Glejser test
In statistics, the Glejser test for heteroscedasticity, developed in 1969 by Herbert Glejser (:fr: Herbert Glejser), regresses the residuals on the explanatory variable that is thought to be related to the heteroscedastic variance.[1] After it was found not to be asymptotically valid under asymmetric disturbances,[2] similar improvements have been independently suggested by Im,[3] and Machado and Santos Silva.[4]
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.
- [math]\displaystyle{ \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} }[/math]
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.[5] It can also be implemented in SHAZAM econometrics software.[6]
See also
Breusch–Pagan test
Goldfeld–Quandt test
Park test
White test
References
- ↑ Glejser, H. (1969). "A New Test for Heteroskedasticity". Journal of the American Statistical Association 64 (235): 315–323. doi:10.1080/01621459.1969.10500976.
- ↑ Godfrey, L. G. (1996). "Some results on the Glejser and Koenker tests for heteroskedasticity". Journal of Econometrics 72 (1–2): 275–299. doi:10.1016/0304-4076(94)01723-9.
- ↑ Im, K. S. (2000). "Robustifying Glejser test of heteroskedasticity". Journal of Econometrics 97: 179–188. doi:10.1016/S0304-4076(99)00061-5.
- ↑ Machado, José A. F.; Silva, J. M. C. Santos (2000). "Glejser's test revisited". Journal of Econometrics 97 (1): 189–202. doi:10.1016/S0304-4076(00)00016-6.
- ↑ "skedastic: Heteroskedasticity Diagnostics for Linear Regression Models". https://cran.r-project.org/web/packages/skedastic/index.html.
- ↑ "Testing for Heteroskedasticity". http://www.econometrics.com/intro/testhet.htm.
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