Analysis using codes: example 2
Using iMap4, we created the single-trial 2D fixation duration map and smoothed at 1° of visual angle. Importantly, to keep in line with Miellet, et al (2012), spatial normalization was performed by Z-scoring the fixation map across all pixels independently for each trial (the result is identical without spatial normalization in this example). We also applied a mask generated with the default option.
%% Load data
clear all
clc
filename=dir('data*.mat');
% create condition table
sbj = repmat([1:30],1,4)';
group = repmat([ones(1,15) ones(1,15)*2],1,4)';
blinkspot= repmat(1:4,30,1);
blinkspot= blinkspot(:);
Tbl = dataset(sbj,group,blinkspot);
% deg0cau = 1:15;
% deg0as = 16:30;
% deg2cau = 31:45;
% deg2as = 46:60;
% deg5cau = 61:75;
% deg5as = 76:90;
% deg8cau = 91:105;
% deg8as = 106:120;
% parameters for smoothing
ySize = 382;
xSize = 390;
smoothingpic= 10;
[x, y] = meshgrid(-floor(xSize/2)+.5:floor(xSize/2)-.5, -floor(ySize/2)+.5:floor(ySize/2)-.5);
gaussienne = exp(- (x .^2 / smoothingpic ^2) - (y .^2 / smoothingpic ^2));
gaussienne = (gaussienne - min(gaussienne(:))) / (max(gaussienne(:)) - min(gaussienne(:)));
f_fil = fft2(gaussienne);
Nitem=length(filename);
Ntall=zeros(Nitem,1);
for item=1:Nitem
load(['data' num2str(item) '.mat'])
Trials=unique(summary(:,4));
Ntall(item)=length(Trials);
end
Trialall=sum(Ntall);
rawmapMatST = zeros(Trialall,ySize, xSize);
fixmapMatST = zeros(Trialall,ySize, xSize);
groupST=zeros(Trialall,1);
sbjST=zeros(Trialall,1);
blinkspotST=zeros(Trialall,1);
stDurST=zeros(Trialall,1);
ii=0;
for item=1:Nitem
load(['data' num2str(item) '.mat'])
Nfix=size(summary,1);
Trials=summary(:,4);
UTrials=unique(Trials);
Nt=length(UTrials);
% condition based
fixmaptmp=zeros(Nt,ySize, xSize);
rawmaptmp=zeros(Nt,ySize, xSize);
for it=1:Nt
ii=ii+1;
coordX=round(summary(Trials==UTrials(it),2));%switch matrix coordinate here
coordY=round(summary(Trials==UTrials(it),1));
intv=summary(Trials==UTrials(it),3);
indx1=coordX>0 & coordY>0 & coordX<ySize & coordY<xSize;
rawmap=full(sparse(coordX(indx1),coordY(indx1),intv(indx1),ySize,xSize));
f_mat = fft2(rawmap); % 2D fourrier transform on the points matrix
filtered_mat = f_mat .* f_fil;
smoothpic = real(fftshift(ifft2(filtered_mat)));
fixmaptmp(it,:,:)=(smoothpic-mean(smoothpic(:)))./std(smoothpic(:));%
fixmapMatST(ii,:,:)=fixmaptmp(it,:,:);
rawmaptmp(it,:,:)=rawmap;
rawmapMatST(ii,:,:)=rawmaptmp(it,:,:);
groupST(ii)=Tbl.group(item);
sbjST(ii)=Tbl.sbj(item);
blinkspotST(ii)=Tbl.blinkspot(item);
stDurST(ii)=sum(indx1);
end
if Nt<10
fixmapMat(item,:,:)=mean(fixmaptmp,1);
rawmapMat(item,:,:)=mean(rawmaptmp,1);
else
fixmapMat(item,:,:)=trimmean(fixmaptmp,30);
rawmapMat(item,:,:)=trimmean(rawmaptmp,30);
end
end
TblST=dataset(sbjST,groupST,blinkspotST,stDurST);
TblST.blinkspotST=nominal(TblST.blinkspotST);
TblST.groupST=nominal(TblST.groupST);
TblST.groupST(TblST.groupST=='1')='WC';
TblST.groupST(TblST.groupST=='2')='EA';
TblST.groupST=nominal(TblST.groupST);
%% rescale
scale=150/mean([xSize,ySize]);
[ySize2,xSize2]=size(imresize(ones(ySize,xSize),scale));
fixmapMat2ST=zeros(size(TblST,1),ySize2,xSize2);
for it=1:size(TblST,1)
fixmapMat2ST(it,:,:)=imresize(squeeze(fixmapMatST(it,:,:)),scale);
end
%% mean map
figure('NumberTitle','off','Name','Mean fixation bias');
race=unique(TblST.groupST);
condi=unique(TblST.blinkspotST);
ii=0;
for ig=1:length(race)
for ipp=1:length(condi)
indxtmp=TblST.groupST==race(ig) & TblST.blinkspotST==condi(ipp);
TempMap=squeeze(mean(fixmapMat2ST(indxtmp,:,:),1));
% subplot(2,4,(ig-1)*4+ipp)
subplot(4,2,ipp*2-(2-ig))
ii=ii+1;betanew(ii,:,:)=TempMap;
imagesc(TempMap);colorbar
axis square, axis off,
title(char(race(ig)))
end
end
%
figure('NumberTitle','off','Name','all fixation bias');
subplot(1,2,1)
imagesc(squeeze(mean(fixmapMat2ST,1)));axis('equal','off')
subplot(1,2,2)
masktmpST=squeeze(mean(fixmapMat2ST,1))>.0045;
imagesc(masktmpST);axis('equal','off')
We then applied a full model on the single-trial fixation duration map made used of the “single-trial” option in iMap4:
Pixel_Intensity ~ Observer culture + Blindspot size + Observer culture * Blindspot size + (1 | subject)
Only the predictor of subject was treated as random effects and the model was fitted with maximum likelihood estimation (ML).
