Effects of Multicollinearity on Type I Error of Some Methods of Detecting Heteroscedasticity in Linear Regression Model  

作　　者：Olusegun Olatayo Alabi Kayode Ayinde Omowumi Esther Babalola Hamidu Abimbola Bello Edward Charles Okon Olusegun Olatayo Alabi;Kayode Ayinde;Omowumi Esther Babalola;Hamidu Abimbola Bello;Edward Charles Okon(Department of Statistics, Federal University of Technology, Akure, Nigeria)

机构地区：[1]Department of Statistics, Federal University of Technology, Akure, Nigeria

出　　处：《Open Journal of Statistics》2020年第4期664-677,共14页统计学期刊（英文）

摘　　要：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</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(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 of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em>_{<span style="font-family:Verdana;">0</span>}<span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em>_{<span style="font-family:Verdana;">1</span>}<span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em>_{<span style="font-family:Verdana;">2</span>}<span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-familyHeteroscedasticity 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</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(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 of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em>_{<span style="font-family:Verdana;">0</span>}<span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em>_{<span style="font-family:Verdana;">1</span>}<span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em>_{<span style="font-family:Verdana;">2</span>}<span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family

关 键 词：Regression Model Heteroscedasticity Methods Heteroscedasticity Structures MULTICOLLINEARITY Monte Carlo Study Significance Levels Type I Error Rates 

分 类 号：O17[理学—数学]