# Visually weighted/ Watercolor Plots, new variants: Please vote!

September 6, 2012
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Update Oct-23: Added a new parameter `add` to the function. Now multiple groups can be plotted in a single plot (see example in my comment)

As a follow-up on my R implementation of Solomon’s watercolor plots, I made some improvements to the function. I fine-tuned the graphical parameters (the median smoother line now diminishes faster with increasing CIs, and the shaded watercolors look more pretty). Furthermore, the function is faster and has more features:

• You can define any standard regression function for the bootstrap procedure.
• vwReg(y ~ x, df, method=lm)
• vwReg(y ~ x + I(x^2), df, method=lm)
• Provide parameters for the fitting function.
• You can make the smoother’s span larger. Then it takes more points into account when doing the local fitting. Per default, the smoother fits a polynomial of degree two – that means as you increase span you will approach the overall quadratic fit: vwReg(y ~ x, df, span=2)
• You can also make the smoother’s span smaller, then it takes less points for local fitting. If it is too small, it will overfit and approach each single data point. The default span (.75) seemed to be the best choice for me for a variety of data sets: vwReg(y ~ x, df, span=0.5)
• Use a robust M-estimator for the smoother; see ?loess for details: vwReg(y ~ x, df, family=”symmetric”)
• Provide your own color scheme (or, for example, a black-and-white scheme). Examples see pictures below.
• Quantize the color ramp, so that regions for 1, 2, and 3 SD have the same color (an idea proposed by John Mashey).

At the end of this post is the source code for the R function.

## Some picture – please vote!

Here are some variants of the watercolor plots – at the end, you can vote for your favorite (or write something into the comments). I am still fine-tuning the default parameters, and I am interested in your opinions what would be the best default.

Plot 1: The current default

Plot 2: Using an M-estimator for bootstrap smoothers. Usually you get wider confidence intervalls.

Plot 3:Increasing the span of the smoothers

Plot 4: Decreasing the span of the smoothers

Plot 5: Changing the color scheme, using a predefined ColorBrewer palette. You can see all available palettes by using this command: library(RColorBrewer); display.brewer.all()

Plot 6: Using a custom-made palette

Plot 7: Using a custom-made palette; with the parameter bias you can shift the color ramp to the “higher” colors:

Plot 8: A black and white version of the plot

Plot 9: The anti-Tufte-plot: Using as much ink as possible by reversing black and white (a.k.a. “the Milky-Way Plot“)

Plot 10: The Northern Light Plot/ fMRI plot. This plotting technique already has been used by a suspicious company (called IRET – never heard of that). I hurried to publish the R code under a FreeBSD license before they can patent it! Feel free to use, share, or change the code for whatever purpose you need. Isn’t that beautiful?

Plot 11: The 1-2-3-SD plot. You can use your own color schemes as well, e.g.: vwReg(y~x, df, bw=TRUE, quantize=”SD”)

Any comments or ideas? Or just a vote? If you produce some nice plots with your data, you can send it to me, and I will post a gallery of the most impressive “data art”!

Cheers,

Felix

Note: There is a poll embedded within this post, please visit the site to participate in this post’s poll.

