Question

I am reading a book by Cohen, Cohen, Aiken and West(2003) “Applied Multiple Regression Correlation Analysis for the Behavioral Sciences” and have come across a 3d plot of a Regression surface showing interaction and no interaction (p. 259). The graphs look like they may have been created using R. I like the graphs as a teaching tool and would like to reproduce them. The plots look something like this:

The only addition to the Coehn et al. plots were lines across the planes at the mean, +1sd, and =1sd for x2. This would be an excellent addition if possible (generally most things are possible with R)

I have provided a sample data set below with an IV, 2 predictors and centered predictors. How would I use R to generate the regression surface (plane) plot showing interaction and an additive model for both the centered and uncentered data (I assume the technique will be the same but want to make sure).

Total of 4 plots:
1. uncentered no interaction
2. uncentered interaction
3. centered no interaction
4. centered interaction

DF<-structure(list(y = c(-1.22, -1.73, -2.64, -2.44, -1.11, 2.24, 
3.42, 0.67, 0.59, -0.61, -10.77, 0.93, -8.6, -6.99, -0.12, -2.29, 
-5.16, -3.35, -3.35, -2.51, 2.21, -1.18, -5.21, -7.74, -1.34), 
    x1 = c(39.5, 41, 34, 30.5, 31.5, 30, 41.5, 24, 43, 39, 25.5, 
    38.5, 33.5, 30, 41, 31, 25, 37, 37.5, 24.5, 38, 37, 41, 37, 
    36), x2 = c(61L, 53L, 53L, 44L, 49L, 44L, 57L, 47L, 54L, 
    48L, 46L, 59L, 46L, 61L, 55L, 57L, 59L, 59L, 55L, 50L, 62L, 
    55L, 55L, 52L, 55L), centered.x1 = c(5.49702380952381, 6.99702380952381, 
    -0.0029761904761898, -3.50297619047619, -2.50297619047619, 
    -4.00297619047619, 7.49702380952381, -10.0029761904762, 8.99702380952381, 
    4.99702380952381, -8.50297619047619, 4.49702380952381, -0.50297619047619, 
    -4.00297619047619, 6.99702380952381, -3.00297619047619, -9.00297619047619, 
    2.99702380952381, 3.49702380952381, -9.50297619047619, 3.99702380952381, 
    2.99702380952381, 6.99702380952381, 2.99702380952381, 1.99702380952381
    ), centered.x2 = c(9.80357142857143, 1.80357142857143, 1.80357142857143, 
    -7.19642857142857, -2.19642857142857, -7.19642857142857, 
    5.80357142857143, -4.19642857142857, 2.80357142857143, -3.19642857142857, 
    -5.19642857142857, 7.80357142857143, -5.19642857142857, 9.80357142857143, 
    3.80357142857143, 5.80357142857143, 7.80357142857143, 7.80357142857143, 
    3.80357142857143, -1.19642857142857, 10.8035714285714, 3.80357142857143, 
    3.80357142857143, 0.803571428571431, 3.80357142857143)), .Names = c("y", 
"x1", "x2", "centered.x1", "centered.x2"), row.names = c(NA, 
25L), class = "data.frame")

Thank you in advance.

EDIT: The following code plots the plane but will not work for when you have an interaction (which is really what I’m interested in). Additionally, I don’t know how to plot the high (+1sd), low(-1sd) and mean for x2 either.

x11(10,5)
 s3d <- scatterplot3d(DF[,c(2,3,1)], type="n", highlight.3d=TRUE,
      angle=70, scale.y=1, pch=16, main="scatterplot3d")

   # Now adding a regression plane to the "scatterplot3d"
    my.lm <-  with(DF, lm(y ~ x1 + x2))
 s3d$plane3d(my.lm, lty.box = "solid")

An attempt to plot an interaction plane (Seen here):

s3d <- scatterplot3d(DF[,c(2,3,1)], type="n", highlight.3d=TRUE,
      angle=70, scale.y=1, pch=16, main="scatterplot3d")

    my.lm <-  with(DF, lm(y ~ x1 + x2 + x1:x2 ))
 s3d$plane3d(my.lm, lty.box = "solid")

Yielded the following error:

Error in segments(x, z1, x + y.max * yx.f, z2 + yz.f * y.max, lty = ltya,  : 
  cannot mix zero-length and non-zero-length coordinates

Answer 1

Here’s how I would do it (adding a bit of color) with packages ‘rms’ and ‘lattice’:

require(rms)  # also need to have Hmisc installed
require(lattice)
ddI <- datadist(DF)
options(datadist="ddI")
lininterp <- ols(y ~ x1*x2, data=DF)
 bplot(Predict(lininterp, x1=25:40, x2=45:60), 
       lfun=wireframe,  # bplot passes extra arguments to wireframe
       screen = list(z = -10, x = -50), drape=TRUE)

And the non-interaction model:

 bplot(Predict(lin.no.int, x1=25:40, x2=45:60), lfun=wireframe, col=2:8, drape=TRUE, 
screen = list(z = -10, x = -50),
 main="Estimated regression surface with no interaction")