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st: interpreting quantile regression with categorical predictors


From   Samantha Batchelor <S.Batchelor@griffith.edu.au>
To   statalist@hsphsun2.harvard.edu
Subject   st: interpreting quantile regression with categorical predictors
Date   Tue, 9 Aug 2011 14:24:59 +1000

Hi,
this is more a quantile regression question than a STATA question but hope someone can help anyway.
I have a QR with a number of demographic variables predicting reading comprehension achievement e.g. small vs large family size and ethnicity.  
These are my coefficients for family size - makes sense to say that kids in large families don't do as well as kids in small families.
                       q10     q20      q30       q40       q50       q60       q70       q80      q90
large family      -7.00   -9.00   -10.00    -12.00   -14.00   -13.00   -15.00   -11.00   -2.00
 
These are my coefficients for ethnicity (Anglo-Australian is the reference group).
 
                            q10      q20    q30     q40     q50    q60      q70       q80       q90
Vietnamese             4.00    8.00   12.00   9.00   6.00    10.00   -1.00    -3.00    -3.00
Pacific Islander        6.00    8.00   7.00     5.00   0.00   -1.00    -6.00    -5.00    -5.00
Indigenous              6.00    8.00   12.00   9.00   3.00   -3.00    -5.00    -4.00     -6.00
Other                     6.00    5.00   10.00   5.00   4.00   -2.00   -12.00   -16.00   -15.00
 
How do I interpret the ones with positive coefficients at the bottom end of the distribution and negative coefficients at the top?  If I interpret this the same way I interpreted family size then I would be saying that Islander and Indigenous kids do better than Australians at the bottom end of the distribution (they are statistically significant) - this doesn't even make sense to me - it's like saying they're doing better when they're doing badly?
I asked a statistician for advice and was told that with categorical variables I should treat the coeffient more like a "rate" - so I would interpret the above as meaning that there are more Indigenouse kids at the lower end and fewer at the higher end - this makes sense.  BUT - if I then interpret family size this way I would have to say that there are fewer kids in large families across the whole distribution.
I've spent ages looking for books or websites that explain this to no avail and am totally confused.  Can someone help?
Thanks very much,  Sam.

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