Comparisons Between First Order and Second Order Approximations in Regression Diagnostics

Abstract

Several authors have obtained the first order one-step approximation for diagnostic measures when a single observation is deleted from the data in a normal nonlinear regression (Fox, Hinkley and Larntz, 1980) and in generalized linear models (Pregibon, 1981). In this paper, we suggest nonlinearity and skewness measures to assess the adequacy of this first order one-step approximation. If one of these measures is large, compared to its guide values, then we recommend the second order one-step approximation as a better alternative. Furthermore, regression diagnostics such as Cook's distance, likelihood distance and deviance calculated from the second order one-st ... p approximat.ion provide mor .. accurat.e result.s than those ca.lculated from the first order one-step approximation.