On Identifying Influential Observations in the Presence of Multicollinearity

Chinwendu Alice Uzuke,Ifeyinwa Christiana Ezeilo

doi:10.4236/ojs.2021.112016

Abstract

Influential observation is one which either individually or together with several other observations has a demonstrably large impact on the values of various estimates of regression coefficient. It has been suggested by some authors that multicollinearity should be controlled before attempting to measure influence of data point. In using ridge regression to mitigate the effect of multicollinearity, there arises a problem of choosing possible of ridge parameter that guarantees stable regression coefficients in the regression model. This paper seeks to check whether the choice of ridge parameter estimator influences the identified influential data points.

Highlights

It is well understood that not all observations in the data set play equal role when fitting a regression model
In using ridge regression to mitigate the effect of multicollinearity, there arises a problem of choosing possible of ridge parameter that guarantees stable regression coefficients in the regression model
We occasionally find that a single or small subset of the data exerts a disproportionate influence on the fitted regression model

Summary

Introduction

It is well understood that not all observations in the data set play equal role when fitting a regression model. Andrew and Pregibon [4] highlighted the need to find outliers that matter They stated that it is not all outliers that need to be harmful in the way that they have undue influence on for instance, the estimation of the parameters in the regression model. If k = 0, βR becomes the unbiased OLS estimator ( β ).The choice of ridge parameter k has always been a problem in using RR to solve for multicollinearity, methods of estimating the value of k had been suggested by several authors. In using Ridge Regression to mitigate multicollinearity problem, there is always a problem of the method to use to estimate the ridge parameter (k) to achieve reduction in variance larger than increase in bias one may want to know whether multiticollinearity affects identification of influential observations

Methodology

Illustration

Findings

Summary and Conclusion