Visualizing a 3D dataset of proportions

Question

I'm looking for visualization ideas for the following data:

• I have a $10\times 12$ grid of points $(x_i,m_j)$, where the $x_i$ are a set of distances (e.g. 1,2,..., 10 m) and the $m_j$ are the 12 months.

• At each $(x_i,m_j)$, I have 4 values $q_1,\ldots,q_4$ which total to 1.

• I'm trying to show how the proportion of $q_i$ varies with $x$ and $m$, so that one can see the changes across the months and distance.

To explain with some dummy data (Mathematica):

data = Table[{x m/12, x Tanh[m/6], x/m, x^2/m^2} ~Normalize~ Total, {x, 10}, {m, 12}];

For a single distance, I could do something like

BarChart[First@data, ChartLayout -> "Stacked"]

Or for a single $q_i$, I could do

BarChart[data[[;; , ;; , 1]], ChartLayout -> "Stacked"]

I could perhaps even compress the bars and stack up the 10 different distances (since it's a small number) along the Y axis to show this, but it seems overcrowded. I'm not certain a 3D bubble chart might help either.

Perhaps the simplest solution might be to have 4 plots, each showing how the respective quantity $q_i$ changes... this is certainly an option for me, but I wanted to ask if there are other better alternatives of visualizing the data.

Answer 1

Each alternative will excel in showing some features of the data, so the "best" view depends on what question you want answered. Or you may need multiple views to answer multiple questions (preferably with software that links them together).

Below are a few alternatives. I'm not a regular Mathematica user (so there is likely a better way to make higher quality plots) and I haven't bothered with labeling or legends.

To see the distribution of each component, a series of heatmaps works well.

Table[MatrixPlot[data[[;; , ;; , q]], ColorFunctionScaling -> False, 
  ColorFunction -> Function[{z}, Hue[1, z, 0.9]]], {q, 4}]

If the data is really this smooth, the contour plots may work better:

Table[ListContourPlot[data[[;; , ;; , q]], ImageSize -> 250, 
  PlotRange -> {0, 1}, ColorFunctionScaling -> False, Contours -> 10, 
  ContourStyle -> None, 
  ColorFunction -> Function[{z}, Hue[1, z, 0.9]]], {q, 4}]

(A smoothed version of the first option, except with the Y axis reversed.)

For more precise value representation (position is more precise that color perceptually), overlaid line plots may work (one per distance value):

Table[ListLinePlot[data[[;; , ;; , q]],  PlotRange -> {0, 0.9}, 
  PlotStyle -> {Thick}, ImageSize -> 250], {q, 4}]

None of the above show proportions. For that you might try a 10 x 12 grid of line charts or bar charts:

Table[ListLinePlot[data[[x, m]], Axes -> None, PlotRange -> {0, 1}, 
  Filling -> Axis, ImageSize -> 35], {x, 10}, {m, 12}]

Table[BarChart[data[[x, m]], Axes -> None, PlotRange -> {0, 1}, 
  ImageSize -> 35, ChartStyle -> "Rainbow", 
  ChartBaseStyle -> EdgeForm[None]], {x, 10}, {m, 12}]

The line charts emphasize the change between consecutive q values while the bar chart has a more categorical connotation.

Finally, a similar grid of pie charts will make it easier to see certain features like whether one component has over 50% of the value at a given cell, at the expense of precision for other values.

Table[PieChart[{x m/12, x Tanh[m/6], x/m, x^2/m^2}, 
  ImageSize -> 30], {x, 10}, {m, 12}]