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imapLMMresample.m
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imapLMMresample.m
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function [ResampStat]=imapLMMresample(FixMap,LMMmap,c,h,effect,method,nboot,grouping,rmRE,varargin)
% imapLMMresample performs a nonparametric statistical test by calculating
% Monte-Carlo estimates of the significance probabilities and/or critical values
% from the resampling distribution.
% This function is called by imapLMMmcc with bootstrap or permutation
% option, but you can call it independently as well.
% input: FixMap, LMMmap,
% DX - fixed effect design matrix
% Zx - random effect design matrix
% c - contrast matrix
% h - hypothesis matrix
% effect - fixed/random
% method - permutation/bootstrap
% nboot - number of resampling
% grouping - specify group index to keeping the group variance constant
% during bootstrap. This is done by sampling independently per
% group.
% rmRE - 1 remove random effect, 0 keeping subject variance
% varargin - Optional: specify a subject vector. This is important when
% there are multiple grouping variables exist in the mixed model
% such as (1|subject) + (1|stimuli)
% output: ResampStat with field {parameters} {resampleTABLE} {resampleFvalue}
% {resamplePvalue} {resmapleBeta}
%
% 2014-09-14 Junpeng Lao, University of Fribourg.
% 2014-12-02 Option implemented for random with replacement within group
% during bootstrap
%--------------------------------------------------------------------------
% Copyright (C) iMap Team 2015
v = ver;
has_fsolve = any(strcmp({v.Name},'Parallel Computing Toolbox'));
if has_fsolve == 1
if isfield(LMMmap.runopt,'parallelname') == 0
gridname = 'local';
else
gridname = LMMmap.runopt.parallelname;
end
end
warning('off')
effect = lower(effect);
Zx = LMMmap.RandomEffects.DX;
tbl = LMMmap.Variables;
fitml = strcmp(upper(LMMmap.FitMethod),'ML');
if nargin > 9
sbjvec = varargin{1};
else
sbjvec = [];
end
% exclude empty trials/conditions
outtrial = full(sum(Zx, 2))==0;
tbl (outtrial,:) = [];
Zx (outtrial,:) = [];
FixMap (outtrial,:,:) = [];
grouping(outtrial,:) = [];
if ~isempty(sbjvec)
sbjvec(outtrial,:) = [];
end
if isa(tbl,'dataset')
VarNames = tbl.Properties.VarNames;
elseif isa(tbl,'table')
VarNames = tbl.Properties.VariableNames;
tbl = table2dataset(tbl);
end
coefname = LMMmap.CoefficientNames;
categypredi = LMMmap.VariableInfo.InModel ...
& LMMmap.VariableInfo.IsCategorical;
categyprediname = VarNames(categypredi);
contiupredi = LMMmap.VariableInfo.InModel ...
& ~LMMmap.VariableInfo.IsCategorical;
contiuprediname = VarNames(contiupredi);
% remove subject/grouping/random predictor if there is any
exclu1 = zeros(length(categyprediname), 1);
exclu2 = zeros(length(contiuprediname), 1);
for icate = 1:length(categyprediname)
catename = categyprediname{icate};
logictmp = strncmp(catename, coefname, length(catename));
if sum(logictmp) == 0
exclu1(icate) = 1;
end
end
categyprediname( exclu1==1 ) = [];
for iconu = 1:length(contiuprediname)
conuname = contiuprediname{iconu};
logictmp = strncmp(conuname, coefname, length(conuname));
if sum(logictmp) == 0
exclu2(iconu) = 1;
end
end
contiuprediname( exclu2==1 ) = [];
label = cell(length(tbl),length(categyprediname));
if ~isempty(label)
strlabel = cell(length(tbl),1);
for icc = 1:length(categyprediname)
label(:,icc) = cellstr(eval(['tbl.' categyprediname{icc}]));
end
for ii = 1:length(label)
strlabel{ii,:} = strjoin(label(ii,:),'_');
end
[CatePredictor,~] = unique(strlabel,'rows');
end
[GroupPredictor,~] = unique(grouping,'rows');
if strcmp(effect,'random')
effect2 = 'random';
elseif strcmp(effect,'fixed') || strcmp(effect,'model beta')
DX = LMMmap.modelX;
effect2 = 'fixed';
elseif strcmp(effect,'predictor beta')
DX = LMMmap.SinglePred.DesignMatrix;
effect2 = 'fixed';
end
DFmodel = LMMmap.modelDFE;
mask = isnan(LMMmap.MSE) == 0;
nonnan = find( mask==1 );
[Nitem,cSize,rSize] = size(FixMap);
ResampStat = struct;
parameters{1} = c;
parameters{2} = h;
parameters{3} = effect;
parameters{4} = method;
parameters{5} = nboot;
ResampStat.params = parameters;
if size(DX, 1) ~= Nitem
error('The input FixMap is not the correct one!')
