Journal of Basic and Applied Research International
 

Journal of Basic and Applied Research International, ISSN No. : 2395-3438 (Print), 2395-3446 (Online), Vol.: 22, Issue.: 3

Original Research Article

A COMPARATIVE STUDY OF THE PREDICTION PERFORMANCE METHODS OF HANDLING MULTICOLLINEARIY BASED ON NORMAL AND UNIFORM DISTRIBUTIONS

 

U. USMAN1*, Y. ZAKARI1 AND Y. MUSA1

1Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.

Abstracts

From the assumption of linear regression model which states that there is no correlation between the explanatory variables fails then the variance of least square estimator become large and unstable. Thus, we resort to biased regression methods which stabilize the variance of the parameter estimate. In this paper, three biased regression methods for overcoming multicollinearity, Principal Components Regression (PCR), Partial Least Square Regression (PLSR) and Ridge Regression (RR) were used. Data that follows normal, and uniform distributions were successfully simulated to estimate the regression coefficients by PCR, PLSR and RR methods. A comparison between the three methods were done by using symmetric loss functions like root mean square errors, mean absolute errors and mean absolute percentage errors. Based on this study, it is observed that PLSR has a lower measure of accuracy in normal distribution while RR shows better results in uniform distribution. Therefore, these techniques can be applied to the same distributions used in this study by varying the sample sizes and equally be used to look at the behaviours of other distributions other than those used in this paper.

Keywords :

Regression; multicollinearity; ridge; partial least square; principal component regression.