Measuring a binary response's range of influence in logistic regression.
Landsittel-D; Singh-H; Arena-VC; Anderson-SJ
Am Stat 2002 Nov; 56(4):337-342
The recent article by Fay in which he proposed the range of influence (ROI) statistic for logistic regression, provides a useful diagnostic approach for assessing an observation's "potential influence" on the predicted value (or other statistic of interest). We agree with the author's conclusion that results of this procedure may add substantial information to existing diagnostics. This article was of particular interest to us since we have been investigating the same quantity in a completely different context, namely quantifying degrees of freedom for neural networks and other complex modeling procedures. The primary purpose of this letter is to show how the ROI statistic related to the concept of "generalized degrees of freedom" as developed by Ye (1998). In the special case of logistic regression, simulation results indicate that the absolute value of the ROI statistic asymptotically corresponds to the diagonal of the hat matrix.
Simulation-methods; Mathematical-models; Models; Statistical-analysis; Sampling
The American Statistician