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Re: st: Quantile Regression Coefficient Investigation for Individual Observations
From
George Bentley <[email protected]>
To
[email protected]
Subject
Re: st: Quantile Regression Coefficient Investigation for Individual Observations
Date
Wed, 30 Jan 2013 10:56:21 -0500
On Mon, Jan 28, 2013 at 10:22 AM, George Bentley
<[email protected]> wrote:
>
> Hi David,
>
> My apologies for the delayed response but I used your advice and thought
> about my end goal. I have decided that identifying EKC conformity on a
> county by county basis is not necessary. Due to the presence of spatial
> autocorrelation in the indicators I am going to use an spatial error
> regression model. Thank you again for your assistance, it is appreciated.
>
> Best,
> George
>
>
> On Fri, Jan 18, 2013 at 10:35 PM, David Hoaglin <[email protected]>
> wrote:
>>
>> Hi, George.
>>
>> The additional information is helpful. Thank you.
>>
>> Though you probably do not intend it that way, I could read the
>> description of the EKC as longitudinal. Your data are
>> cross-sectional. If the EKC was formulated from a longitudinal point
>> of view, cross sectional data may show a different pattern of
>> behavior.
>>
>> I am not an expert on quantile regression, but I don't see why it
>> would be desirable to use that approach with your data. What happens
>> when you use ordinary regression?
>>
>> A U-shaped pattern may not be quadratic. If the distribution of per
>> capita income is reasonable, you could explore the pattern by setting
>> up categories of per capita income (perhaps as many as 10 of them) and
>> using the corresponding dummy variables (for the categories other than
>> the reference category) as the predictors (instead of per capita
>> income and per capita income squared). Plotting the coefficients of
>> those dummy variables against the midpoints of the categories should
>> give you an idea of the pattern, after adjusting for the contributions
>> of the other variables.
>>
>> So far, I don't see a reason for fitting quantile regressions and
>> identifying the counties that happen to have a zero residual for a
>> particular quantile regression. I also don't see the logic of making
>> statements about whether the coefficients of per capita income and per
>> capita income squared are correct.
>>
>> David Hoaglin
>>
>> On Fri, Jan 18, 2013 at 8:57 AM, George Bentley
>> <[email protected]> wrote:
>> > Hi David,
>> >
>> > Thank you for your response. I would be happy to supply more
>> > information to better detail what I am hoping to achieve.
>> >
>> > I am investigating an empirical model called the Environmental Kuznets
>> > Curve (EKC), it is used to model the relationship between a measure of
>> > environmental quality/degradation and a measure of income. When
>> > investigating the relationship between environmental quality and
>> > income if an EKC exists it appears as a U-shaped curve (quality on y
>> > axis, income on x axis). The general idea is that at low levels of
>> > income prior to economic development very little damage occurs to the
>> > environment, then as economic development and consequent increases in
>> > income take place there is greater damage to environment/decrease in
>> > environmental quality, finally it is believed an inflection point is
>> > reached where further increases in income correspond to improved
>> > levels of environmental quality (better technology, greater demand for
>> > cleaner environment, etc.).
>> >
>> >
>> > The functional form of the EKC is captured in the EKC income
>> > polynomial consisting the per capita income term and per capita income
>> > term squared. In this scenario I am treating agriculture as an
>> > environmental quality measure so if an EKC exists there should be a
>> > negative sign on the per capita income term and positive sign on the
>> > per capita income squared term. The county area, county population,
>> > and county topography are acting as controls.
>> >
>> > You are correct, each county of the 153 counties has a value for per
>> > capita income, per capita income squared, county area, county
>> > population, and county topography. My rationale and train of thought
>> > for using quantile regression, please correct me if this is wrong is
>> > as follows.
>> >
>> > After running the code in my original email and constructing the
>> > quantile plot I could see that there were cases where the coefficient
>> > on the per capita income term is negative and the coefficient on the
>> > per capita income squared term is positive. At this point I went into
>> > Stata and began running single quantiles individually finding that the
>> > quantile range where the values match what I am looking for is
>> > .52-.70. As I ran each quantile from .52 to .70 individually I
>> > generated the residuals for each observation. After reading that in
>> > quantile regression there are as many observations with residuals of
>> > zero as indepedent variables (5 indepedent variables + 1 intercept
>> > term in my case) I found the six observations in each quantile with a
>> > residual of zero. I believed that I could then say for these six
>> > counties (in a single quantile) the coefficients on the per capita
>> > income term and per capita income squared term were correct. Is this
>> > the wrong way to look at the outputs?
>> >
>> > Again, I appreciate any help and insight you can offer.
>> >
>> > Thank you,
>> > George Bentley
>> >
>> > On Thu, Jan 17, 2013 at 4:32 PM, David Hoaglin <[email protected]>
>> > wrote:
>> >> 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
>> >> <[email protected]> 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
>> >> *
>> >> * For searches and help try:
>> >> * http://www.stata.com/help.cgi?search
>> >> * http://www.stata.com/support/faqs/resources/statalist-faq/
>> >> * http://www.ats.ucla.edu/stat/stata/
>> > *
>> > * For searches and help try:
>> > * http://www.stata.com/help.cgi?search
>> > * http://www.stata.com/support/faqs/resources/statalist-faq/
>> > * http://www.ats.ucla.edu/stat/stata/
>> *
>> * For searches and help try:
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>> * http://www.stata.com/support/faqs/resources/statalist-faq/
>> * http://www.ats.ucla.edu/stat/stata/
>
>
*
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