How to generate a smoothed surface for a three dimensional dataset?
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