Influence analysis in response surface methodology

• We focus on developing influence functions based on Hampel's (1974) method for sensitivity analysis in response surface methodology (RSM).
• Three types of influence functions are considered: empirical influence, deleted empirical influence and sample influence.
• We also develop pair-perturbation influence functions to uncover the masked potentially influential points in RSM.
• Two real data show that the proposed single-perturbation influence functions provide a useful tool for the influence analysis in RSM.
• The proposed pair-perturbation influence functions provide a feasible auxiliary scheme to detect masked unusual points.

The study of response surface methodology (RSM) involves both experimental planning and data modeling and analysis. Once a design is selected, and data obtained from it, models for representing the data need to be considered and fitted. During the fitting process, observations that are suspicious (e.g. outliers and/or influential points) may cause problems. Such observations need to be detected so that appropriate adjustments can be made to analysis. Thus far, the work on influence analysis of RSM is unexplored in statistical research. This will be the focus of this paper. We not only generalize the single perturbation scheme in Hampel's (1974) method, but also implement the pair-perturbation scheme in Huang et al., 2007a, Huang et al., 2007b and Huang et al., 2007c to develop influence functions for sensitivity analysis in RSM. A simulation study and two real data examples for illustrating the effectiveness of the proposed method are provided.