Hello everyone! I would like to inquire about determining the R-squared (R2) for quantile regression. I have consistently obtained low R2 values in my results ( Eviews). Any insights or suggestions would be greatly appreciated.
I guess the first question would be, Do you know how the software you're using is calculating what they are calling r-squared ?
The second question would be, How would you feel about the explanation that the model doesn't fit the particularly well ?
It's an interesting question, and I'm mulling it over a bit. I'm wondering how different ways to calculate a pseudo r-squared would reflect a situation where we know that there are outlying values, and so have chosen quantile regression for this reason.
I was playing with an example.
A = c(1,2,3,4,5, 6,7,8,9,10)
B = c(1,2,3,4,15,6,7,8,9,10)
model = quantreg(B ~ A, tau=0.5)
I get a Nagelkerke pseudo r-square of 0.9, but an Efron pseudo r-square of 0.4. So, part of the answer is going to depend on how the software is calculating what they're calling r-squared, and how appropriate that is for the type of regression you are conducting.
Sal Mangiafico Thank you for your reply. It's very interesting. Is R-squared suitable for directly evaluating quantile regression because R-squared is based on the ordinary least squares (OLS) regression framework? If not, what is the best software to calculate R-squared?
Well, technically there is no r-squared per se for quantile regression, because, as you say, r-squared is based on OLS. However, there are various pseudo r-squares available for other models. This gives a good overview: https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/ .
It sounds like Eviews uses a Koenker and Machado pseudo r-square, which sounds like it is appropriate for quantile regression.
(See: https://eviews.com/help/helpintro.html#page/content/quantreg-Estimating_Quantile_Regression_in_EViews.html#ww184662 )
and (See: https://www.maths.usyd.edu.au/u/jchan/GLM/Koenker&Machado1999InferenceQuantileReg.pdf ).
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