Local versus global models for classification problems: Fitting models where it matters

It is generally argued that predictive or decision making steps in statistics are separate from the model building or inferential steps. In many problems, however, predictive accuracy matters more in some parts of the data space than in others, and it is appropriate to aim for greater model effectiveness in those regions. If the relevant parts of the space depend on the use to which the model is to be put, then the best model will depend also on this intended use. We illustrate using examples from supervised classification.