I am interested in using quantile regression for some of my models, but would like to have some clarifications on what can I achieve using this methodology. I understand I can obtain a more robust analysis of IV/DV relationship, especially when faced with outliers and heteroscedasticity, but in my case the focus is on prediction.
In particular I'm interested in improving the fit of my models, without resorting to more complex non-linear models, or even piecewise linear regression. At prediction, is it possible to select the highest probability outcome quantile based on the value of the predictors? In other words, is it possible to determine each predicted outcome quantile probability, based on the value of the predictors?
Best Answer
The right hand side of a model in quantile regression has the same structure and types of assumptions as other regression models such as OLS. The main differences with quantile regression are that one directly predicts quantiles of the distribution of $Y$ conditional on $X$ without resorting to parametric distributional manipulations (e.g., $\bar{x} \pm 1.96s$), and that no distributional shape of residuals is assumed other than assuming that $Y$ is a continuous variable.