I have used the "quantreg" package in R to find quantiles for my data. All my data, both predictors and responses are limited between 0 and 1, while a number of quantiles given by "rq" or "rqss" functions have values less than 0 or more than one. I was wondering if there is a solution for this problem, maybe a different function which gives truncated quantiles. Thanks
Quantile regression is an additive model. No purely additive linear model can prevent predicted values from going outside any given range. You can either hope to find a transformation of $Y$ that does not have a limited range that will fit the model, or consider the use of ordinal regression. For example the R
orm function handles continuous $Y$ and allows estimation of quantiles, the mean, and exceedance probabilities
Thanks to the property of equivariance to monotonic transformations, shared by all quantile methods, one can simply operate a logit transformation and run a linear quantile regression on the transformed outcome.
For further information you might consider referring to this paper on quantile regression for bounded outcomes (Bottai & McKeown 2010).