Linear regression is often used as a diagnostic tool to understand the relative contributions of operational variables to some key performance indicator or response variable. However, owing to the nature of plant operations, predictor variables tend to be correlated, often highly so, and this can lead to significant complications in assessing the importance of these variables. Shapley regression is seen as the only axiomatic approach to deal with this problem but has almost exclusively been used with linear models to date. In this paper, the approach is extended to random forests, and the results are compared with some of the empirical variable importance measures widely used with these models, i.e., permutation and Gini variable importance measures. Four case studies are considered, of which two are based on simulated data and two on real world data from the mineral process industries. These case studies suggest that the random forest Shapley variable importance measure may be a more reliable indicator of the influence of predictor variables than the other measures that were considered. Moreover, the results obtained with the Gini variable importance measure was as reliable or better than that obtained with the permutation measure of the random forest.