end
switch effect2
case 'fixed'
% prelocate memory
Nc = length(c);
DF = zeros(Nc,2);
DF(:,2) = LMMmap.modelDFE;
for ic = 1:Nc
DF(ic,1) = rank(c{ic});
end
if rmRE == 1
% for Y ~ X*b + Z*B + e, remove random effect Z*B
ZB = NaN(Nitem,cSize,rSize);
BLUP = squeeze(LMMmap.RandomEffects.RandomStat(:,1,:,:));
for it = 1:Nitem
ZB(it,:) = Zx(it,:) * BLUP(:,:);
end
Y = FixMap - ZB;
else
Y = FixMap;
end
Yfixed = Y(:, mask);
% Yfixed = FixMap(:, mask);
% reproduce the beta (should be the same as fixed effect beta from
% the LMM estimation)
% beta = (reshape(DX\Y(:,:),size(DX,2),size(FixMap,2),size(FixMap,3)));
% find subject vector
[~, b] = find( Zx~=1 & Zx~=0 );
if ~isempty(b)
Zx(:, b) = [];
end
if ~isempty(sbjvec)
indxsbj = dummyvar(sbjvec);
else
indxsbj = full(Zx);
end
if sum(indxsbj(:)==1) == Nitem
indxsbj( indxsbj==1 ) = 1:Nitem;
else
try
Nmatrix = round(sum(indxsbj(:)==1)/Nitem);
columnsum = sum(indxsbj,1);
matrixblock = zeros(size(columnsum));
tmpsum = 0;
blocktype = 1;
for ii = 1:size(columnsum,2)
tmpsum = tmpsum + columnsum(ii);
if tmpsum <= Nitem
matrixblock(ii) = blocktype;
elseif tmpsum > Nitem
blocktype = blocktype+1;
tmpsum = 0;
matrixblock(ii) = blocktype;
end
end
NNmatrix = zeros(Nmatrix,1);
for iN = 1:Nmatrix
NNmatrix(iN) = sum(matrixblock==iN);
end
sbjindxtmp = matrixblock == find( NNmatrix==max(NNmatrix) );
indxsbj(:,~sbjindxtmp) = [];
indxsbj(indxsbj==1) = 1:Nitem;
catch
error('imapLMMresample error: Can not retrieve Subject column for resampling.')
end
end
% take data within mask.
npixel = size(Yfixed,2);
switch method
case 'permutation'
%%
bY = Yfixed;
Forg = NaN(Nc,cSize,rSize);
resampleFvalue = NaN(nboot, Nc, cSize, rSize);
for ic = 1:Nc
c2 = c{ic};
h2 = h{ic};
% Partition design matrix
cu = null(c2,'r');
% C = [c2;cu'];
c2 = c2';
% the following part is from Appendix A. of Winkler, et al (2014).
% Permutation inference for the general linear model. Neuroimage, 92,
% 381-397.
D = pinv(DX' * DX);
cv = cu-c2*pinv(c2'*D*c2)*c2'*D*cu;
parX = DX*D*c2*pinv(c2'*D*c2);
parZ = DX*D*cv*pinv(cv'*D*cv);
M = [parX, parZ];
cnew = zeros(size(c2'));
for ir = 1:rank(parX)
cnew(ir, ir) = 1;
end
% contruct permutation table
% 2015-05-05
% Permutation table should be compute according to Winkler,
% et al (2014). Permutation inference for the general
% linear model. Neuroimage, 92, 381-397.
