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Re: st: Quantile vs Quartile regression


From   Nick Cox <njcoxstata@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Quantile vs Quartile regression
Date   Wed, 29 May 2013 05:57:41 +0100

In addition to David's fundamental point, the means of the four
-xtile- classes you produced should be at  cumulative probabilities
.125 .375 .625 .875 in a uniform distribution with no predictors and
somewhere else otherwise. There is no reason to suppose that they
would ever match your chosen quantiles for -sqreg-. I think this is
the point Prakash Singh is making in  a different way. (I set aside
the small distortions associated with tied values in practice.)
Nick
njcoxstata@gmail.com


On 29 May 2013 04:38, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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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