[R] How to generate a smoothed surface for a three dimensional dataset?

[Bert Gunter]

... or, more simply

lm(z ~ polym(x,y, degree=2) )

?polym

Cheers,
Bert





On Wed, Dec 4, 2013 at 10:30 AM, David Winsemius <dwinsemius at comcast.net> wrote:
>
> On Dec 4, 2013, at 8:56 AM, Duncan Murdoch wrote:
>
>> On 04/12/2013 11:36 AM, Jun Shen wrote:
>>> Hi,
>>>
>>> I have a dataset with two independent variables (x, y) and a response
>>> variable (z). I was hoping to generate a response surface by plotting x, y,
>>> z on a three dimensional plot. I can plot the data with rgl.points(x, y,
>>> z). I understand I may not have enough data to generate a surface. Is there
>>> a way to smooth out the data points to generate a surface? Thanks a lot.
>>
>> There are many ways to do that.  You need to fit a model that predicts z from (x, y), and then plot the predictions from that model.
>> An example below follows yours.
>>>
>>> Jun
>>>
>>> ===========================
>>>
>>> An example:
>>>
>>> x<-runif(20)
>>> y<-runif(20)
>>> z<-runif(20)
>>>
>>> library(rgl)
>>> rgl.points(x,y,z)
>>
>> Don't use rgl.points, use points3d() or plot3d().  Here's the full script:
>>
>>
>> x<-runif(20)
>> y<-runif(20)
>> z<-runif(20)
>>
>> library(rgl)
>> plot3d(x,y,z)
>>
>> fit <- lm(z ~ x + y + x*y + x^2 + y^2)
>>
>
>  Newcomers to R may think they would be getting a quadratic in x and y. But R's formula interpretation will collapse x^2 to just x and then it becomes superfluous and is discarded. The same result is obtained with z ~ (x + y)^2).   I would have thought that this would have been the code:
>
> fit <- lm(z ~ poly(x,2) +poly(y,2) + x:y )
>
>
>> xnew <- seq(min(x), max(x), len=20)
>> ynew <- seq(min(y), max(y), len=20)
>> df <- expand.grid(x = xnew,
>>                  y = ynew)
>>
>> df$z <- predict(fit, newdata=df)
>>
>> surface3d(xnew, ynew, df$z, col="red")
>
> With the modified fitting formula one sees a nice saddle (for that particular random draw) using rgl.snapshot().
>
>
> The result with the earlier formula is a more restrained:
>
>
>
>
> Continued thanks to you Duncan for making this great tool available.
>
> --
> David.
>
>
>> Duncan Murdoch
>>>
>
> David Winsemius
> Alameda, CA, USA
>
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-- 

Bert Gunter
Genentech Nonclinical Biostatistics

(650) 467-7374