Leverage and influential observations on the Liu type estimator in the linear regression model with the severe collinearity

Abstract

In the process of building a linear regression model, the essential part is to identify influential observations. Various influence measures involving Cook's distance and DFFITS are designed to detect the linear regression's influential observations using the Least Squares (LS). The existence of influential observations in the data is complicated by the presence of severe collinearity and affects the efficiency of the detection measures. This paper proposes new diagnostic methods based on the Liu type estimator (LTE) defined by Liu [1]. The Cook's distance and DFFITS for the LTE are introduced. Moreover, approximate formulas for Cook's distance and DFFITS are also proposed for LTE. Two real data sets with a high level of multicollinearity among the explanatory variables as well as the simulation study are used to illustrate and evaluate performance of the methodologies presented in this paper.

Keywords: Cook's distance; DFFITS; Leverage; Multicollinearity; Ridge regression.

Figure 1

Leverage values for the Longley data set.

Figure 2

The two versions Cook's D for LTE in the Longley data for the two values of $\hat{d}$.

Figure 3

DFFITS statistic for LTE in the Longley data for the two values of $\hat{d}$.

Figure 4

Leverage values for the Hald data set.