I am trying to predict the 10th, 30th, 50th, 70th and 90th quantiles of dependent variable. I have 110 independent variables in the data set. I can think of two approaches to do this.
I am ultimately interested in coefficient values of independent variables at different quantiles.
With approach 1 - I mostly see either increasing or decreasing trend of coefficients from 10th quantile to 90 quantile.
I do not see such trend with second approach. However, what could be the potential pitfalls of second approach.