%
% We dont do sign flips or block permutation
B = 1;
boot_index1 = zeros(nboot+500,Nitem);
% if length(GroupPredictor)>1 % more than 1 groups
% while size(unique(boot_index1,'rows'),1)<nboot+1
% tmp = [];
% for ig=1:length(GroupPredictor)
% sbjtmp=find(grouping==GroupPredictor(ig));
% tmp=[tmp sbjtmp(randperm(length(sbjtmp)))'];
% end
% boot_index1(B,:) = tmp;
% B=B+1;
% end
% else
while size(unique(boot_index1,'rows'),1)<nboot+1
tmp = randperm(Nitem);
boot_index1(B,:) = tmp;
B = B+1;
end
% end
boot_index = unique(boot_index1(boot_index1(:,1)~=0,:),'rows');
ResampStat.resTABLE = boot_index;
% orignial statistic for the fixed effect (revisit)
% bY2 = (1-parZ*pinv(parZ))*bY;
obeta = M\bY;
cz = ones(1,rank(M))-sum(cnew,1);
bY2 = bY - M(:, cz==1) * obeta(cz==1, :);
bbeta = M\bY2;
if fitml
bMSE = mean((M*bbeta-bY2).^2);
else
bMSE = sum((M*bbeta-bY2).^2)./DFmodel;
end
bMSEinv = bMSE.^-1;
% covprj = inv(M'*M);
% instead of calculating the covariance matrix and
% the inverse of the quadratic form c*covb*c'; here
% do QR decomposition to get the cholesky factor
X = qr(M,0);Rtmp = triu(X);
R = Rtmp(1:size(Rtmp,2), :);
S = inv(R);
quadformCOV = cnew/R*S'*cnew';%same as (c*(S*S')*c) == (c*covb*c')
qualCOVinv = inv(quadformCOV);
cbeta_h = (cnew*bbeta-h2)';
I = repmat(1:npixel,[DF(ic,1),1]);
trc = cbeta_h';
cmt_sp = sparse(I(:),1:npixel*DF(ic,1),trc);
covb = repmat(qualCOVinv,[1,1,npixel]);
I = repmat(reshape(1:DF(ic,1)*npixel,DF(ic,1),1,npixel),[1 DF(ic,1) 1]);
J = repmat(reshape(1:DF(ic,1)*npixel,1,DF(ic,1),npixel),[DF(ic,1) 1 1]);
covb_sp = sparse(I(:),J(:),covb(:));
tmp_sp = cmt_sp*covb_sp;
tmpproj = tmp_sp*cmt_sp';
Itmp = speye(npixel);
proj = tmpproj(logical(Itmp));
Forg(ic,nonnan) = bMSEinv'.*proj./DF(ic,1);
% resampling nboot times
if has_fsolve == 1
% parpool;
try
parpool(gridname);
pctRunOnAll warning('off')
end
parfor ib = 1:nboot
% contruct index (we do this in this loop to adapt for unbalance design)
bs = boot_index(ib,:);
bDX = M(bs,:);
% orignial statistic for the fixed effect (revisit)
bbeta = bDX\bY2;
if fitml
bMSE = mean((bDX*bbeta-bY2).^2);
else
bMSE = sum((bDX*bbeta-bY2).^2)./DFmodel;
end
bMSEinv = bMSE.^-1;
% covprj=inv(bDX'*bDX);
% instead of calculating the covariance matrix and
% the inverse of the quadratic form c*covb*c'; here
% do QR decomposition to get the cholesky factor
X = qr(bDX,0);Rtmp = triu(X);
R = Rtmp(1:size(Rtmp,2),:);
S = inv(R);
quadformCOV = cnew/R*S'*cnew';%same as (c*(S*S')*c) == (c*covb*c')
qualCOVinv = inv(quadformCOV);
cbeta_h = (cnew*bbeta-h2)';
I = repmat(1:npixel,[DF(ic,1),1]);
trc = cbeta_h';
cmt_sp = sparse(I(:),1:npixel*DF(ic,1),trc);
covb = repmat(qualCOVinv,[1,1,npixel]);
I = repmat(reshape(1:DF(ic,1)*npixel,DF(ic,1),1,npixel),[1 DF(ic,1) 1]);
J = repmat(reshape(1:DF(ic,1)*npixel,1,DF(ic,1),npixel),[DF(ic,1) 1 1]);
covb_sp = sparse(I(:),J(:),covb(:));
tmp_sp = cmt_sp * covb_sp;
tmpproj = tmp_sp * cmt_sp';
Itmp = speye(npixel);
proj = tmpproj(logical(Itmp));
Ftmp1 = bMSEinv'.*proj./DF(ic,1);
resampleFvalue(ib,ic,nonnan) = Ftmp1;
end
% delete(gcp)
else
waith = waitbar(0,'Resampling...');
