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Re: st: Quantile vs Quartile regression


From   David Hoaglin <dchoaglin@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Quantile vs Quartile regression
Date   Tue, 28 May 2013 23:38:18 -0400

Dear Shikha,

The analyses are intended to produce different summaries, so you
should not expect OLS to give the same result as a quantile
regression.  In general, the answer to your question is No.

It may help to recall that the definition of the regression of Y on X
(when x is a single "continuous" predictor) is the mean of the
distribution of Y at each value of X, formally E(Y|X =x).  The
definition does not require that this function of x be a straight
line, though that is often a good approximation.

Similarly, with several "continuous" predictors, the regression of Y
on those predictors is the mean of the distribution of Y at each
combination of predictor values: E(Y|X1 = x1, X2 = x2, ...).

For the .50 quantile, the summary you are fitting is the conditional
median, as a function of the predictors.  In general it differs from
the conditional mean (i.e., the OLS regression).

When you form the quartiles of Y and summarize by OLS, the fit is the
conditional mean of the distribution of Y in the particular quartile.

I hope this helps.

David Hoaglin

On Tue, May 28, 2013 at 10:11 PM, Shikha Sinha
<shikha.sinha414@gmail.com> wrote:
> I want to estimate a quantile regression at four quantiles (0.25 0.50 0.75
> 0.90). I used -sqreg command in stata. However, I was trying another
> method, i.e. divide the sample into four quartiles based on distribution of
> dependent variable (weightGRAM) and run a simple OLS for each quartile. The
> results are shown below in 2. The OLS results are very different from
> -sqreg results.
>
> Can someone explain me the difference between 1 and 2, and is there way to
> replciate results in 1 by running an OLS model?
>
>
> 1. sqreg weightGRAM member child_age , quantile(.25 .50 .75 .90) nolog
>
> 2.  xtile qweight=weightGRAM,nq(4)
>
> . ta qweight
>
> 4 quantiles
> of
> weightGRAM       Freq.     Percent        Cum.
>
> 1       2,738       25.13       25.13
> 2       2,778       25.49       50.62
> 3       2,730       25.05       75.67
> 4       2,651       24.33      100.00
>
> Total      10,897      100.00
>
> . bys qweight:  reg weightGRAM member child_age
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