scatterplot3d:带残差的回归平面

Question

使用R中的scatterplot3d，我试图从观察到回归平面绘制红线：

wh <- iris$Species != "setosa"
x  <- iris$Sepal.Width[wh]
y  <- iris$Sepal.Length[wh]
z  <- iris$Petal.Width[wh]
df <- data.frame(x, y, z)

LM <- lm(y ~ x + z, df)
library(scatterplot3d)
G  <- scatterplot3d(x, z, y, highlight.3d = FALSE, type = "p")
G$plane3d(LM, draw_polygon = TRUE, draw_lines = FALSE)

​

​

若要获得以下图片的3D等效：

​

​

在2D中，我可以使用segments

pred  <- predict(model) 
segments(x, y, x, pred, col = 2)

但在3D中，我被坐标搞混了。

Answer 1

使用统计学习概论中的广告数据集，您可以

advertising_fit1 <- lm(sales~TV+radio, data = advertising)
sp <- scatterplot3d::scatterplot3d(advertising$TV, 
                                   advertising$radio, 
                                   advertising$sales, 
                                   angle = 45)
sp$plane3d(advertising_fit1, lty.box = "solid")#,
           # polygon_args = list(col = rgb(.1, .2, .7, .5)) # Fill color
orig <- sp$xyz.convert(advertising$TV, 
                       advertising$radio, 
                       advertising$sales)
plane <- sp$xyz.convert(advertising$TV, 
                        advertising$radio,  fitted(advertising_fit1))
i.negpos <- 1 + (resid(advertising_fit1) > 0)
segments(orig$x, orig$y, plane$x, plane$y,
         col = c("blue", "red")[i.negpos], 
         lty = 1) # (2:1)[i.negpos]
sp <- FactoClass::addgrids3d(advertising$TV, 
                             advertising$radio, 
                             advertising$sales,
                             angle = 45,
                             grid = c("xy", "xz", "yz"))

​

​

和使用包的另一个rgl交互式版本

rgl::plot3d(advertising$TV, 
             advertising$radio, 
             advertising$sales, type = "p", 
             xlab = "TV", 
             ylab = "radio", 
             zlab = "Sales", site = 5, lwd = 15)
rgl::planes3d(advertising_fit1$coefficients["TV"], 
              advertising_fit1$coefficients["radio"], -1, 
              advertising_fit1$coefficients["(Intercept)"], alpha = 0.3, front = "line")
rgl::segments3d(rep(advertising$TV, each = 2), 
                rep(advertising$radio, each = 2),
                matrix(t(cbind(advertising$sales, predict(advertising_fit1))), nc = 1),
                col = c("blue", "red")[i.negpos], 
                lty = 1) # (2:1)[i.negpos]
rgl::rgl.postscript("./pics/plot-advertising-rgl.pdf","pdf") # does not really work...

​

​

Answer 2

我决定也包括我自己的实现，以防其他人想要使用它。

回归平面

require("scatterplot3d")

# Data, linear regression with two explanatory variables
wh <- iris$Species != "setosa"
x  <- iris$Sepal.Width[wh]
y  <- iris$Sepal.Length[wh]
z  <- iris$Petal.Width[wh]
df <- data.frame(x, y, z)
LM <- lm(y ~ x + z, df)

# scatterplot
s3d <- scatterplot3d(x, z, y, pch = 19, type = "p", color = "darkgrey",
                     main = "Regression Plane", grid = TRUE, box = FALSE,  
                     mar = c(2.5, 2.5, 2, 1.5), angle = 55)

# regression plane
s3d$plane3d(LM, draw_polygon = TRUE, draw_lines = TRUE, 
            polygon_args = list(col = rgb(.1, .2, .7, .5)))

# overlay positive residuals
wh <- resid(LM) > 0
s3d$points3d(x[wh], z[wh], y[wh], pch = 19)

​

​

残差

# scatterplot
s3d <- scatterplot3d(x, z, y, pch = 19, type = "p", color = "darkgrey",
                     main = "Regression Plane", grid = TRUE, box = FALSE,  
                     mar = c(2.5, 2.5, 2, 1.5), angle = 55)

# compute locations of segments
orig     <- s3d$xyz.convert(x, z, y)
plane    <- s3d$xyz.convert(x, z, fitted(LM))
i.negpos <- 1 + (resid(LM) > 0) # which residuals are above the plane?

# draw residual distances to regression plane
segments(orig$x, orig$y, plane$x, plane$y, col = "red", lty = c(2, 1)[i.negpos], 
         lwd = 1.5)

# draw the regression plane
s3d$plane3d(LM, draw_polygon = TRUE, draw_lines = TRUE, 
            polygon_args = list(col = rgb(0.8, 0.8, 0.8, 0.8)))

# redraw positive residuals and segments above the plane
wh <- resid(LM) > 0
segments(orig$x[wh], orig$y[wh], plane$x[wh], plane$y[wh], col = "red", lty = 1, lwd = 1.5)
s3d$points3d(x[wh], z[wh], y[wh], pch = 19)

​

​

最终结果：

虽然我真的很欣赏scatterplot3d函数的方便性，但最后我还是得到了从github复制整个函数，因为基plot中的几个参数要么是由scatterplot3d强制的，要么是没有正确传递给scatterplot3d的(例如，las的轴旋转，cex的字符扩展，cex.main等等)。我不确定这么长和混乱的代码块在这里是否合适，所以我包括了上面的MWE。

总之，这就是我在书中所包含的内容：

​

​

(是的，这实际上只是虹膜数据集，不要告诉任何人。)