Quantile regression uses L1 loss and thus works by doing linear programming A unique optimum is not guaranteed. This seems especially true if the data have ties and for relatively extreme quantiles. If you can look at the solutions see how different they are---often they are essentially the same. Nick's idea of adding in a little noise makes sense to see how unstable the solution is. If the alternate solution is an artifact you should find it gets wiped out by the noise while the primary solution should be mildly degraded.
Look at Roger Koenker's book Quantile Regression, Cambridge, 2005. In fact it you are doing any quantreg I highly suggest buying it or at least getting one of Roger's introduction pieces from his web page. They are all written with Roger's typical rigorous clarity.
-----Original Message-----
From: "Kyle Caswell" <[email protected]>
To: [email protected]
Sent: 10/8/2008 9:02 PM
Subject: st: qreg: alternate solution exists
Hello. I have been running quantile regressions (p25 p50 p75) using the
qreg command. In the iteration log, I get the following note (several
times) sandwiched in between the usual reported sum of absolute weighted
deviations: "note: alternate solution exists"
The following official STATA web-site, explaining the qreg command, displays
a regression log with same "note":
http://www.stata.com/capabilities/qreg.html
Can someone tell me:
(1) What does this mean, explicitly?
(2) When one receives this message, can the resulting output be considered
O.K., insofar as any quantile regression result which converges is O.K.? Or
is this an indication that the coefficients from the model shouldn't be
trusted?
I appreciate any feedback.
best,
-kyle
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