Why the standard errors obtained from PROC GLM (for analysis of multiple regression) is larger compared to those from PROC QUANTREG (for analysis of quantile regression)?
1$\begingroup$ Add some screenshots and sample code for the careful reader... $\endgroup$– Giuseppe Biondi-ZoccaiSep 30, 2016 at 10:09
$\begingroup$ proc glm data=ashu; class B4 M18 V714 V149 V501 V130 V101 V102 V190; model BMICHILD=B8 B4 M18 V012 V439111 V714 V149 V501 V130 V101 V102 V190/solution ss3; run; $\endgroup$– ashuSep 30, 2016 at 10:26
$\begingroup$ proc quantreg data=ashu; class B4 M18 V714 V149 V501 V130 V101 V102 V190; model BMICHILD=B8 B4 M18 V012 V439111 V714 V149 V501 V130 V101 V102 V190/quantile=0.25 0.5 0.75; run; $\endgroup$– ashuSep 30, 2016 at 10:29
$\begingroup$ The SAS System St.Error (proc quantreg) 0.2641 0.0118 0.0029 0.0054 0.0343 0.1414 0.0978 0.0797 0.0858 0.1195 Stand.Error (proc glm) 0.34143132 0.01436368 0.00313305 0.00698080 0.04021688 0.14241718 0.10932573 0.08581348 0.10279831 0.11945417 $\endgroup$– ashuSep 30, 2016 at 10:41
2$\begingroup$ Please edit the question rather than append extra information in comments, & include enough context for the question to be understandable even for those unfamiliar with the SAS procedures you're using. $\endgroup$– Scortchi - Reinstate Monica ♦Sep 30, 2016 at 10:53
Simple answer: Since they are estimating different things, there is no reason to expect they would have the same standard errors. This is especially true for quantiles other than the median - which should at least be similar to the mean being estimated in OLS regression.
Standard errors for quantile regression are calculated in various ways. SAS PROC QUANTREG allows three methods and, by default, uses various methods (see the link).
To determine why the SE is smaller for quantile regression in your particular case, you would have to compare the formulas for your particular data. However, one general reason could be that quantile regression is less affected by outliers or other extreme points.
1$\begingroup$ The variables i am using for both models (proc glm and proc quantreg) is the same. I am trying to compare the results obtained from both models. The above answer you share it me is very helpful. $\endgroup$– ashuSep 30, 2016 at 11:27