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# Re: st: Multivariate kernel regression

 From Josh Hyman To statalist@hsphsun2.harvard.edu Subject Re: st: Multivariate kernel regression Date Fri, 19 Oct 2012 12:20:41 -0400

```Thank you so much Austin and Shan.

Shan - I very much appreciate your pointing out the .ado files on
will be a great place for me to start, and seem very to be very
similar to what Austin recommended I try starting with. Ideally I
would like to use slightly more than 4 covariates, but this is
terrific for now, and I will see if I can augment the code to accept a
few more.

Austin - Thanks a lot for your suggestions. I met with John DiNardo
multivariate kernel regression. I sent him an email yesterday to see
if he will discuss this with me. I will begin by coding up your
for me in understanding how the multivariate kernel regression is
operating.

Thanks again to you both! This was my first time posting a question to
the Stata listserve, and I found it incredibly helpful.
Thanks,
Josh

On Wed, Oct 17, 2012 at 2:25 PM, Austin Nichols <austinnichols@gmail.com> wrote:
>
> 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),
> >
> > 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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