Solving Multicollinearity Problem in Linear Regression Model: The Review Suggests New Idea of Partitioning and Extraction of the Explanatory Variables

Kayode Ayinde, Olusegun O Alabi Kayode Ayinde, Olusegun O Alabi,Ugochinyere Ihuoma Nwosu

doi:10.32996/jmss.2021.2.1.2

Abstract

Multicollinearity has remained a major problem in regression analysis and should be sustainably addressed. Problems associated with multicollinearity are worse when it occurs at high level among regressors. This review revealed that studies on the subject have focused on developing estimators regardless of effect of differences in levels of multicollinearity among regressors. Studies have considered single-estimator and combined-estimator approaches without sustainable solution to multicollinearity problems. The possible influence of partitioning the regressors according to multicollinearity levels and extracting from each group to develop estimators that will estimate the parameters of a linear regression model when multicollinearity occurs is a new econometrics idea and therefore requires attention. The results of new studies should be compared with existing methods namely principal components estimator, partial least squares estimator, ridge regression estimator and the ordinary least square estimators using wide range of criteria by ranking their performances at each level of multicollinearity parameter and sample size. Based on a recent clue in literature, it is possible to develop innovative estimator that will sustainably solve the problem of multicollinearity through partitioning and extraction of explanatory variables approaches and identify situations where the innovative estimator will produce most efficient result of the model parameters. The new estimator should be applied to real data and popularized for use.

Highlights

1 Multicollinearity is an important econometric problem that has received increased attention in recent times (Ayinde et al, 2015; Lukman et al, 2015; Ismail and Manjula, 2016; Olanrewaju et al, 2017; Tyagi and Chandra, 2017)
The possible influence of partitioning the regressors according to multicollinearity levels and extracting from each group to develop estimators that will estimate the parameters of a linear regression model when multicollinearity occurs is a new econometrics idea and requires attention
Based on a recent clue in literature, it is possible to develop innovative estimator that will sustainably solve the problem of multicollinearity through partitioning and extraction of explanatory variables approaches and identify situations where the innovative estimator will produce most efficient result of the model parameters

Summary

The ridge regression estimator

The ridge regression estimator is a single-estimator approach to solving muticolinearity problems. Combining the knowledge from these works and comparing with simulated data, results showed that best estimator of the ridge parameter technique are of the different forms and types and include fixed maximum original, varying maximum original, harmonic mean original and arithmetic mean square root. It has got a smaller mean square error than the ordinary least square estimator, a feature which gives it an edge over the ordinary least square estimator in the presence of multicollinearity (Lukman et al, 2014). B1i is the parameter, X 1i explanatory variables where the weights w1i sum to one

Go back to step one updating the index

Idea of Partitioning and Extraction of the Explanatory Variables

Concluding Remarks

Methods