ABSTRACT
In a linear regression model, testing for uniformity
of the variance of the residuals is a significant integral part of statistical analysis.
This is a crucial assumption that requires statistical confirmation via the use
of some statistical tests mostly before carrying out the Analysis of Variance
(ANOVA) technique. Many academic researchers have published series of papers
(articles) on some tests for detecting variance heterogeneity assumption in
multiple linear regression models. So many comparisons on these tests have been
made using various statistical techniques like biases, error rates as well as
powers. Aside comparisons, modifications of some of these statistical tests for
detecting variance heterogeneity have been reported in some literatures in
recent years. In a multiple linear regression situation, much work has not been
done on comparing some selected statistical tests for homoscedasticity
assumption when linear, quadratic, square root, and exponential forms of
heteroscedasticity are injected into the residuals. As a result of this fact,
the present study intends to work extensively on all these areas of interest
with a view to filling the gap. The paper aims at providing a comprehensive
comparative analysis of asymptotic behaviour of some selected statistical tests
for homoscedasticity assumption in order to hunt for the best statistical test
for detecting heteroscedasticity in a multiple linear regression scenario with
varying variances and levels of significance. In the literature, several tests
for homoscedasticity are available but only nine: Breusch-Godfrey test,
studentized Breusch-Pagan test, White’s test, Nonconstant Variance Score test,
Park test, Spearman Rank, Glejser test,
Goldfeld-Quandt test, Harrison-McCabe test were considered for this study; this
is with a view to examining, by Monte Carlo simulations, their asymptotic behaviours. However, four different forms of heteroscedastic
structures: exponential and linear (generalize of square-root and quadratic
structures) were injected into the residual part of the multiple linear
regression models at different categories of sample sizes: 30, 50, 100, 200,
500 and 1000. Evaluations of the performances were done within R environment.
Among other findings, our investigations revealed that Glejser and Park tests
returned the best test to employ to check for heteroscedasticity in EHS and LHS
respectively also White and Harrison-McCabe tests returned the best test to
employ to check for homoscedasticity in EHS and LHS respectively for sample
size less than 50.
Share and Cite:
Onifade, O.C. and Olanrewaju, S.O. (2020) Investigating Performances of Some Statistical Tests for Heteroscedasticity Assumption in Generalized Linear Model: A Monte Carlo Simulations Study. Open Journal of Statistics, 10, 453-493. https://doi.org/10.4236/ojs.2020.103029