%% imapLMM
tic
opt.singlepredi=1;
[LMMmap,lmexample]=imapLMM(fixmapMat2ST,TblST,masktmpST,opt, ...
'PixelIntensity ~ groupST + blinkspotST + groupST:blinkspotST + (1|sbjST)','DummyVarCoding','effect');
toc
First check the model fitting parameters:
%% plot model fitting
close all
opt1.type='model';
% perform contrast
[StatMap]=imapLMMcontrast(LMMmap,opt1);
% output figure;
imapLMMdisplay(StatMap,0)
After model fitting, we perform ANOVA to test the two main effects and their interactions. The code block below applied a bootstrap clustering test using cluster dense as criteria with 1000. We found a significant interaction and the main effect of Blindspot size, but not the main effect of culture (See Figure_a below).
%% plot fixed effec(anova result)
% close all
opt=struct;% clear structure
mccopt=struct;
opt.type='fixed';
opt.alpha=.05;
mccopt.methods='bootstrap';
mccopt.bootgroup={'groupST'};
% mccopt.methods='FDR';
mccopt.nboot=1000;
% mccopt.permute=1;
mccopt.bootopt=1;
% mccopt.sigma=smoothingpic*scale;
mccopt.tfce=0;
% perform contrast
[StatMap]=imapLMMcontrast(LMMmap,opt);
% mulitple comparison correction
[StatMap_c]=imapLMMmcc(StatMap,LMMmap,mccopt,fixmapMat2ST);
% output figure;
imapLMMdisplay(StatMap_c,1)
Moreover, by performing linear contrast of the model coefficients, we reproduced the figure 2 as in Miellet, et al (2012). (See Figure_b below)
%% Compute linear contrast (reproduce figure 2 as in the orignial paper)
% close all
opt=struct;% clear structure
mccopt=opt;
opt.type='predictor beta';
opt.alpha=.05;
opt.c={[-1 0 0 0 1 0 0 0];[0 -1 0 0 0 1 0 0];[0 0 -1 0 0 0 1 0];[0 0 0 -1 0 0 0 1];[1 0 0 -1 0 0 0 0];[0 0 0 0 1 0 0 -1]};
opt.name={'WC-EA NV';'WC-EA 2dg';'WC-EA 5dg';'WC-EA 8dg';'WC NV-8dg'; 'EA NV-8dg'};
% opt.c=limo_OrthogContrasts([3,2]);
% opt.name={'Spotlight';'Position';'Interaction'};
% opt.h={[0.005],[0.005],[0.005],[0.005],[0.005],[0.005]};
% opt.onetail='>';
% mccopt.methods='Randomfield';
mccopt.methods='bootstrap';
mccopt.bootgroup={'groupST'};
% mccopt.methods='FDR';
mccopt.nboot=1000;
% mccopt.permute=1;
mccopt.bootopt=1;
% mccopt.sigma=smoothingpic*scale;
mccopt.tfce=0;
% perform contrast
[StatMap]=imapLMMcontrast(LMMmap,opt);
[StatMap_c]=imapLMMmcc(StatMap,LMMmap,mccopt,fixmapMat2ST);
% output figure;
imapLMMdisplay(StatMap_c,1)
For each unique categorical condition, we can compute an "above chance" fixation pattern map.
%% Single predictor (above chance fixate)
opt=struct;% clear structure
mccopt=opt;
opt.type='predictor beta';
opt.alpha=.05;
opt.c={[1 0 0 0 0 0 0 0];[0 1 0 0 0 0 0 0];[0 0 1 0 0 0 0 0];[0 0 0 1 0 0 0 0];[0 0 0 0 1 0 0 0];[0 0 0 0 0 1 0 0];[0 0 0 0 0 0 1 0];[0 0 0 0 0 0 0 1]};
opt.name={'EA-NV';'EA-2deg';'EA-5deg';'EA-8deg';'WC-NV';'WC-2deg';'WC-5deg';'WC-8deg'};
h0=mean(fixmapMat2ST(repmat(masktmpST,[size(fixmapMat2ST,1),1,1])==1));
opt.h={h0,h0,h0,h0,h0,h0,h0,h0};
% opt.c=limo_OrthogContrasts([3,2]);
% opt.name={'Spotlight';'Position';'Interaction'};
% opt.h={[0.005],[0.005],[0.005],[0.005],[0.005],[0.005]};
opt.onetail='>';
% mccopt.methods='Randomfield';
mccopt.methods='bootstrap';
mccopt.bootgroup={'groupST'};
% mccopt.methods='FDR';
mccopt.nboot=1000;
% mccopt.permute=1;
mccopt.bootopt=1;
% mccopt.sigma=smoothingpic*scale;
mccopt.tfce=0;
% perform contrast
[StatMap]=imapLMMcontrast(LMMmap,opt);
[StatMap_c]=imapLMMmcc(StatMap,LMMmap,mccopt,fixmapMat2ST);
% output figure;
imapLMMdisplay(StatMap_c,1,[],'parula')
The result using iMap4:
iMap4 results of Miellet et al. (2012). a) ANOVA result of the linear mixed model. b) Replication of figure 2 in Miellet et al. (2012) using linear contrast of the model coefficients. The solid black line circles the significant region for all the above figures.
You can find the analysis code here