Solved – Plotting functions of three variables

data visualization

What are some ways that people know to plot a function of three variables, in a way that is relatively easy to understand on paper?

Although this could be generalized to pretty much any scenario, I'm specifically looking at a process where I can control pressure, power, and temperature. My output is a single number. I'd be interested to know what kind of answers people come up with.

My closest attempt:
One could use a regular 3D plot, where two axes represent two of the three independent variables, and the third one represents the output. Then color can be used to indicate the third independent variable. But this plot gets cluttered with information, especially when the input space is sampled well.

Best Answer

You could use a reactive 3D surface, with reactivity with respect to the value of the third variable.

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Solved – Plotting relationship between three variables in Matlab

I attached some code that might help get you started. (I am essentially treating your example as being equivalent to displaying confidence intervals around a curve)

X = linspace(0, 2*pi, 100);
X = X';
Y = sin(X);
%scatter(X,Y, '.')

Noise = randn(100, 1000);
data = bsxfun(@plus, Y, Noise);

% Calculate mean and standard deviation
meanData = mean(data, 2);
stdData = std(data, 0, 2);

%%

figure;

% Create multiples of standard deviation
stdevRange = 0.5:0.5:4;
numColormap = length(stdevRange);

% The patch colors will be shades of red
cm = [linspace(1, .97, numColormap);
    linspace(.3, .97, numColormap);
    linspace(.3, .97, numColormap)]';
set(gcf, 'Colormap', cm);
caxis(gca, stdevRange([1 end]));

% Create patch data along with corresponding colors
colorscale = numColormap:-1:1;
pY = arrayfun(@(z) [meanData-z*stdData;flipud(meanData+z*stdData)], fliplr(stdevRange), 'UniformOutput', false);
pY = [pY{:}];
cD = arrayfun(@(z) z*ones(length(X)*2, 1), colorscale, 'UniformOutput', false);
cD = [cD{:}];

% Create confidence bound patches
hCBPatch = patch(repmat([X; flipud(X)], 1, length(stdevRange)), ...
    pY, cD, 'FaceColor', 'flat', 'CDataMapping', 'direct', ...
    'EdgeColor', 'none');

% Plot mean data
line(X, meanData);

% Create colorbar with appropriate labels
stp = range(stdevRange)/(numel(stdevRange)*2);
hColorbar = colorbar;
ytick = stdevRange(1)+stp:stp*2:stdevRange(end)-stp;
yticklabels = cellstr(num2str(stdevRange', '%-g'));
yticklabels{end} = [yticklabels{end}, '+'];
set(hColorbar, 'YTick', ytick, 'YTickLabel', yticklabels);

enter image description here

Solved – Plotting gam model output – not component smooth functions

@Kate when I run your code, I get the following error from the last line, which is the key to the solution:

Error in eval(expr, envir, enclos) : object 'Loc' not found In addition: Warning message: In predict.gam(mod1, newdata = pred) : not all required variables have been supplied in newdata!

If you want to predict from a model, any model not just gam(), you must provide all the variables in the dataframe to predict from (the argument newdata).

pred <- data.frame(Doy = 1:365,  Tod=median(DatNew$Tod),
    Loc=factor('NewYork',levels=levels(DatNew$Loc)))
predict(mod1, newdata = pred)

And this works giving a predicted value of temperature for each day of the year in New York, assuming that they are measured at the median time of day. I tweaked your Doy values to be simply from 1 to 365, as presumably you only want one prediction for each day of the year. The value is almost completely flat because you simulated the data with no effect of Doy on temp, and it is almost exactly the expected value for a uniform(0,1) distribution, which is how you generated your random temperatures.

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Related Solutions

Solved – Plotting relationship between three variables in Matlab

Solved – Plotting gam model output – not component smooth functions

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