When we build predictive models, we often want to understand why the model behaves the way it does, or in other words, which variables are the most influential in the predictions. But how can we tell which are most influential? And more importantly for many applications, which variables are most influential and how influential at the top end of the predicted values? The variables most important for the largest predictions are not necessarily the same as are important in the middle or the smallest model predictions.
To demonstrate the importance of these questions, I will begin with an idealized example and then move to a more realistic example typical of predictive modeling.