# Mantel test suffers of collinearity in the similarity matrices

If mantel test is run on data that has collinearity, mantel results will be inflated. Reference: https://besjournals.onlinelibrary.wiley.com/doi/10.1111/2041-210x.12018 (see summary point 4)

clear all
close all
rng(0)
features=randn(100,10);
brain=randn(100,10);

sim_f=corr(features);
sim_b=corr(brain);
[r p]=bramila_mantel(sim_f,sim_b,10000,'spearman')
% output for rng(0)
% r = 0.1324
% p = 0.1899 % this number might change a bit due to parpool



% let's repeat it with some extra autocorrelation added by repeating the
% same feature / brain map

featuresAC=[features(:,1) features(:,1) features(:,1) features];
brainAC=[brain(:,1) brain(:,1) brain(:,1) brain];

% when the similarity matrix has too similar features, then the final
% results are inflated

sim_fAC=corr(featuresAC(:,1:13)); % you can use the same number of columns 10 if you want, it won't change
sim_bAC=corr(brainAC(:,1:13));

[rAC pAC]=bramila_mantel(sim_fAC,sim_bAC,10000,'spearman')
% output for rng(0)
% rAC = 0.3965
% pAC = 0.0014 % this number might change a bit due to parpool