how binary quantile regression divides the dependent variable into quantiles

Question

I am not very clear with binary quantile regression.

As if it was ordinary quantile regression, it would divide the dependent variable's value by its ascending value into quantiles.

But I cannot imagine how it divides y {0;1} value into quantiles.

Can you explain it tome

Answer 1

Well suppose you have 9 observations of Y:

0 0 0 0 1 1 1 1 1

then the 50th percentile will be 1 and you can similarly calculate percentiles as you would any other list of numbers.

Also, remember that quantile regressions assign the check-fucntion to the residual, not Y directly.