Plot an Interpolation Between Two Related Data Sets

Plot an interpolation between two related data sets, typically transformations of each other. This function is designed to be used in animations.

Usage

interpPlot(
  xy1,
  xy2,
  alpha,
  xlim,
  ylim,
  points = TRUE,
  add = FALSE,
  col = palette()[1],
  ellipse = FALSE,
  ellipse.args = NULL,
  abline = FALSE,
  col.lines = palette()[2],
  lwd = 2,
  id.method = "mahal",
  labels = rownames(xy1),
  id.n = 0,
  id.cex = 1,
  id.col = palette()[1],
  segments = FALSE,
  segment.col = "darkgray",
  ...
)

Arguments

xy1: First data set, a 2-column matrix or data.frame
xy2: Second data set, a 2-column matrix or data.frame
alpha: The value of the interpolation fraction, typically (but not necessarily) 0 <= alpha <= 1).
xlim, ylim: x, y limits for the plot. If not specified, the function uses the ranges of rbind(xy1, xy2).
points: Logical. Whether to plot the points in the current interpolation?
add: Logical. Whether to add to an existing plot?
col: Color for plotted points.
ellipse: logical. TRUE to plot a dataEllipse
ellipse.args: other arguments passed to dataEllipse
abline: logical. TRUE to plot the linear regression line for XY
col.lines: line color
lwd: line width
id.method: How points are to be identified. See showLabels.
labels: observation labels
id.n: Number of points to be identified. If set to zero, no points are identified.
id.cex: Controls the size of the plotted labels. The default is 1
id.col: Controls the color of the plotted labels.
segments: logical. TRUE to draw lines segments from xy1 to xy
segment.col: line color for segments
...: other arguments passed to plot()

Value

Returns invisibly the interpolated XY points.

Details

Points are plotted via the linear interpolation, $$ XY = XY1 + \alpha (XY2 - XY1)$$

The function allows plotting of the data ellipse, the linear regression line, and line segments showing the movement of points.

Interpolations other than linear can be obtained by using a non-linear series of alpha values. For example alpha=sin(seq(0,1,.1)/sin(1) will give a sinusoid interpolation.

Note

The examples here just use on-screen animations to the console graphics window. The animation package provides facilities to save these in various formats.

Author

Michael Friendly

Examples


#################################################
# animate an AV plot from marginal to conditional
#################################################
data(Duncan, package="carData")
duncmod <- lm(prestige ~ income + education, data=Duncan)
mod.mat <- model.matrix(duncmod)

# function to do an animation for one variable
dunc.anim <- function(variable, other, alpha=seq(0, 1, .1)) {
  var <- which(variable==colnames(mod.mat))
  duncdev <- scale(Duncan[,c(variable, "prestige")], scale=FALSE)
  duncav <- lsfit(mod.mat[, -var], cbind(mod.mat[, var], Duncan$prestige), 
          intercept = FALSE)$residuals
  colnames(duncav) <- c(variable, "prestige")
  
  lims <- apply(rbind(duncdev, duncav),2,range)
  
  for (alp in alpha) {
    main <- if(alp==0) paste("Marginal plot:", variable)
      else paste(round(100*alp), "% Added-variable plot:", variable)
    interpPlot(duncdev, duncav, alp, xlim=lims[,1], ylim=lims[,2], pch=16,
      main = main,
      xlab = paste(variable, "| ", alp, other),
      ylab = paste("prestige | ", alp, other),
      ellipse=TRUE, ellipse.args=(list(levels=0.68, fill=TRUE, fill.alpha=alp/2)), 
      abline=TRUE, id.n=3, id.cex=1.2, cex.lab=1.25)
    Sys.sleep(1)
  }
}

# show these in the R console
if(interactive()) {
dunc.anim("income", "education")

dunc.anim("education", "income")
}

############################################
# correlated bivariate data with 2 outliers
# show rotation from data space to PCA space
############################################

set.seed(123345)
x <- c(rnorm(100), 2, -2)
y <- c(x[1:100] + rnorm(100), -2, 2)
XY <- cbind(x=x, y=y)
rownames(XY) <- seq_along(x)
XY <- scale(XY, center=TRUE, scale=FALSE)

# start, end plots

car::dataEllipse(XY, pch=16, levels=0.68, id.n=2)
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
mod <- lm(y~x, data=as.data.frame(XY))
abline(mod, col="red", lwd=2)


pca <- princomp(XY, cor=TRUE)
scores <- pca$scores
car::dataEllipse(scores, pch=16, levels=0.68, id.n=2)
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
#> Warning: "id.n" is not a graphical parameter
abline(lm(Comp.2 ~ Comp.1, data=as.data.frame(scores)), lwd=2, col="red")


# show interpolation

# functions for labels, as a function of alpha
main <- function(alpha) {if(alpha==0) "Original data" 
  else if(alpha==1) "PCA scores"
  else paste(round(100*alpha,1), "% interpolation")}
xlab <- function(alpha) {if(alpha==0) "X"
  else if(alpha==1) "PCA.1"
  else paste("X +", alpha, "(X - PCA.1)")}
ylab <- function(alpha) {if(alpha==0) "Y"
  else if(alpha==1) "PCA.2"
  else paste("Y +", alpha, "(Y - PCA.2)")}

interpPCA <- function(XY, alpha = seq(0,1,.1)) {
  XY <- scale(XY, center=TRUE, scale=FALSE)
  if (is.null(rownames(XY))) rownames(XY) <- 1:nrow(XY)
  pca <- princomp(XY, cor=TRUE)
  scores <- pca$scores

  for (alp in alpha) {
    interpPlot(XY, scores, alp, 
      pch=16,
      main = main(alp),
      xlab = xlab(alp),
      ylab = ylab(alp),
      ellipse=TRUE, ellipse.args=(list(levels=0.68, fill=TRUE, fill.alpha=(1-alp)/2)), 
      abline=TRUE, id.n=2, id.cex=1.2, cex.lab=1.25, segments=TRUE)
    Sys.sleep(1)
  }
}

# show in R console
if(interactive()) {
interpPCA(XY)
}

if (FALSE) {
library(animation)
saveGIF({
  interpPCA(XY, alpha <- seq(0,1,.1))},
  movie.name="outlier-demo.gif", ani.width=480, ani.height=480, interval=1.5)

}