Ordinary linear regression assumes a constant variance for the response of dependent variable (DV). It answers “How does the conditional mean of Y depend on the covariates X?”. QR can model the conditional distribution of the response can vary with independent variables (IV), which gives you insights about extreme conditions. QR calculates the conditional mean of Y depend on covariates X at each quantile of the conditional distribution.
difference between QR and standard linear regression
| Linear regression |
Quantile Regression |
| Predict conditional mean |
predict conditional distribution |
| Applies with limited n |
Needs sufficient data in tails |
| Assumes normality |
Distribution agnostic |
| Sensitive to outliers |
Robust to outliers |
| Computationally inexpensive |
Computationally intensive |
Test whether two QR coefficients are different
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| Qreg25=rq(Y~X, tau=0.25)
Qreg75=rq(Y~X, tau=0.75)
anova(Qreg25, Qreg75)
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Run several QR
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| QR=rq(Y~X, tau=seq(0.2, 0.8, by=0.1))
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Reference
- Three things you should know about quantile regresson
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