An assessment of the jackknife and bootstrap procedures on uncertainty estimation in the variable importance in the projection metric

• We explore the performance of several methods of uncertainty estimation via the jackknife and bootstrap procedures in terms of the variable importance in the projection metric (PLS-VIP).
• Additionally, the standard 'greater than one' rule for the PLS-VIP will be included as a comparator method for variable importance selection.
• A high-level overview of the both jackknife and bootstrap confidence intervals is also presented.

Industrial manufacturing processes can be very complex systems where in the manufacture of a single batch hundreds of processing variables and raw materials is monitored. In these processes, where there is a high degree of multicollinearity between predictor variables, identifying the candidate variables responsible for any changes in product quality can prove to be extremely challenging. Within this context partial least squares (PLS), in conjunction with the variable importance in the projection (PLS-VIP) metric, is currently an important tool in determining the most correlated variables and helping to determine the root cause for changes in a product's quality attributes. Using the standard ‘greater than one’ important variable cut-off rule for the PLS-VIP, our approach is to measure the performance of seven methods of uncertainty estimation with the goal of assessing which method performs best in reducing the false positive rate while at the same time not impacting the true positive rate. Our findings demonstrate that the implementation of either the normal or basic bootstrap confidence intervals for the PLS-VIP will result in a more consistent determination of the important variables. If computation speed is a concern, the use of the bias-corrected jackknife confidence interval is recommended in place of the un-corrected jackknife.