Is it possible to interpret coefficients from a quantile regression on standardized data?
Suppose I standardize the dependent variable $y$ and the independent variable $x$ (subtract the mean and divide by the standard deviation) and then run a quantile regression for the median such as
qreg y x, q(0.5)
in stata. The estimated coefficient for the independent variable is $0.5$. Is then the following interpretation correct:
A one standard deviation increase of the independent variable, increases the median of the dependent variable by $0.5$ standard deviation?
Best Answer
Yes, that is the interpretation. One way in which you can see this is by predicting the median for different values of your standardized, each 1 unit (in this case standard deviation) appart. Than you can look at how much these predicted medians differ, and you will see that that is exactly the same number as your standardized quantile regression coefficient. Here is an example: