# Is it possible to specify different quantile regression models for each quantile?

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.

• To underscore, by different models you mean models that differ not only by their coefficient values but also by that they contain different variables or have different functional form? Because if we consider different coefficient values to imply different models, then the answer is obvious. Jun 8, 2021 at 15:18
• @RichardHardy I take it to mean something like 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.
– Dave
Jun 8, 2021 at 15:28
• "...the other quantiles do NOT change linearly" is how it should read. And yes, @RichardHardy, I think we agree.
– Dave
Jun 8, 2021 at 16:06
• @RichardHardy by different models I mean models containing different variables ("different sets of variables bearing predictive value"). Jun 9, 2021 at 7:25