Glejser test
{{Technical|date = October 2014}}
Glejser test for heteroscedasticity, developed in 1969 by Herbert Glejser, is a statistical test, which regresses the residuals on the explanatory variable that is thought to be related to the heteroscedastic variance.{{cite journal |last1=Glejser |first1=H. |title=A New Test for Heteroskedasticity |journal=Journal of the American Statistical Association |year=1969 |volume=64 |issue=235 |pages=315–323 |jstor=2283741|doi=10.1080/01621459.1969.10500976 }} After it was found not to be asymptotically valid under asymmetric disturbances,{{Cite journal | doi = 10.1016/0304-4076(94)01723-9| title = Some results on the Glejser and Koenker tests for heteroskedasticity| journal = Journal of Econometrics| volume = 72| pages = 275–299| year = 1996| last1 = Godfrey | first1 = L. G. | issue = 1–2}} similar improvements have been independently suggested by Im,{{Cite journal | doi = 10.1016/S0304-4076(99)00061-5| title = Robustifying Glejser test of heteroskedasticity| journal = Journal of Econometrics| volume = 97| pages = 179–188| year = 2000| last1 = Im | first1 = K. S. }} and Machado and Santos Silva.{{Cite journal | last1 = Machado | first1 = José A. F. | last2 = Silva | first2 = J. M. C. Santos | year = 2000 | title = Glejser's test revisited | journal = Journal of Econometrics | volume = 97 | issue = 1 | pages = 189–202 | doi = 10.1016/S0304-4076(00)00016-6}}
Steps for using the Glejser method
Step 1: Estimate original regression with ordinary least squares and find the sample residuals ei.
Step 2: Regress the absolute value |ei| on the explanatory variable that is associated with the heteroscedasticity.
:
\begin{align}
|e_i| & = \gamma_0 + \gamma_1 X_i + v_i \\[8pt]
|e_i| & = \gamma_0 + \gamma_1 \sqrt{X_i} + v_i \\[8pt]
|e_i| & = \gamma_0 + \gamma_1 \frac 1 {X_i} + v_i
\end{align}
Step 3: Select the equation with the highest R2 and lowest standard errors to represent heteroscedasticity.
Step 4: Perform a t-test on the equation selected from step 3 on γ1. If γ1 is statistically significant, reject the null hypothesis of homoscedasticity.
Software Implementation
Glejser's Test can be implemented in R software using the glejser function of the skedastic package.{{cite web|title=skedastic: Heteroskedasticity Diagnostics for Linear Regression Models|url=https://cran.r-project.org/web/packages/skedastic/index.html}} It can also be implemented in SHAZAM econometrics software.{{cite web|title=Testing for Heteroskedasticity|url=http://www.econometrics.com/intro/testhet.htm}}
See also
References
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