Multicollinearity and Regression Analysis (original) (raw)

Investigating the Impact of Multicollinearity on Linear Regression Estimates

MALAYSIAN JOURNAL OF COMPUTING, 2021

Multicollinearity is a case of multiple regression in which the predictor variables are themselves highly correlated. The aim of the study was to investigate the impact of multicollinearity on linear regression estimates. The study was guided by the following specific objectives, (i) to examined the asymptotic properties of estimators and (ii) to compared lasso, ridge, elastic net with ordinary least squares. The study employed Monte-carlo simulation to generate set of highly collinear and induced multicollinearity variables with sample sizes of 25, 50, 100, 150, 200, 250, 1000 as a source of data in this research work and the data was analyzed with lasso, ridge, elastic net and ordinary least squares using statistical package. The study findings revealed that absolute bias of ordinary least squares was consistent at all sample sizes as revealed by past researched on multicollinearity as well while lasso type estimators were fluctuate alternately. Also revealed that, mean square err...

How to get away with multicollinearity: a users' guide

This paper explains how to detect and overcome multicollinearity problems. In particular, we describe four procedures to handle high levels of correlation among explanatory variables: (1) to check variables coding and transformations; (2) to increase sample size; (3) to employ some data reduction technique and (4) to check specific literature on the subject. Methodologically, the research design uses basic simulation to show how multicollinearity affects coefficients efficiency. In addition, we adopted TIER 2.0 documentation protocol in order to increase transparency and to ensure results replicability. We argue that significant progress can occur in our discipline if scholars check their data for multicollinearity using the checklist presented in this article.

Estimation of the Effect of Multicollinearity on the Standard Error for Regression Coefficients

IOSR Journal of Mathematics, 2014

This research was set to examine the effect Multicollinearity has, on the standard error for regression coefficients when it is present in a Classical Linear Regression model (CLRM). A classical linear regression model was fitted into the GDP of Nigeria ,and the model was examined for the presence of Multicollinearity using various techniques such as Farrar-Glauber test, Tolerance level, Variance inflation factor, Eigen values etc and the result obtained shows that Multicollinearity has contributed to the increase of the standard error for regression coefficients, thereby rendering the estimated parameters less efficient and less significant in the class of Ordinary Least Squares estimators. Tolerance levels of 0.012, 0.005, 0.002 and 0.001 for 1 , 2 , 3 , and 4 respectively clearly shown a very low tolerance among all the explanatory variables with very high Variance Inflation Factors of 84.472, 191.715,502.179 and 675.633 respectively. A Coefficient of determination (R-Square) of 99%, though signaled a very high validity for the CLRM but it is equally an indications of a very high degree of Multicollinearity among the explanatory variables. The Eigen values of 0.431, 0.005, 0.002 and 0.000 for 0, 1 , 2 , 3 , and 4 respectively clearly shown a very low Eigen value among the explanatory variables, which are closer to zero with very high Condition index of 30.983, 49.759 and 100.810 for 2 , 3 , and 4 respectively which indicate that the Multicollinearity present is due greatly to the influence of regressors X 2 , X 3 , and X 4. .

Multicollinearity: Causes, Effects and Remedies

If there is no linear relationship between the regressors, they are said to be orthogonal. Multicollinearity is a case of multiple regression in which the predictor variables are themselves highly correlated. If the goal is to understand how the various X variables impact Y, then multicollinearity is a big problem. Multicollinearity is a matter of degree, not a matter of presence or absence. In presence of multicollinearity the ordinary least squares estimators are imprecisely estimated. There are several methods available in literature for detection of multicollinearity. By observing correlation matrix, variance influence factor (VIF), eigenvalues of the correlation matrix, one can detect the presence of multicollinearity. The degree of the multicollinearity becomes more severe as X X′ approaches zero. Complete elimination of multicollinearity is not possible but the degree of multicollinearity can be reduced by adopting ridge regression, principal components regression, etc.

Multicollinearity

Wiley Interdisciplinary Reviews: Computational Statistics, 2010

Multicollinearity refers to the linear relation among two or more variables. It is a data problem which may cause serious difficulty with the reliability of the estimates of the model parameters. In this article, multicollinearity among the explanatory variables in the multiple linear regression model is considered. Its effects on the linear regression model and some multicollinearity diagnostics for this model are presented.

A Comparative Analysis on Some Estimators of Parameters of Linear Regression Models in Presence of Multicollinearity

2018

Linear regression is the measure of relationship between two or more variables known as dependent and independent variables. Classical least squares method for estimating regression models consist of minimising the sum of the squared residuals. Among the assumptions of Ordinary least squares method (OLS) is that there is no correlations (multicollinearity) between the independent variables. Violation of this assumptions arises most often in regression analysis and can lead to inefficiency of the least square method. This study, therefore, determined the efficient estimator between Least Absolute Deviation (LAD) and Weighted Least Square (WLS) in multiple linear regression models at different levels of multicollinearity in the explanatory variables. Simulation techniques were conducted using R Statistical software, to investigate the performance of the two estimators under violation of assumptions of lack of multicollinearity. Their performances were compared at different sample sizes. Finite properties of estimators' criteria namely, mean absolute error, absolute bias and mean squared error were used for comparing the methods. The best estimator was selected based on minimum value of these criteria at a specified level of multicollinearity and sample size. The results showed that, LAD was the best at

A Suggested Method of Detecting Multicollinearity in Multiple Regression Models

TANMIYAT AL-RAFIDAIN, 2012

In literature, several methods suggested for the detection of multicollinearity in multiple regression models, and one of the multicollinearity problems solutions is to omit the explanatory variables in the model, which cause the multicollinearity. In this paper, we concentrated on the extra sum of squares method as a suggested method that can be used for detecting multicollinearity. The method of extra sum of squares is applied to real data on the annually surveys about smoking were conducted by the American Federal Trade Commission (FTC). In this data, we detected multicollinearity, then we solved this problem by using the ridge regression and we got the new estimates of the new model without omitting any of the explanatory variables.

Regression Model in Social Science Research: The Issue of Multicollinearity, Detection Method, and Solution in SPSS

Volume 1, 2024

One of the objectives of social science researchers in an inferential test is to build a reliableregression model. Multi-linear regression aims to find or predict the effect of predictor variables on predicted variables. However, when there is a high linear correlation between predictor variables in multi-linear regression, the predictor variables in the model cannot accurately define their impact on predicted variables. This statistical condition is called multicollinearity. Without testing and detecting multicollinearity and its precise treatment, the regression model can create difficulties in defining the impact of individual predictor variables on the predicted variable, leading to a faulty interpretation of the impact on the whole model. In this study, 36 primary-level teachers were selected randomly as the respondents. The respondents' data included their tentative salary, age, years of education, academic percentage in their final degree, and years of service. In the first round, the Karl Pearson correlation test is conducted among four independent variables: tentative current salary, age of respondent teachers, years of education completed, academic percentage in the final degree, and years of service s/he is involved in. SPSS version 25 is applied to find a correlation matrix between predictor variables, a matrix scatter plot, and linear regression with a collinearity diagnostic test. After finding a strong correlation between two variables, a collinearity diagnostic test is performed to locate and confirm the multicollinearity issue between the predictor variables. Once multicollinearity is confirmed, precise treatment is provided to solve the issue. The study found multicollinearity issues in two predictor variables; thus, further solutions were explained.