TITLE:
Effects of Multicollinearity on Type I Error of Some Methods of Detecting Heteroscedasticity in Linear Regression Model
AUTHORS:
Olusegun Olatayo Alabi, Kayode Ayinde, Omowumi Esther Babalola, Hamidu Abimbola Bello, Edward Charles Okon
KEYWORDS:
Regression Model, Heteroscedasticity Methods, Heteroscedasticity Structures, Multicollinearity, Monte Carlo Study, Significance Levels, Type I Error Rates
JOURNAL NAME:
Open Journal of Statistics,
Vol.10 No.4,
August
12,
2020
ABSTRACT: Heteroscedasticity
and multicollinearity are serious problems when they exist in econometrics
data. These problems exist as a result of violating the assumptions of equal
variance between the error terms and that of independence between the
explanatory variables of the model. With these assumption violations, Ordinary
Least Square Estimator (OLS)
will not give best linear unbiased, efficient and consistent estimator. In
practice, there are several structures of heteroscedasticity and several
methods of heteroscedasticity detection. For better estimation result, best
heteroscedasticity detection methods must be determined for any structure of
heteroscedasticity in the presence of multicollinearity between the explanatory
variables of the model. In this paper we examine the effects of multicollinearity
on type I error rates of some methods of heteroscedasticity detection in linear
regression model in other to determine the best method of heteroscedasticity
detection to use when both problems exist in the model. Nine heteroscedasticity
detection methods were considered with seven heteroscedasticity structures.
Simulation study was done via a Monte Carlo experiment on a multiple linear
regression model with 3 explanatory variables. This experiment was conducted
1000 times with linear model parameters ofβ0 = 4 , β1 = 0.4 , β2= 1.5and β3= 3.6.Five (5)levels ofmulicollinearity are with seven (7) different sample
sizes. The method’s performances were compared with the aids of set confidence
interval (C.I.) criterion.
Results showed that whenever multicollinearity exists in the model with any
forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best
method to determine the existence of heteroscedasticity at all chosen levels of
significance.