Techniques to Handle Non-Normal Residuals
Techniques to Handle Non-Normal Residuals:
Transformation:
- Apply mathematical transformations (e.g., logarithm, square root) to the response variable or predictor variables to stabilize variance and make residuals more normal.
Box-Cox Transformation:
- A statistical method that identifies the most suitable transformation to normalize residuals.
Weighted Least Squares:
- Assign weights to observations based on the variance of residuals, giving more importance to observations with smaller variances.
Robust Regression:
- Use robust regression methods that are less sensitive to outliers and violations of normality assumptions.
Residual Plots and Diagnostics:
- Examine residual plots, QQ plots, and other diagnostic plots to identify patterns or outliers that might be causing non-normality. Address influential points or outliers as needed.
Generalized Linear Models (GLMs):
- If the response variable is not continuous or the error structure is not normally distributed, consider using GLMs that can accommodate various distributions and link functions.
Bootstrapping:
- Use resampling techniques like bootstrapping to estimate confidence intervals and test statistics, which can be more robust to violations of normality assumptions.
Data Segmentation:
- Divide the dataset into subgroups based on certain criteria and build separate models for each subgroup if the relationship between variables or error distribution varies across groups.
By addressing non-normal residuals through appropriate techniques, you can improve the reliability and validity of regression analysis results, ensuring more accurate interpretations and predictions.
References:
https://stats.stackexchange.com/questions/100214/assumptions-of-linear-models-and-what-to-do-if-the-residuals-are-not-normally-di
https://www.statalist.org/forums/forum/general-stata-discussion/general/1663870-what-to-do-if-residuals-are-not-normally-distributed