for ib = 1:nboot
waitbar(ib / nboot)
% contruct index (we do this in this loop to adapt for unbalance design)
bs = boot_index(ib,:);
bDX = M(bs,:);
% orignial statistic for the fixed effect (revisit)
bbeta = bDX\bY2;
if fitml
bMSE = mean((bDX*bbeta-bY2).^2);
else
bMSE = sum((bDX*bbeta-bY2).^2)./DFmodel;
end
bMSEinv = bMSE.^-1;
% covprj=inv(bDX'*bDX);
% instead of calculating the covariance matrix and
% the inverse of the quadratic form c*covb*c'; here
% do QR decomposition to get the cholesky factor
X = qr(bDX,0);Rtmp = triu(X);
R = Rtmp(1:size(Rtmp,2),:);
S = inv(R);
quadformCOV = cnew/R*S'*cnew';%same as (c*(S*S')*c) == (c*covb*c')
qualCOVinv = inv(quadformCOV);
cbeta_h = (cnew * bbeta - h2)';
I = repmat(1:npixel,[DF(ic,1),1]);
trc = cbeta_h';
cmt_sp = sparse(I(:),1:npixel*DF(ic,1),trc);
covb = repmat(qualCOVinv,[1,1,npixel]);
I = repmat(reshape(1:DF(ic,1)*npixel,DF(ic,1),1,npixel),[1 DF(ic,1) 1]);
J = repmat(reshape(1:DF(ic,1)*npixel,1,DF(ic,1),npixel),[DF(ic,1) 1 1]);
covb_sp = sparse(I(:),J(:),covb(:));
tmp_sp = cmt_sp*covb_sp;
tmpproj = tmp_sp*cmt_sp';
Itmp = speye(npixel);
proj = tmpproj(logical(Itmp));
Ftmp1 = bMSEinv'.*proj./DF(ic,1);
resampleFvalue(ib,ic,nonnan) = Ftmp1;
end
close(waith)
end
end
ResampStat.Forg = Forg;
ResampStat.resFvalue = resampleFvalue;
case 'bootstrap'
%%
resampleFvalue = NaN(nboot, Nc, cSize, rSize);
resamplePvalue = NaN(nboot, Nc, cSize, rSize);
resmapleBeta = NaN(nboot, Nc, cSize, rSize);
% center data
% beta=DX\Yfixed;
% Yc=Yfixed-DX*beta;
Yc = zeros(size(Yfixed));
if ~isempty(label)
for icate = 1:length(CatePredictor)
tmpcate = CatePredictor{icate};
c_ind = strcmp(strlabel,tmpcate);
Yc(c_ind,:) = Yfixed(c_ind,:)-repmat(mean(Yfixed(c_ind,:)),[sum(c_ind),1]);
end
else
Yc = Yfixed(randperm(Nitem,Nitem),:);
end
Yc = Yc(randperm(Nitem,Nitem),:);
% contruct bootstrap table
% random with replacement for all subject
Ns = rank(indxsbj); % number of subject
% sample with replacement, create boot_table
% boot_index=randi(Ns,nboot,Ns);
B = 1;
boot_index = zeros(nboot,Ns);
while B ~= nboot+1
if length(GroupPredictor) > 1 % more than 1 groups
tmp = [];
for ig = 1:length(GroupPredictor)
sbjtmp = find(sum(indxsbj( grouping==GroupPredictor(ig) ,:)) ~= 0);
tmp = [tmp sbjtmp(randi(length(sbjtmp),1,length(sbjtmp)))];
end
boot_index(B,:) = tmp;
B = B+1;
else
tmp = randi(Ns,1,Ns);
if length(unique(tmp)) >= 2 % at least 3 different observations per boot
boot_index(B,:) = tmp;
B = B+1;
end
end
end
ResampStat.resTABLE = boot_index;
% resampling nboot times
if has_fsolve == 1
% parpool;
try
parpool(gridname);
pctRunOnAll warning('off')
end
parfor ib = 1:nboot
% contruct index (we do this in this loop to adapt for unbalance design)
bindx = indxsbj(:,boot_index(ib,:));
bs = bindx(bindx~=0);
bDX = DX(bs,:);
bY = Yc(bs,:);
df2 = size(DX,1)-size(DX,2);
bbeta = bDX\bY;
if fitml
bMSE = mean((bDX*bbeta-bY).^2);
else
bMSE = sum((bDX*bbeta-bY).^2)./DFmodel;
end
bMSEinv = bMSE.^-1;
% covprj=inv(bDX'*bDX);
% instead of calculating the covariance matrix and
% the inverse of the quadratic form c*covb*c'; here
