Finding x position of color-grouped boxchart boxes for overlaying jittered errorbar plot

I'm writing a GUI that creates a boxchart from the results of a fitting operation. Each data point has an x and color category and a confidence interval associated with it. I'd like to create a boxchart that groups data points categorically on x and color, and then overlay an errorbar plot that shows each individual data point data point and its confidence interval. There could be any number of color and x categories.

My issue is that I can't figure out how to calculate or find the x position of each of the boxes, which I need to ensure the errorbar plots line up. It seems like this should be a property of the BoxChart object, but I can't find it.

For example, if I create the following data set, which uses either a two or three color categories:

% Generate some data
xcat = categorical({'a', 'b', 'c'});
ccat = categorical({'c1'; 'c2'; 'c3'}); % 3 color categories
%ccat = categorical({'c1'; 'c2'; 'c2'}); % 2 color categories
xdata = reshape(repmat(xcat, 12, 1), [], 1);
cdata = reshape(repmat(ccat, 4, 3), [], 1);
ydata = reshape([normrnd(10, 1, 12, 1), normrnd(11, 1, 12, 1), normrnd(8, 1, 12, 1)], [], 1);
cfdata = reshape(normrnd(0, 0.5, 12, 3), [], 1);

And I create a boxchart from it like this:

% Convert from categorical to numerical for plot
xcat_names = categories(xdata);
xdata_num = double(xdata);

% Create boxchart
figure
b = boxchart(xdata_num, ydata, 'GroupByColor', cdata);
set(gca, "XTick", unique(xdata_num), "XTickLabel", xcat_names);
legend

The following error bar code works perfectly when there's three colors, but doesn't align properly if there's two:

% Estimate errorbar positions
ccat_names = categories(cdata);
cgroupwidth = 1-1/length(ccat_names);
xspacing = cgroupwidth/length(ccat_names);
xcoloroffset = (0:length(ccat_names)-1) * xspacing - cgroupwidth/2 + xspacing/2;

% Add some jitter for readability
xjitteroffset = zeros(size(xdata)); % Zeros for testing alignment with no jitter
%xjitteroffset = randn(size(xdata))*cgroupwidth/length(ccat_names)/4;

% Overlay jittered errorbars on boxchart
cmap_c = lines(length(categories(cdata))); % match color of boxchart
hold on
for ix = 1:length(xcat_names)
    for ic = 1:length(ccat_names)
        ibox = xdata == xcat(ix) & cdata == ccat(ic); % find data that fits criteria
        errorbar(xdata_num(ibox) + xcoloroffset(ic) + xjitteroffset(ibox),...
            ydata(ibox), cfdata(ibox), '.', 'Color', cmap_c(ic,:),...
            'HandleVisibility','off')
    end
end
grid on

This code results in the following graphs depending on which ccat definition is commented out. You can see that the errorbars don't align in the 2 Color scenario.

So in summary, I'm interested if anyone knows:

• A way to get the x position of the boxes from the BoxChart object
• A way to calculate the x position of the boxes reliably with varying numbers of color and x categories.

[Mathieu NOE]

A similar question was raised here :

How to get position of single box in grouped box chart on x-axis? - MATLAB Answers - MATLAB Central

A possible solution to your problem might be here :

X-Axis Boxplot Shift - MATLAB Answers - MATLAB Central

Using boxchart, how can I get the boxes to align with my labels? - MATLAB Answers - MATLAB Central

[Theo Husby]

Thanks! This is helpful. I missed some of these.

I've got a solution now. I'm just writing it up as an answer.

Answer 1

[Theo Husby]

I figured out a solution based on this answer given for bar graphs in this answer.

The box position can be calculated reliably, and I was close with my position estimate, but had the wrong definition of cgroupwidth. In my original question, the line should be:

cgroupwidth = min(0.8, length(ccat_names)/(length(ccat_names) + 1.5));

Here is the implementation written out as a function in case it's useful to anyone who encounters the same problem in the future:

function xboxpos = get_boxchart_x_position(xdata_num, nc)
    % Return the x position of each individual box in a boxchart that uses 'GroupByColor'. 
    % xdata_num is a numerical vector. Same as the first input to boxchart.
    % nc is the number of color categories

    xgroup = unique(xdata_num);
    nx = length(xgroup);

    % Calculate offset for colors
    cgroupwidth = min(0.8, nc/(nc + 1.5));
    xspacing = cgroupwidth/nc;
    xcoloroffset = (0:nc-1) * xspacing - cgroupwidth/2 + xspacing/2;

    % Calculate x positions of each boxchart box assuming the same number
    % of colors for each x position.
    xboxpos = zeros(nx * nc, 1);
    for ix = 1:nx
        for ic = 1:nc
            xboxpos((ix-1)*nc + ic) = xgroup(ix) + xcoloroffset(ic);
        end
    end
end

Example usage:

% Create a boxchart
boxchart(xdata_num, ydata, 'GroupByColor', cdata);

% Get number of color categories. cdata is categorical in my case.
nc = length(categories(cdata));

% Call function to get x position of each box in the chart.
xboxpos = get_boxchart_x_position(xdata_num, nc);

If anyone knows a cleaner solution, please let me know.