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For plotting in 3 dimensions, I would say that there are two top level approaches.

  1. Plot with 3 axes: one dimension per axis.
  2. Plot with 2 axes with the 3rd dimension represented in color.

What are some general rules or guidelines about choosing between these two approaches?

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  • $\begingroup$ I'd say IF you plot 3 axes make the plot interactive (e.g. with scatterplot3d), otherwise it's hard to decode. Also 3rd (or 4th or 5th) dimension need not necessarily be color, it can also be shape or size (or even something else like facets or transparent overlaid different geometric objects, if you really want to get fancy). $\endgroup$ – miura Oct 12 '12 at 12:59
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I personally find graphs with 3 axes nearly impossible to interpret. I would much prefer to graph using something else to represent the third dimension, but there are various choices depending on need. Color, which you mention, works well when the third dimension has a small number of discrete categories (but be aware that quite a few people are color blind; for more on using color, see ColorBrewer). Lattice graphs (e.g. the lattice package in R) can work very well for 3 or more dimensions. ggplot, another R package, offers faceting.

I don't know, then, if there are "general" rules - I think it depends on what sort of data you have (in each dimension) and what you want to emphasize in the plots.

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  • $\begingroup$ Hi Peter "I think it depends on what sort of data you have (in each dimension) and what you want to emphasize in the plots". I suppose these are the guidelines I'm looking for. You mention a small number of discrete categories for color as the 3rd dim, so I guess that's one. By lattice graphs, do you mean plotting different combinations of x,y as a panel, or am I misinterpreting? $\endgroup$ – oisyutat Oct 12 '12 at 11:50
  • $\begingroup$ ggplot2s guide_colourbar() works pretty well for mapping continuous variables to color. $\endgroup$ – miura Oct 12 '12 at 12:57
  • $\begingroup$ yes, lattice graphs make separate graphs of two variables along the third variable. e.g. a scatter plot of x and y at various levels of z $\endgroup$ – Peter Flom - Reinstate Monica Oct 12 '12 at 16:58

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