Quantile Regression Analysis

Quantile regression is a regression method that estimates the effect of predictors on specified conditional quantiles of an outcome, such as the median or 90th percentile, rather than the mean.

분위수회귀는 결과변수의 평균이 아니라 중앙값이나 90번째 백분위수 같은 특정 조건부 분위수에 대한 예측변수의 효과를 추정하는 회귀방법이다.

How do I see whether a predictor affects the high or low end of an outcome differently from the average?

예측변수가 결과변수의 평균이 아니라 상위나 하위 값에 다르게 영향을 주는지 어떻게 확인하나요?

Quantile regression estimates predictor effects at chosen quantiles of the outcome distribution, showing whether effects differ between low, middle and high values. It fits skewed outcomes, outliers and heteroscedastic data where ordinary least squares describes only the mean.

When to use Quantile Regression Analysis

• A continuous outcome with skew, outliers or spread that changes with predictors
• Effects on the median or on upper or lower tails, such as income or test score distributions
• Comparing coefficients across several quantiles

When to use something else

• Interest is only in the mean with well-behaved residuals; use ordinary least squares regression
• Binary or count outcomes; use logistic or Poisson regression

Assumptions and requirements

• Independent observations
• Correctly specified linear form at each quantile
• No normality or constant-variance assumption on errors

What the analysis reports

• Coefficients for each quantile
• Standard errors and confidence intervals (often bootstrapped)
• Coefficient plots across quantiles
• Pseudo R-squared

How to report it

At the [value]th percentile of [outcome], [predictor] was associated with a [value]-unit increase (B = [value], 95% CI [[value], [value]]).

Related methods

• Ordinary Least Squares Regression
• Robust Regression
• Median Regression

Run Quantile Regression Analysis on Quorant