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Weekend update: In quest of 3d graphic for risk perception distributions

ideology, risk, & science literacy in *2* graphs (click it!)In response to the scatter plots from "politicization of science Q&A" post, @thompn4 on twitter (optimal venue for in depth scholarly exchange) observed that it would be nice to have a three-dimensional graphic that combined partisanship, risk perception, and science comprehension (or perhaps two risk perceptions -- like nuclear and global warming -- along with science comprehension or partisanship) into one figure.

Great idea!

I supplied @thompn4 with data, and he came up with some interesting topographical plots.

Pretty cool!

But these are all 2 dimensional -- and so fail to achieve what I understand to be his original goal-- to have 3d representations of the raw data so that all the relevant comparisons could be in one figure and so there'd be no need to aggregate & split the data along one dimension  (as the science comprehension plots do).

When I pressed him, he came up with a 3d version, but with only 2 dimensions of individual difference -- science comprehension & risk perception:

Really great, but I want what he asked for -- three graphic dimensions for three dimensions of individual difference.

I've been fumbling with 3d scatter plots.  Here's ideology (x), risk perception (y), and science compression (z)-- with observations color-coded, as in 2d scatter plots, to denote perceived risk of global warming (blue = low to red = high):


Not great, but it gets at least a bit better when one rotates the axes counter-clockwise:

I suspect a topographical or wireframe will work better than a scatter plot -- but that's something beyond my present graphic capabilities.

In the end, too, the criteria for judging these 3d graphs, in my view, is whether they enable a curious, reflective person readily to discern the relevant information -- and in particular the existence of an important contrast.  Being ornate & attention-grabbing are not really the point, in my view. So far not clear to me that anything really improves upon the original 2 graphic solution.

If anyone else wants to try, feel free.  The data are here. Please do share your results -- you can email them to me or post them somewhere w/ URL I can link to.


1. The data are tab delimited.

2. Zconservrepub is a standardized sum of 7-point partyid & 5-point liberal-conservative ideology, valenced toward conservative/republican.

3. scicomp_i is score on a science-comprehension assessment (scored with item response theory; details here)

4.GWRISk & NUKERISK are "industrial strength risk perception measures" for "global warming" & "nuclear power. Each item is 0-7: 0 “no risk at all”; 1 “Very low risk”;  2 “Low risk”; 3 “Between low and moderate risk”; 4 “Moderate risk”; 5 “Between moderate and high risk”; 6 “High risk”; 7 “Very high risk”

There are 2000 observations total.  Some observations have missing data.



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Reader Comments (5)

The serious climate sceptic community generally use R for doing data analysis - if you've not played with it before, it's well worth looking at. You can download it for free from here.

If you download and install R, you should be able to cut and paste the following script into it to get some nice interactive 3D plots. Just use the mouse to spin them around. I've not bothered to neaten it up, as I would if I was doing this properly - for example, I put the data into bins for the second plot but I didn't bother to rescale them to the original numeric scales, and I've not labelled all the columns properly in intermediate results. This wouldn't be acceptable for publication, and it might make it a bit difficult for an R novice to figure out. But it's fine for playing with.

I've not spent much time on it. If anyone is interested in playing with it some more I'd be happy to follow up over the weekend.

# ----------------------------------
# The following line downloads and installs the 3D library if you don't already have it
install.packages("rgl") # Remove if not needed

# Load 3D graphics library

# Load data file - tab-separated
# Change path to point to file on your own filesystem
# path has to double '\' characters because R treats \ as an escape character
d <- read.delim("C:\\Users\\Data\\ExampleForDan\\for_nt.txt")

# First plot ----------------------------------
# Plot columns 2 to 4 from the data, using red spheres of equal size
title3d(xlab="Conservatism",ylab="Science Comp",zlab="GW Risk")
# You can use the mouse to rotate the 3D image

# Second plot ----------------------------------
# Divide continuous data into bins, count observations in each bin
counts <- aggregate(d$id,

# Plot with sphere volume proportional to count
title3d(xlab="Conservatism",ylab="Science Comp",zlab="GW Risk")

# Spin the display about the z axis at 5 rpm for 30 secs

May 23, 2015 | Unregistered CommenterNiV


Cool -- I'll try it.

As you likely have observed, I use Stata for most things. Sometimes use R via Gary King's Zelig; maybe he is a climate skeptic?

May 24, 2015 | Unregistered Commenterdmk38

Could be, but a lot of people use R. It seems to be one of the fastest growing.

Climate sceptics like R I think primarily because it's open source / free, which means lots more people can check your work, which is good for scientific quality. Several have argued that if scientists published their code in a widely-available statistics package (it doesn't have to be R, but it does meet all the criteria), there'd be no arguments over exactly how a calculation was done, with what data, or what the results actually were. That's often quite difficult to determine from the purely verbal descriptions of methods in papers, which are often ambiguous or incomplete. (Or wrongly implemented, in some cases.) Journal limitations on space often lead to inessentials like 'methods' to be cut out. It would resolve quite a few long-running disputes if more climate scientists were willing to publish their data and code.

The ideal would be that when a paper is published the data and code are also provided as part of the SI, or on a separate website. Then anyone interested in looking at the work for you has a flying start in checking it and extending it. It avoids the common misunderstandings that plague this debate, and is seen very positively by potential critics. It advances the state of the art faster, and avoids duplicating effort and wasting time, which in these times of finite grants is considered by many as a good thing - at least from the perspective of scientific progress and the benefit to mankind. Quite a few people seem to think that's a good idea in science generally, not just in the controversial domain of climate science.

But back to the 3D graphics. There's a lot of different things you can do with R. Some other ideas are to draw your point cloud with rods down to the bottom plane to give perspective, use transparency to represent density, to stack perspective views of 2D slices through the volume with density and/or contour plots, 3d bar graphs, to plot 3d kernel density contour isosurface plots (perhaps using the 3D kernel density function in the ks package and the contour3d function in R package misc3d), But some of these require considerable mathematical and programming sophistication to create, so are probably not so hot for a quick exploratory play wit the data.

Personally, I find the point cloud (scatterplot) sufficient for most purposes if you're able to rotate it or animate it. A static view makes it hard to perceive depth, but spinning it makes the perspective clear.

May 24, 2015 | Unregistered CommenterNiV

If you can spin the 3-d graph around, make two of them with not more than 3 degrees of spin and post both of them side-by-side for "stereoscopic" vision. This can be accomplished by crossing your eyes or using a viewing aid. You can also use parallel freeviewing but the distance cannot be wider than your eyes are spaced for that sort of thing. You can also use prismatic or mirror assisted parallel viewing.

Stereoscopic viewing greatly "declutters" a busy graph plus it's awesome when done well.

May 26, 2015 | Unregistered CommenterMichael Gordon

@MichaelGordon-- can you do that? That would be awesome. Who knows, too, what we might see in that box; I suspect Maxwell's Demon is in there ...

May 26, 2015 | Registered CommenterDan Kahan

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