% do QR decomposition to get the cholesky factor
X = qr(bDX,0);Rtmp = triu(X);
R = Rtmp(1:size(Rtmp,2),:);
S = inv(R);
Ftmp1 = NaN(Nc, npixel);
ptmp1 = NaN(Nc, npixel);
betamap = NaN(Nc, npixel);
for ic = 1:Nc
c2 = c{ic};
% h2 = h{ic};
h2 = 0;%%%% important as c*beta is already equal to 0 as the H0
quadformCOV = c2/R*S'*c2';%same as (c*(S*S')*c) == (c*covb*c')
qualCOVinv = inv(quadformCOV);
cbeta_h = (c2*bbeta-h2)';
if size(c2,1) > 1
betamap(ic,:) = mean(cbeta_h,2);
else
betamap(ic,:) = c2 * bbeta;
end
I = repmat(1:npixel,[DF(ic,1),1]);
trc = cbeta_h';
cmt_sp = sparse(I(:),1:npixel*DF(ic,1),trc);
covb = repmat(qualCOVinv,[1,1,npixel]);
I = repmat(reshape(1:DF(ic,1)*npixel,DF(ic,1),1,npixel),[1 DF(ic,1) 1]);
J = repmat(reshape(1:DF(ic,1)*npixel,1,DF(ic,1),npixel),[DF(ic,1) 1 1]);
covb_sp = sparse(I(:),J(:),covb(:));
tmp_sp = cmt_sp * covb_sp;
tmpproj = tmp_sp * cmt_sp';
Itmp = speye(npixel);
proj = tmpproj(logical(Itmp));
Ftmp1(ic,:) = bMSEinv'.*proj./DF(ic,1);
ptmp1(ic,:) = 1-fcdf(Ftmp1(ic,:),DF(ic,1),df2);
end
resampleFvalue(ib,:,nonnan) = Ftmp1;
resamplePvalue(ib,:,nonnan) = ptmp1;
resmapleBeta (ib,:,nonnan) = betamap;
end
% delete(gcp)
else
waith = waitbar(0,'Resampling...');
for ib = 1:nboot
waitbar(ib / nboot)
% contruct index (we do this in this loop to adapt for unbalance design)
bindx = indxsbj(:, boot_index(ib,:));
bs = bindx( bindx~=0 );
bDX = DX(bs, :);
bY = Yc(bs, :);
df2 = size(DX,1)-size(DX,2);
bbeta = bDX\bY;
if fitml
bMSE = mean((bDX*bbeta-bY).^2);
else
bMSE = sum((bDX*bbeta-bY).^2)./DFmodel;
end
bMSEinv = bMSE.^-1;
% covprj=inv(bDX'*bDX);
% instead of calculating the covariance matrix and
% the inverse of the quadratic form c*covb*c'; here
% do QR decomposition to get the cholesky factor
X = qr(bDX,0);Rtmp = triu(X);
R = Rtmp(1:size(Rtmp,2),:);
S = inv(R);
Ftmp1 = NaN(Nc,npixel);
ptmp1 = NaN(Nc,npixel);
betamap = NaN(Nc,npixel);
for ic = 1:Nc
c2 = c{ic};
% h2 = h{ic};
h2 = 0;%%%% important as c*beta is already equal to 0 as the H0
quadformCOV = c2/R*S'*c2';%same as (c*(S*S')*c) == (c*covb*c')
qualCOVinv = inv(quadformCOV);
cbeta_h = (c2*bbeta-h2)';
if size(c2,1) > 1
betamap(ic,:) = mean(cbeta_h,2);
else
betamap(ic,:) = c2 * bbeta;
end
I = repmat(1:npixel,[DF(ic,1),1]);
trc = cbeta_h';
cmt_sp = sparse(I(:),1:npixel*DF(ic,1),trc);
covb = repmat(qualCOVinv,[1,1,npixel]);
I = repmat(reshape(1:DF(ic,1)*npixel,DF(ic,1),1,npixel),[1 DF(ic,1) 1]);
J = repmat(reshape(1:DF(ic,1)*npixel,1,DF(ic,1),npixel),[DF(ic,1) 1 1]);
covb_sp = sparse(I(:),J(:),covb(:));
tmp_sp = cmt_sp * covb_sp;
tmpproj = tmp_sp * cmt_sp';
Itmp = speye(npixel);
proj = tmpproj(logical(Itmp));
Ftmp1(ic,:) = bMSEinv'.*proj./DF(ic,1);
ptmp1(ic,:) = 1-fcdf(Ftmp1(ic,:),DF(ic,1),df2);
end
resampleFvalue(ib,:,mask) = Ftmp1;
resamplePvalue(ib,:,mask) = ptmp1;
resmapleBeta (ib,:,mask) = betamap;
end
close(waith)
end
ResampStat.resFvalue = resampleFvalue;
ResampStat.resPvalue = resamplePvalue;
ResampStat.resBeta = resmapleBeta;
end
case 'random'
error('Resampling method for random effect is not available yet')
end
warning('on')
end