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Re: st: Multivariate kernel regression


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Multivariate kernel regression
Date   Wed, 17 Oct 2012 14:25:47 -0400

Josh Hyman <hyman.josh@gmail.com>:
Taking the mean of Y for values of X near X0 *is* a regression; you
are calculating the conditional mean of Y. What you describe is a
zero-degree local polynomial regression in -lpoly- (a regression on
just a constant), which is inadvisable (though -lpoly- default
behavior) for the reasons given in the -lpoly- manual entry. Better to
regress on X and interactions (all in deviation form from point X0)
and predict at X=X0.  I recommend you start with a simple example with
say 100 values of a one-dimensional X and try calculating the means of
Y at (say) 10 values using a couple different approaches, to get a
sense of what you are doing.  Then generalize to 100*100 values of X1
and X2 and calculate mean Y at (say) 100 points on that grid.

Did you look at http://fmwww.bc.edu/repec/bocode/t/tddens
(multivariate kernel density estimation)?

Ask John DiNardo if you have conceptual questions--if he is currently
accessible to you at the Ford school--the big ideas may easier to
explain in person.

On Wed, Oct 17, 2012 at 1:04 PM, Josh Hyman <hyman.josh@gmail.com> wrote:
> Hi Austin (and others),
>
> Thank you very much for your reply. Sorry about my delayed response -
> I wanted to investigate more to make sure I understood your
> suggestion.
>
> I'm not sure your suggestion gets me exactly what I was looking for,
> and I want to clarify. My reference to -lpoly- in my initial post may
> have been confusing. I don't actually want to do kernel-weighted local
> regressions. I want to estimate "multivariate kernel regression",
> which to my understanding, doesn't actually involve any regressions at
> all. It takes the weighted average of Y for all observations near to
> the particular value of X, weighted using the kernel function. And
> where X represents more than 2 variables. So, this actually seems the
> same to me as multivariate kernel density estimation, which I also
> don't see any user-written commands for in Stata. What I am looking
> for, I guess is like a version of -kdens2- that allows for more than
> one "xvar", and wouldn't output a graph (since it would be in greater
> than 3 dimensions), but rather would output the fitted or predicted
> values of the Y (like -predict, xb-) for each observation.
>
> Regardless, it sounds like given your suggestion, one way to do this
> is to loop over all possible combinations of the values of the X
> variables and calculate the weighted Y for each combination using the
> kernel of my choice? Please let me know if this would be your
> suggestion, or if given my further clarification, if you know of any
> user-written commands in Stata to do this, or if you have any other
> suggestions.
>
> Thanks a lot for your help, and sorry again for the delayed response.
> Josh
>
>
> On Fri, Oct 12, 2012 at 3:31 PM, Austin Nichols <austinnichols@gmail.com> wrote:
>> Josh Hyman <hyman.josh@gmail.com>:
>> If you know the multivariate kernel you want to use, and the grid you
>> want to smooth over, it is straightforward to loop over the grid and
>> compute the regressions.  To program a general estimator for a wide
>> class of kernels would be substantially more work.  See e.g. -kdens-
>> on SSC and
>> http://fmwww.bc.edu/repec/bocode/m/mf_mm_kern
>> http://fmwww.bc.edu/RePEc/bocode/k/kdens.pdf
>>
>> A simple conic (triangle) kernel in 2 dimensions is easiest, see e.g.
>> http://fmwww.bc.edu/repec/bocode/t/tddens
>>
>> On Fri, Oct 12, 2012 at 1:49 PM, Josh Hyman <hyman.josh@gmail.com> wrote:
>>> Dear Statalist users,
>>>
>>> I am trying to figure out if there is a way in Stata to perform
>>> multivariate kernel regression. I have investigated online and on the
>>> Statalist, but with no success. What I am looking for would be similar
>>> conceptually to the -lpoly- command, but with the ability to enter more
>>> than one "xvar".
>>>
>>> If there are no Stata commands to do this (user-written or otherwise), then
>>> do you recommend coding up a program to do this manually? I have used Stata
>>> for many years, and written programs before, but have never had to code up
>>> a regression manually. If you have suggestions on how to do this, or
>>> resources to consult, that would be greatly appreciated.
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