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Re: st: Semi parametric regression plreg


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Semi parametric regression plreg
Date   Mon, 26 Nov 2012 18:26:58 +0100

Lisa Meisel <Lisa.Meisel@stud.uni-regensburg.de>:
If you read the article you cited, you noticed that the crucial
assumption is that the t in
p = f(t) + b*Z + e
has a natural ordering, as does time or number of customers, which
block numbers do not.

However, your model with geography is probably naturally modeled as
smoothly evolving across two dimensions x and y.
In this case, you can run a set of local linear regressions,
estimating both f(.) and b semiparametrically.
See also
http://www.stata.com/statalist/archive/2012-10/msg00558.html
for some ideas.

Essentially, you can loop over values of x and y, redefining kernel
weights at each iteration x0 and y0 (choosing a new origin in each
iteration), and estimating a local linear regression
p = a*t + b*Z + d*x + c*y + g*x*y + e
or somesuch, using weights that decay to zero as x and y get farther
from x0 and y0.

You do need to assume that the surface is smooth in (x,y) for a
semiparametric approach to work well, and there is no guarantee for
your type of data:
http://www.jstor.org/stable/2587017
http://eprints.lse.ac.uk/30814/1/sercdp0018.pdf
http://research.stlouisfed.org/publications/review/10/05/Chiodo.pdf

On Mon, Nov 26, 2012 at 3:39 PM, Lisa Meisel
<Lisa.Meisel@stud.uni-regensburg.de> wrote:
> Ok, thanks.
>
>>>> Nick Cox  11/26/12 1:20 PM >>>
> I can't see that -plreg- makes any sense for your situation.
>
> Nick
>
> On Mon, Nov 26, 2012 at 11:11 AM, Lisa Meisel
>  wrote:
>> Hi Nick,
>>
>> "location" here is a nominal variable represented by blocknumbers (similar to postal codes) of the city. So I need to know the value/price of this postal code for a house located there. Does the plreg command only work with metric variables?
>>
>>
>> Thank you so far!
>> Lisa
>>
>>>>> Nick Cox  11/26/12 11:35 AM >>>
>> The paper cited gives an example of how you can plot the results. If
>> this method is any good, the plot will make sense when you think about
>> results using your substantive (e.g. economic) knowledge.
>>
>> How is "location" quantified as a single metric?
>>
>> Nick
>>
>> On Mon, Nov 26, 2012 at 8:23 AM, Lisa Meisel
>>  wrote:
>>
>>> I want to use the plreg command written by Michael Lokshin (Difference-based semiparametric estimation of partial linear regression models, The Stata Journal 6(3), p.377-383, 2006).
>>>
>>> My problem is to interpret the values of the new variable generated by the option generate(newvar).
>>> My semi parametric model is the following
>>>
>>> p = f(l) + b*Z + e
>>>
>>> with p being the house price, Z being a vector of housing attributes and f(l) being the part of the house related to its location l. f(l) is supposed to be a non-linear function.
>>> When checking help of the plreg command in Stata it says that the new variable contains the smoothed values of depvar. In the paper of Lokshin they write it is containing the smoothed values of the argument of f. So how can I interpret the values of this generated variable?
>>> The values I get when running the regression are similar to the ones of p. So I guess they are not the values for f(l), but rather the smoothed values of p? How can I find the portion of the house price related to f(l)?

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