I recently employed multiple quantile regression in my area of research and found some interesting quantile differences across the distribution of Y, but I don't quite understand what they all really mean. Unlike the traditional methods such as dividing the sample into multiple groups where I have access to the groups' data on various variables which then allows me to make sense of, for example, why the correlation between X and Y is 0 for group 1 and .7 for group 2, I feel like I have no idea where those quantile regression estimates come from, especially when there are more than 2 predictors in the QR model. Another way of putting this is I don't know which specific data points contribute heavily to a given quantile regression estimate and so this makes it very difficult for me to understand what the quantile differences really mean.
Based on my understanding of QR, it uses all the data points in the full sample but weights the data points that are farther from a quantile of interest less heavily than the data points that are closer to that same quantile of interest, is this correct? If so, as a follow up, can I divide my full sample into 10 groups, e.g., 10th quantile, 20th quantile, 30th quantile group, and then examine how the 10 groups differ on various variables of interest in order to make sense of the 10 quantile regression estimates that I got? I know the subgroups approach is not ideal, which is why I used QR, but if you think this is a terrible idea, please let me know why. And if you know of any other methods that allow me to have a more fine-grained understanding of my results, please help. I conducted QR using the
quantreg package in R.