Assessing Influence in Variable Selection Problems
研究了在变量选择过程中，单个数据点对最终模型选择的影响，提出了无条件影响度量方法，并通过实例比较了条件与无条件方法的差异。
Variable selection techniques are often used in combination with multiple linear regression to produce a parsimonious model that fits the data well.It is clearly undesirable for the final model to depend strongly on the inclusion of a few influential cases (data points) in the data set.This article discusses a measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression.When variables are selected objectively using the data, deletion of individual cases can strongly affect the choice of model.Influence is often assessed conditionally upon the selected model.However, this does not take the model selection process into account.Nowadays, it is feasible to use an unconditional criterion to determine the influence of each case on the selection procedure.A number of examples are discussed to illustrate the differences between these approaches.Heuristics are developed to explain the examples.We conclude that, although the conditional approach gives valuable information about the selected model, the use of the unconditional approach can lead to greater insight about the influence of individual observations on the process of model selection.