Variable importance in PLS in the presence of autocorrelated data — Case studies in manufacturing processes

Abstract An integral part of interpreting atypical process performance in manufacturing processes is a multivariate understanding of process parameters and their relationship to a product's critical quality attributes. In this endeavor, Partial Least Squares (PLS) has greatly advanced the analysis of data that exhibits a high level of multicollinearity, but has not fully explored the impact to important variable selection in the presence of autocorrelation, particularly in the residuals, wherein a current observation is correlated to some degree with the previous observation(s). This autocorrelation provides an additional challenge to understand model performance and important variable selection. This paper introduces an autocorrelation correction factor formulation to PLS in an attempt to address this concern and illustrates its application to the recently proposed Significant Multivariate Correlation (SMC) variable selection method. Our results demonstrate that the correction factor formulation presented in this paper has the desired effect of driving down the false positive rate when applied to the SMC.