?View Code RSPLUS
 ```# Copyright 2012 Felix Schönbrodt # All rights reserved. # # FreeBSD License # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are # met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDER `AS IS'' AND ANY # EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR # PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR # CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, # EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, # PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR # PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF # LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING # NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS # SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. # # The views and conclusions contained in the software and documentation # are those of the authors and should not be interpreted as representing # official policies, either expressed or implied, of the copyright # holder.   # Version history: # 0.1: original code # 0.1.1: changed license to FreeBSD; re-established compability to ggplot2 (new version 0.9.2)   ## Visually weighted regression / Watercolor plots ## Idea: Solomon Hsiang, with additional ideas from many blog commenters     # B = number bootstrapped smoothers # shade: plot the shaded confidence region? # shade.alpha: should the CI shading fade out at the edges? (by reducing alpha; 0 = no alpha decrease, 0.1 = medium alpha decrease, 0.5 = strong alpha decrease) # spag: plot spaghetti lines? # spag.color: color of spaghetti lines # mweight: should the median smoother be visually weighted? # show.lm: should the linear regresison line be plotted? # show.CI: should the 95% CI limits be plotted? # show.median: should the median smoother be plotted? # median.col: color of the median smoother # shape: shape of points # method: the fitting function for the spaghettis; default: loess # bw = TRUE: define a default b&w-palette # slices: number of slices in x and y direction for the shaded region. Higher numbers make a smoother plot, but takes longer to draw. I wouldn'T go beyond 500 # palette: provide a custom color palette for the watercolors # ylim: restrict range of the watercoloring # quantize: either "continuous", or "SD". In the latter case, we get three color regions for 1, 2, and 3 SD (an idea of John Mashey) # add: if add == FALSE, a new ggplot is returned. If add == TRUE, only the elements are returned, which can be added to an existing ggplot (with the '+' operator) # ...: further parameters passed to the fitting function, in the case of loess, for example, "span = .9", or "family = 'symmetric'" vwReg <- function(formula, data, title="", B=1000, shade=TRUE, shade.alpha=.1, spag=FALSE, spag.color="darkblue", mweight=TRUE, show.lm=FALSE, show.median = TRUE, median.col = "white", shape = 21, show.CI=FALSE, method=loess, bw=FALSE, slices=200, palette=colorRampPalette(c("#FFEDA0", "#DD0000"), bias=2)(20), ylim=NULL, quantize = "continuous", add=FALSE, ...) { IV <- all.vars(formula)[2] DV <- all.vars(formula)[1] data <- na.omit(data[order(data[, IV]), c(IV, DV)])   if (bw == TRUE) { palette <- colorRampPalette(c("#EEEEEE", "#999999", "#333333"), bias=2)(20) }   print("Computing boostrapped smoothers ...") newx <- data.frame(seq(min(data[, IV]), max(data[, IV]), length=slices)) colnames(newx) <- IV l0.boot <- matrix(NA, nrow=nrow(newx), ncol=B)   l0 <- method(formula, data) for (i in 1:B) { data2 <- data[sample(nrow(data), replace=TRUE), ] data2 <- data2[order(data2[, IV]), ] if (class(l0)=="loess") { m1 <- method(formula, data2, control = loess.control(surface = "i", statistics="a", trace.hat="a"), ...) } else { m1 <- method(formula, data2, ...) } l0.boot[, i] <- predict(m1, newdata=newx) }   # compute median and CI limits of bootstrap library(plyr) library(reshape2) CI.boot <- adply(l0.boot, 