Re: st: Quantile Regression Coefficient Investigation for Individual Observations

[David Hoaglin <dchoaglin@gmail.com>]

Hi, George.

It would help if you gave some more information about your analysis
and its goals.

Am I correct that your data consist of one observation for each of the
153 counties?

What is the motivation for the quantile regressions?

Each of the quantile regressions has an overall coefficient for per
capita income and an overall coefficient for per capita income
squared, but not separate coefficients for the individual counties.

How confident are you that per capita income and per capita income
squared capture the functional relation between a given quantile and
per capita income?  Does the way in which the coefficients of those
two predictors vary across the quantiles make substantive sense?  Many
departures from a linear relation are not quadratic.  You may be able
to get the data to guide the choice of functional form.

I hope this discussion is helpful.

David Hoaglin

On Wed, Jan 16, 2013 at 6:24 PM, George Bentley
<george.bentley@uconn.edu> wrote:
> Good evening,
>
> I am new to Stata software and Statalist.  So far I have been using
> Stata solely for quantile regression.  I am able to run quantile
> regression without issue but would like to delve deeper and am unsure
> of how to proceed.  In a project, I am working with 153 counties where
> agricultural cover is the dependent variable and the independent
> variables are per capita income, per capita income squared, county
> area, county population, and county topography.
>
> Here is an excerpt of my Stata code:
>
> quietly qreg  laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.1)
> estimates store QR_10
> quietly qreg  laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.2)
> estimates store QR_20
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.3)
> estimates store QR_30
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.4)
> estimates store QR_40
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.5)
> estimates store QR_50
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.6)
> estimates store QR_60
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.7)
> estimates store QR_70
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.8)
> estimates store QR_80
> quietly qreg   laagrpc  larea  lapop  topo  lainc  lainc2, quantile(.9)
> estimates store QR_90
> estimates table QR_10 QR_20 QR_30 QR_40 QR_50 QR_60 QR_70 QR_80 QR_90,
> b(%7.3f) se
>
>
> Excerpt of Estimates Table (Standard errors removed):
>
>                                  Q = 0.1    Q = 0.2     Q = 0.3     Q
> = 0.4     Q = 0.5     Q = 0.6     Q = 0.7     Q = 0.8     Q = 0.9
> Per capita Income        61.581     76.360       65.790      50.775
>    3.250       -18.945      -6.001      30.653      17.331
>
> Per Capita Income Sq. -3.039      -3.764        -3.260       -2.553
>   -0.209         0.840        0.196       -1.579      -0.885
>
>
>  From my estimates table I can see that the per capita income term has
> a negative coefficient at quantile = 0.6 and quantile = 0.7.  Also, I
> can see that the per capita income squared term has a positive
> coefficient at quantile = 0.6 and quantile = 0.7.  My main goal is to
> determine the counties having a negative coefficient on the per capita
> income term and a positive coefficient on the per capita income
> squared term simultaneously.  Is this possible and is there any advice
> as to how I should proceed?  Thank you for any assistance in advance.
>
> Thank you,
> George Bentley
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