As the title says.
I have never seen it, but I see no point that would prohibit me to do it.
For example, a different set of variables might bear predictive value for the 25th-percentile of the dependent variable than for the 10th-percentile of the dependent variable.
Is it possible or am I missing something? If not, I would appreciate any references (i.e. scientific papers) in which the authors do so.
x <- seq(0, 6, 0.001); y <- 7*x + rnorm(length(x), 0, exp(x))
that clearly has a linearly increasing median, but the other quantiles do change linearly. $\endgroup$