Beware of ‘Good’ Outliers and Overoptimistic Conclusions*
警告研究者注意回归分析中容易被忽视的“好杠杆点”(靠近回归超平面但在x维度上离群的点),它们不影响参数估计但会扭曲统计推断,并给出识别和处理各类异常值的步骤。
Abstract The main goal of this paper is to warn practitioners of the danger of neglecting outliers in regression analysis, in particular, good leverage points (i.e. points lying close to the regression hyperplane but outlying in the x ‐dimension). While the types of outliers which do influence regression estimates (vertical outliers and bad leverage points) have been extensively investigated, good leverage points have been largely ignored, probably because they do not affect the estimated regression parameters. However, their effect on inference is far from negligible. We propose a step‐by‐step procedure to identify and treat all types of outliers. The paper of Persson and Tabellini [ American Economic Review (2004) Vol. 94, pp. 25–46] linking the degree of proportionality of an electoral system to the size of government is discussed to illustrate how the choice of a measure and the existence of atypical observations may substantially influence results.