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Sim_indepANOVA_a_spurInt.m
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Sim_indepANOVA_a_spurInt.m
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%% Test for spurious interactions in an independent, balanced 2-way ANOVA without interaction with increasing main effect A
% Uses FtSimLink_indepANOVA, anova2_cell_mod
stemFolder = pwd;
resDir = [stemFolder filesep 'SimData' filesep 'ResultsIndepANOVA_spurInt' filesep];
savePrefix = '2way_indep_spurInt';
if ~exist(resDir,'dir')
mkdir(resDir);
end;
Rep = 1000; % number of Monte Carlo simulations
a = 3; % number of levels in factor A
b = 4; % number of levels in factor B
n = 5; % number of repetitions in each factor level combination
B = [50 -50 20 -20];
B = reshape(repmat(B,a,n),a,b,n);
design = [repmat([1,2,3],1,b*n);repmat([1 1 1 2 2 2 3 3 3 4 4 4],1,n)]; % design matrix
load([stemFolder filesep 'dummy'],'data');
cfg_neighb.method = 'template';
cfg_neighb.template = 'CTF275_neighb.mat';
neighbours = ft_prepare_neighbours(cfg_neighb, data);
Method_List = {'ftest','raw','res'};
Error_List = {'exp','gauss'};
for ee = 1:length(Error_List)
figure
hold on
for mm = 1:length(Method_List)
method = Method_List{mm};
err_dist = Error_List{ee};
% same as for Sim_indepANOVA_a
if strcmp(err_dist,'exp')
sc = [10000, 40, 20, 12, 10, 8, 6, 4, 3];
elseif strcmp(err_dist,'gauss')
sc = [100000, 200, 100, 70, 50, 40, 35, 30, 25]*3;
end
saveStr = [savePrefix,'_',err_dist,'_',method];
for r = 1:length(sc)
% gradually increase effecr size of factor A
if r ==1
A = [0; 0; 0];
else
A = [50; 0; -50]/sc(r);
end
m_A = mean(A);
par = sqrt(sum(((A - m_A).^2)./a));
A = reshape(repmat(A,b,n),a,b,n);
for j = 1:Rep
% put the model together & add errors
if strcmp(err_dist,'exp')
y = A + B + (exprnd(1,a,b,n)).^3;
elseif strcmp(err_dist,'gauss')
y = A + B + randn(a,b,n);
end
switch method
case 'ftest' % standard F-test
% prepare data input for anova2_cell_mod
c{1,1} = squeeze(y(1,1,:))';
c{1,2} = squeeze(y(1,2,:))';
c{1,3} = squeeze(y(1,3,:))';
c{1,4} = squeeze(y(1,4,:))';
c{2,1} = squeeze(y(2,1,:))';
c{2,2} = squeeze(y(2,2,:))';
c{2,3} = squeeze(y(2,3,:))';
c{2,4} = squeeze(y(2,4,:))';
c{3,1} = squeeze(y(3,1,:))';
c{3,2} = squeeze(y(3,2,:))';
c{3,3} = squeeze(y(3,3,:))';
c{3,4} = squeeze(y(3,4,:))';
[FA, FB, FI, dfa, dfb, dfi] = anova2_cell_mod(c); % adapted from the resampling statistic toolbox
res_I(j) = 1 - fcdf(FI, dfi(1), dfi(2));
case 'raw' % permutation of raw data
fac = 'iaxb';
c = reshape(y,1,a*b*n);
exact = 'no';
statfun = 'indepAnova2way';
% permutation ANOVA is called here
stat = FtSimLink_indepANOVA(data,neighbours,c,design,statfun,fac,exact);
res_I(j) = stat.prob;
case 'res' % permutation of residuals
fac = 'iaxb';
c = reshape(y,1,a*b*n);
ncond_a = a;
ncond_b = b;
for nfac_a = 1:ncond_a
for nfac_b = 1:ncond_b
idx_ab = design(1,:) == nfac_a & design(2,:) == nfac_b;
anovaIn{nfac_a,nfac_b} = c(idx_ab);
end
end
for ii = 1:size(anovaIn,1)
tmp = zeros(size(anovaIn{1,1}));
for jj = 1:size(anovaIn,2)
tmp(:,:,jj) = anovaIn{ii,jj};
end
amean(ii) = squeeze(mean(mean(tmp)));
end
for jj = 1:size(anovaIn,2)
tmp = zeros(size(anovaIn{1,1}));
for ii = 1:size(anovaIn,1)
tmp(:,:,ii) = [(anovaIn{ii,jj})];
end
bmean(jj) = squeeze(mean(mean(tmp)));
end
for ii = 1:size(anovaIn,1)
tmp = zeros(size(anovaIn{1,1}));
for jj = 1:size(anovaIn,2)
tmp(:,:,ii,jj) = anovaIn{ii,jj};
end
end
totmean = squeeze(mean(mean(mean(tmp))));
for ii = 1:size(anovaIn,1)
for jj = 1:size(anovaIn,2)
idx_ab = design(1,:) == ii & design(2,:) == jj;
c_new(idx_ab) = c(idx_ab) - bmean(jj) - amean(ii) + totmean;
end
end
exact = 'no';
statfun = 'indepAnova2way';
stat = FtSimLink_indepANOVA(data,neighbours,c_new,design,statfun,fac,exact);
res_I(j) = stat.prob;
end
end
p_val(r) = length(find(res_I <= 0.05))/Rep;
paramA(r) = par;
end
switch method
case 'ftest'
plot(paramA,p_val,':d','color',[0.4 0.4 0.4],'linewidth',2)
case 'raw'
plot(paramA,p_val,'g:d','linewidth',2)
case 'res'
plot(paramA,p_val,'m:s','linewidth',2)
end
set(gcf,'color','w')
xlabel('\theta_A','FontSize',10,'FontName','Helvetica')
ylabel('Power','FontSize',10,'FontName','Helvetica')
if strcmp(err_dist,'gauss')
title('Gauss. errors','FontSize',11,'FontName','Helvetica','FontWeight','bold','FontAngle','italic')
elseif strcmp(err_dist,'exp')
title('Exp. errors','FontSize',11,'FontName','Helvetica','FontWeight','bold','FontAngle','italic')
end
set(gca, ...
'Box' , 'off' , ...
'TickDir' , 'out' , ...
'TickLength' , [.02 .02] , ...
'XMinorTick' , 'off' , ...
'YMinorTick' , 'off' , ...
'YGrid' , 'off' , ...
'YTick' , [0.05 0.2:0.2:1], ...
'LineWidth' , 1 );
box off
xlim([min(paramA) max(paramA)])
cd(resDir)
save(saveStr,'paramA','p_val*','A','B','sc','method')
clear paramA p_val* c
cd(stemFolder)
end
end