Misplaced Pages

Glejser test

Article snapshot taken from Wikipedia with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.
This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (October 2014) (Learn how and when to remove this message)

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. After it was found not to be asymptotically valid under asymmetric disturbances, similar improvements have been independently suggested by Im, and Machado and Santos Silva.

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.

| e i | = γ 0 + γ 1 X i + v i | e i | = γ 0 + γ 1 X i + v i | e i | = γ 0 + γ 1 1 X i + v i {\displaystyle {\begin{aligned}|e_{i}|&=\gamma _{0}+\gamma _{1}X_{i}+v_{i}\\|e_{i}|&=\gamma _{0}+\gamma _{1}{\sqrt {X_{i}}}+v_{i}\\|e_{i}|&=\gamma _{0}+\gamma _{1}{\frac {1}{X_{i}}}+v_{i}\end{aligned}}}

Step 3: Select the equation with the highest R 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. It can also be implemented in SHAZAM econometrics software.

See also

Breusch–Pagan test
Goldfeld–Quandt test
Park test
White test

References

  1. Glejser, H. (1969). "A New Test for Heteroskedasticity". Journal of the American Statistical Association. 64 (235): 315–323. doi:10.1080/01621459.1969.10500976. JSTOR 2283741.
  2. 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.
  3. Im, K. S. (2000). "Robustifying Glejser test of heteroskedasticity". Journal of Econometrics. 97: 179–188. doi:10.1016/S0304-4076(99)00061-5.
  4. 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.
  5. "skedastic: Heteroskedasticity Diagnostics for Linear Regression Models".
  6. "Testing for Heteroskedasticity".
Category: