Firework Plots for Evaluating the Impact of Outliers and Influential Observations in Generalized Linear Models

Outliers can distort many measures in data analysis and statistical modeling, and influential points can have disproportionate impact on the estimated values of model parameters. Jang and Anderson-Cook (2013) proposed a new set of graphical summaries, called firework plots, as 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. In the generalized linear models analysis setting, the impact of changing model parameters is often less transparent than in the linear model setting and variability can be captured with the deviance. Hence, this paper describes how 3-D firework plots and the pairwise firework plot matrix can be used to increase understanding of contributions of individual observations and as a complement to other regression diagnostics techniques in the generalized linear models setting. Using these firework plots, we can find outliers and influential points and their impact on model parameters. We illustrate the information and understanding gain possible with several examples.