Glejser test

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.^[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 e_i.

Step 2: Regress the absolute value |e_i| on the explanatory variable that is associated with the heteroscedasticity.

${\displaystyle {\begin{aligned}|e_{i}|&=\gamma _{0}+\gamma _{1}X_{i}+v_{i}\\[8pt]|e_{i}|&=\gamma _{0}+\gamma _{1}{\sqrt {X_{i}}}+v_{i}\\[8pt]|e_{i}|&=\gamma _{0}+\gamma _{1}{\frac {1}{X_{i}}}+v_{i}\end{aligned}}}$

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