1, function(x) quantile(x, prob=c(.025, .5, .975, pnorm(c(-3, -2, -1, 0, 1, 2, 3))), na.rm=TRUE))[, -1] colnames(CI.boot)[1:10] <- c("LL", "M", "UL", paste0("SD", 1:7)) CI.boot\$x <- newx[, 1] CI.boot\$width <- CI.boot\$UL - CI.boot\$LL   # scale the CI width to the range 0 to 1 and flip it (bigger numbers = narrower CI) CI.boot\$w2 <- (CI.boot\$width - min(CI.boot\$width)) CI.boot\$w3 <- 1-(CI.boot\$w2/max(CI.boot\$w2))     # convert bootstrapped spaghettis to long format b2 <- melt(l0.boot) b2\$x <- newx[,1] colnames(b2) <- c("index", "B", "value", "x")   library(ggplot2) library(RColorBrewer)   # Construct ggplot # All plot elements are constructed as a list, so they can be added to an existing ggplot   # if add == FALSE: provide the basic ggplot object p0 <- ggplot(data, aes_string(x=IV, y=DV)) + theme_bw()   # initialize elements with NULL (if they are defined, they are overwritten with something meaningful) gg.tiles <- gg.poly <- gg.spag <- gg.median <- gg.CI1 <- gg.CI2 <- gg.lm <- gg.points <- gg.title <- NULL   if (shade == TRUE) { quantize <- match.arg(quantize, c("continuous", "SD")) if (quantize == "continuous") { print("Computing density estimates for each vertical cut ...") flush.console()   if (is.null(ylim)) { min_value <- min(min(l0.boot, na.rm=TRUE), min(data[, DV], na.rm=TRUE)) max_value <- max(max(l0.boot, na.rm=TRUE), max(data[, DV], na.rm=TRUE)) ylim <- c(min_value, max_value) }   # vertical cross-sectional density estimate d2 <- ddply(b2[, c("x", "value")], .(x), function(df) { res <- data.frame(density(df\$value, na.rm=TRUE, n=slices, from=ylim[1], to=ylim[2])[c("x", "y")]) #res <- data.frame(density(df\$value, na.rm=TRUE, n=slices)[c("x", "y")]) colnames(res) <- c("y", "dens") return(res) }, .progress="text")   maxdens <- max(d2\$dens) mindens <- min(d2\$dens) d2\$dens.scaled <- (d2\$dens - mindens)/maxdens   ## Tile approach d2\$alpha.factor <- d2\$dens.scaled^shade.alpha gg.tiles <- list(geom_tile(data=d2, aes(x=x, y=y, fill=dens.scaled, alpha=alpha.factor)), scale_fill_gradientn("dens.scaled", colours=palette), scale_alpha_continuous(range=c(0.001, 1))) } if (quantize == "SD") { ## Polygon approach   SDs <- melt(CI.boot[, c("x", paste0("SD", 1:7))], id.vars="x") count <- 0 d3 <- data.frame() col <- c(1,2,3,3,2,1) for (i in 1:6) { seg1 <- SDs[SDs\$variable == paste0("SD", i), ] seg2 <- SDs[SDs\$variable == paste0("SD", i+1), ] seg <- rbind(seg1, seg2[nrow(seg2):1, ]) seg\$group <- count seg\$col <- col[i] count <- count + 1 d3 <- rbind(d3, seg) }   gg.poly <- list(geom_polygon(data=d3, aes(x=x, y=value, color=NULL, fill=col, group=group)), scale_fill_gradientn("dens.scaled", colours=palette, values=seq(-1, 3, 1))) } }   print("Build ggplot figure ...") flush.console()     if (spag==TRUE) { gg.spag <- geom_path(data=b2, aes(x=x, y=value, group=B), size=0.7, alpha=10/B, color=spag.color) }   if (show.median == TRUE) { if (mweight == TRUE) { gg.median <- geom_path(data=CI.boot, aes(x=x, y=M, alpha=w3^3), size=.6, linejoin="mitre", color=median.col) } else { gg.median <- geom_path(data=CI.boot, aes(x=x, y=M), size = 0.6, linejoin="mitre", color=median.col) } }   # Confidence limits if (show.CI == TRUE) { gg.CI1 <- geom_path(data=CI.boot, aes(x=x, y=UL), size=1, color="red") gg.CI2 <- geom_path(data=CI.boot, aes(x=x, y=LL), size=1, color="red") }   # plain linear regression line if (show.lm==TRUE) {gg.lm <- geom_smooth(method="lm", color="darkgreen", se=FALSE)}   gg.points <- geom_point(data=data, aes_string(x=IV, y=DV), size=1, shape=shape, fill="white", color="black")   if (title != "") { gg.title <- theme(title=title) }     gg.elements <- list(gg.tiles, gg.poly, gg.spag, gg.median, gg.CI1, gg.CI2, gg.lm, gg.points, gg.title, theme(legend.position="none"))   if (add == FALSE) { return(p0 + gg.elements) } else { return(gg.elements) } }```

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