Improved Spread-Location Visualization

Abstract

The spread-location plot has often been used as a diagnostic plot suitable for many types of fitted statistical models. The spread-location plot—which plots the absolute residual or square-root absolute residual versus fitted value along with a robust loess smooth—is a useful replacement for the customary practice of plotting residuals versus fitted values. In this note, we show that neither absolute residual or square-root absolute residual is always appropriate for error distributions likely to be encountered in actual applications. Hence we recommend a multipanel display showing a suitable transformation of the absolute residual versus fitted value along with a boxplot to judge the symmetry achieved by the transformation. We conclude with an illustrative example.

Key Words:

• Loess
• Model diagnostic check
• Monotone spread
• Skewness coefficient
• Variance stabilization
• Visualizing data