# interpPlot: Plot an Interpolation Between Two Related Data Sets In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

## Description

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

Points are plotted via the linear interpolation,

XY = XY1 + α (XY2 - XY1)

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

## Usage

 ```1 2 3 4 5 6 7 8``` ```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? `col` Color for plotted points. `add` Logical. Whether to add to an existing plot? `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()`

## Details

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.

## Value

Returns invisibly the interpolated XY points.

## 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(s)

Michael Friendly

`dataEllipse`, `showLabels`, `animation`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104``` ```################################################# # animate an AV plot from marginal to conditional ################################################# data(Duncan, package="car") 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 dataEllipse(XY, pch=16, levels=0.68, id.n=2) mod <- lm(y~x, data=as.data.frame(XY)) abline(mod, col="red", lwd=2) pca <- princomp(XY, cor=TRUE) scores <- pca\$scores dataEllipse(scores, pch=16, levels=0.68, id.n=2) 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) } ## Not run: library(animation) saveGIF({ interpPCA(XY, alpha <- seq(0,1,.1))}, movie.name="outlier-demo.gif", ani.width=480, ani.height=480, interval=1.5) ## End(Not run) ```