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

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.

Discovery of new deregulated miRNAs in gingivo buccal carcinoma using Group Benjamini Hochberg method: a commentary on “A quest for miRNA bio-marker: a track back approach from gingivo buccal cancer to two different types of precancers”

“…The lack of overlap may be due to the limited sample size of our data. Many statistical methods have such issues with multicollinearity [68]. However, most of these studies [1–3] mainly focus on tongue and floor-of-the-mouth cancer patients, whose clinical behaviors as well as molecular and immunoproteome profile may be different from GBSCC, a cancer predominant in the tobacco-chewing population of South Asia [5].…”