Firework Plots for Evaluating the Impact of Outliers and Influential Observations in Ridge Regression

With many predictors in regression, fitting the full model can induce multicollinearity problems. Thus, ridge regression provides a beneficial means of stabilizing the coefficient estimates in the fitted model. Outliers can distort many measures in data analysis and statistical modeling, while influential points can have disproportionate impact on the estimated values of model parameters. Graphical summaries, called firework plots, are simple tools for evaluating the impact of outliers and influential points in regression. Variations of the plots focus on allowing visualization of the impact on the estimated parameters and variability. This paper describes how three-dimensional and pairwise firework plots as well as scalable waterfall-firework plots can be used to increase understanding of contributions of individual observations and as a complement to other regression diagnostic techniques in the ridge regression setting. Using these firework plots, we can find outliers and influential points and their impact on model parameters and show how in some applications, the type of analysis used changes the impact of various observations. We illustrate the methods with two examples. Copyright (C) 2016 John Wiley & Sons, Ltd.