# st: Re: Re: RE: Quintiles, Quartiles and Tertiles anyone!!!

 From "Scott Merryman" <[email protected]> To <[email protected]> Subject st: Re: Re: RE: Quintiles, Quartiles and Tertiles anyone!!! Date Tue, 23 Dec 2003 19:15:57 -0600

```Zoue,

First, a point of clarification.  The way you have your regression model set up,
hcy1quin is the dependent variable.  It depends on ([in theory] is caused by)
the independent variable(s).  The model you estimated below is simply a median
regression -- you have fit a line through the 50th quantile.

Since I do not know what the variable hcy1quin means and I am not in the tribe
of nutrition and dietetics researchers, let me give you an example from
economics.

Suppose you were looking at how policy variable (say, education spending)
affects the growth rate of Gross Domestic Product, gdp.

OLS (or in Stata: -reg gdp education-) will estimate a conditional mean model
and will be sensitive to outliers. Implicit in this formulation is the idea that
education affects only the location of the conditional distribution of the GDP
growth rates.  However, when education affects the conditional distribution in
other ways, such as its dispersion, estimation of the conditional mean is no

Instead of using OLS, we use quantile regression (specifically -sqreg- to
estimate simultaneous-quantile regression) to examine how education affects
slow-growing countries and fast-growing countries.  We might define slow-growing
countries as those in the 10th quantile or the left tail of the conditional
distribution of growth rates and the fast-growing countries as those in the 90th
quantile or right tail of the conditional distribution of gdp growth rates.

Like OLS, in quantile regression, the estimated coefficients can be interpreted
as the marginal effects.  We may have different estimates for the slope
coefficients.  For example, suppose: 0 < education(10th) < education(90th).  If
this is the case, a marginal change in education spending will affect the GDP
growth rates differently; the growth rate for the fast-growing countries will
increase more than slow-growing countries.  There will be divergence in growth
rates.

In your particular case, I suppose one could do the following (previously, you
mentioned age as a variable, so I included it here):

-sqreg hcy1quin cob1 age, q(.2 .4 .6 .8) reps(1000)-

would tell you the affect of vitamin B12 on different portions of the
distribution (the 20th, 40th, 60th, and 80th quantile) of hcy1quin.  You could
then use -test- to test if the coefficients are equal. Please take a look at
worked examples.

Merry Christmas and I hope this helps,
Scott

----- Original Message -----
From: "Zoue Lloyd Wright" <[email protected]>
To: <[email protected]>
Sent: Tuesday, December 23, 2003 7:03 AM
Subject: st: Re: RE: Quintiles, Quartiles and Tertiles anyone!!!

Dear Scott,

Thankyou so very very much, I am truly grateful.

I have created the variable hcy1quin which is the quantile
with 5 quintiles of the Independent Variable.

Have I correctly below asked if the independent variable
(hcy1quin) is statistically compared to the vitamin B12
levels which is variable cob1 and have I given the correct
instruction to produce 5 quintles or is this automatically
assumed because I have already created it in the hcy1quin.

. qreg  hcy1quin cob1
Iteration  1:  WLS sum of weighted deviations =  131.58135

Iteration  1: sum of abs. weighted deviations =  131.32969
Iteration  2: sum of abs. weighted deviations =  130.31787
Iteration  3: sum of abs. weighted deviations =  130.07767
Iteration  4: sum of abs. weighted deviations =  130.04444

Median Regression                                    Number of obs =       151
Raw sum of deviations      184 (about 3)
Min sum of deviations 130.0444                     Pseudo R2     =    0.2932

------------------------------------------------------------------------------
hcy1quin |      Coef.   Std. Err.       t     P>|t|       [95% Conf. Interval]
---------+--------------------------------------------------------------------
cob1 |  -.0074074   .0008079     -9.168   0.000      -.0090039   -.0058109
_cons |   4.711111   .2162561     21.785   0.000       4.283786    5.138436
------------------------------------------------------------------------------

Thankyou again, you have made my Xmas,
Kind wishes,
Zou�

On Mon, 22 Dec 2003 21:29:38 -0600 Scott Merryman
<[email protected]> wrote:

> Zoue,
>
> You may want to take a look at -xtile-  This command will create a new
> categorical variable containing categories corresponding to the specified
> quantiles.
>
> If I understand your question, you plan to subset the data into quantiles and
> then performing analysis on the subsets will produce incorrect results.
Koenker
> and Hallock (2001 "Quantile Regression" Journal of Economic Perspectives, 15:4
> pages 143 -156) refer to this as "truncation on the dependent variable."  This
> method of truncation is vulnerable to selection bias, since one is truncating
> the full sample based on the dependent variable in the model. This can produce
> both biased and inconsistent estimates.
>
> As Koenker and Hallock make clear, a more appropriate econometric technique is
> quantile regression (-qreg-).  With quantile regression, one can focus on the
> conditional distribution of the dependent variable and avoid the selection
bias
> associated with truncated regression. This is because with a quantile
> regression, one can choose the central tendency point around which to estimate
a
> regression - for example, 10th decile rather than the mean - without
truncating
> the sample to exclude the upper 90 percent of data.
>
>
> Hope this helps,
> Scott
>
>
> ----- Original Message -----
> From: "Zoue Lloyd Wright" <[email protected]>
> To: <[email protected]>
> Sent: Monday, December 22, 2003 6:57 AM
> Subject: st: RE: Quintiles, Quartiles and Tertiles anyone!!!
>
>
> > Help,
> >
> > Sorry to ask, but I am really stuck and desperate and have
> > an overdue Thesis to hand in.
> >
> > Main Question:
> >
> > Is it possible to quintile, quartile or Tertile data
> > By this I mean
> >
> > I have 200 patients with approximately 20 to 30 sets of
> > variables that I wish to examine in respect of each other
> > using quintiles, quartiles or tertiles, to represent one
> > set as THE INDEPENDENT VARIABLE and compare it with the
> > other sets as DEPENDENT VARIABLES and statistically compare
> > the resulting quintiles with each of the dependent
> > variables.
> >
> > In addition to this I would like to perform an AGE
> > ADJUSTMENT on the above variables, since this will also
> > effect there relationship to the independent variable.
> >
> > Thankyou if anyone can help and make it very user friendly
> > I will be eternally grateful
> >
> > Zou�
> >
> > PS. Firstly can I update Stata 5.0 from the Internet to
> > either version 6.0, 7.0 or 8.0?
> >
>
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

----------------------
Zou� Lloyd-Wright
Nutrition and Dietetics Department,
Kings College London,
Franklin-Wilkins Building,
150 Stamford Street,
Waterloo,
London SE1 9NN
email: [email protected]
Phone:  020 7281 9144
Mobile: 07939 561 683

*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/
```