MATLAB: 3-way Repeated Measures ANOVA pairwise comparisons using multcompare

fitrmmultcompareranovarepeated measuresrepeatedmeasuresmodelStatistics and Machine Learning Toolbox

I'm expanding on a helpful question/answer I found here: http://www.mathworks.com/matlabcentral/answers/124353-does-fitrm-ranova-support-within-subject-models-without-between-subject-factors
I have run a 3-way repeated measures ANOVA with 3 within subject factors. I want to make the pairwise comparisons for the 2- and 3-way interactions; I can run these for the 2-way interactions using the method RepeatedMeasuresModel/multcompare but I cannot figure out how to do it for the 3-way interaction. Here is my example:
% generate random data for the example
alpha_power = randn(24,8);
% Create a table storing the respones
varNames = {'Y1','Y2','Y3','Y4','Y5','Y6','Y7','Y8'};
t = array2table(alpha_power,'VariableNames',varNames);
% Create a table reflecting the within subject factors 'TestCond', 'Attention', and 'TMS' and their levels
factorNames = {'TestCond','Attention','TMS'};
within = table({'M';'M';'M';'M';'N';'N';'N';'N'},{'A';'A';'V';'V';'A';'A';'V';'V'},{'T';'S';'T';'S';'T';'S';'T';'S'},'VariableNames',factorNames);
% fit the repeated measures model
rm = fitrm(t,'Y1-Y8~1','WithinDesign',within);
% run my repeated measures anova here
[ranovatbl] = ranova(rm, 'WithinModel','TestCond*Attention*TMS');
% make pairwise comparisons for the two-way interactions
%

% see: help RepeatedMeasuresModel/multcompare
multcompare(rm,'TestCond','By','Attention')
multcompare(rm,'TestCond','By','TMS')
multcompare(rm,'Attention','By','TMS')
% but how can I make pairwise comparisons for the 3-way interaction?
%
% this does not work (it ignores the 'Attention' factor)
multcompare(rm,'TestCond','By','Attention','By','TMS')
I found this old discussion, but it was not helpful (it refers to the standalone multcompare function): http://www.mathworks.com/matlabcentral/answers/2141-how-to-obtain-p-values-for-all-pair-wise-comparisons-from-the-multicompare-function
Is it possible to test the pairwise comparisons in the 3-way interaction?

Best Answer

I received help from the Mathworks support and thought I would post their answer here (thanks to Eric Diaz and colleagues).
% Suppose we want to compare levels of Attention for each combination
% of levels of TestCond and TMS.
% 1. Convert factors to categorical.
within2 = within;
within2.Attention = categorical(within2.Attention);
within2.TestCond = categorical(within2.TestCond);
within2.TMS = categorical(within2.TMS);
% 2. Create an interaction factor capturing each combination of levels
% of TestCond and TMS.
within2.TestCond_TMS = within2.TestCond .* within2.TMS;
% 3. Call fitrm with the modified within design.
rm2 = fitrm(t,'Y1-Y8~1','WithinDesign',within2);
ranovatbl2 = ranova(rm2, 'WithinModel','TestCond*Attention*TMS')
% 4. Use interaction factor TestCond_TMS as the 'By' variable in multcompare.
multcompare(rm2,'Attention','By','TestCond_TMS')
It is also possible to set up a 3-way interaction in a similar way to step 2, run fitrm, and then run multcompare(rm2,'Attention_TestCond_TMS') to get all of the pairwise comparisons (corrected for multiple comparisons).
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