Graphical methods of determining predictor importance and effect

Abstract

Many experiments and studies are designed to discover how a group of predictors affect a single response. For example, an agricultural scientist may perform an experiment to determine how rainfall, sunlight, and fertilizer affect plant growth. In situations like this, graphical methods to show how the various predictors affect the response and the relative importance of each predictor can be invaluable, not only in helping the researcher understand the results, but also in communicating the findings to non-specialists.

For settings where a simple statistical model can be used to fit the data, several graphical methods for showing the effect of individual predictors already exist. However, few methods are available for more complex settings that require more complex models. A framework for understanding the existing methods is developed using Cook's net-effect plots, and a criterion for evaluating and creating methods is proposed. This criterion states that for a plot to be most useful in showing how a given predictor affects the response, the conditional distribution of the vertical axis given the horizontal axis should be independent of the other predictors. That is, the plot should not hide any additional information gained by knowing the other predictors.

This proposed framework and criterion is used to develop graphical methods appropriate for use in more complex modeling algorithms. In particular, these plots have been explored in the context of model combining methods, and various versions compared and analyzed. Additionally, the weights from these model combining methods are used to modify existing methods of determining predictor importance values, resulting in improved values for spurious predictors.