Heteroscedasticity
Statistical concept related to variance
Heteroscedasticity refers to the circumstance in which the variance of the errors in a regression model is not constant across all levels of the independent variable. This is a violation of one of the key assumptions of ordinary least squares (OLS) regression, which assumes that the variance of the errors is constant, or homoscedastic.
Causes[edit | edit source]
Heteroscedasticity can arise from several sources:
- Model misspecification: If the model is not correctly specified, it can lead to heteroscedasticity.
- Measurement error: Errors in measuring the independent variables can cause heteroscedasticity.
- Omitted variable bias: Leaving out a relevant variable can result in heteroscedasticity.
- Non-linear relationships: If the relationship between the independent and dependent variables is non-linear, it can cause heteroscedasticity.
Consequences[edit | edit source]
The presence of heteroscedasticity can lead to inefficient estimates and invalid hypothesis testing. Specifically, the standard errors of the estimates can be biased, leading to incorrect conclusions about the significance of the independent variables.
Detection[edit | edit source]
Several methods can be used to detect heteroscedasticity:
- Graphical analysis: Plotting the residuals against the fitted values can reveal patterns indicating heteroscedasticity.
- Breusch-Pagan test: A statistical test that can be used to detect heteroscedasticity.
- White test: Another test that can be used to detect heteroscedasticity, which is robust to different forms of heteroscedasticity.
Remedies[edit | edit source]
If heteroscedasticity is detected, several approaches can be taken to address it:
- Transformations: Applying a transformation to the dependent variable, such as a logarithm or square root, can stabilize the variance.
- Weighted least squares: This method gives different weights to different observations to account for the heteroscedasticity.
- Robust standard errors: Using robust standard errors can provide valid hypothesis tests even in the presence of heteroscedasticity.
See also[edit | edit source]
References[edit | edit source]
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