THE AUDITORY MODELING TOOLBOX
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EXP_BAUMGARTNER2020 - - Simulations of Baumgartner and Majdak (2020)
Program code:
function data = exp_baumgartner2020(varargin)
%EXP_BAUMGARTNER2020 - Simulations of Baumgartner and Majdak (2020)
% Usage: data = exp_baumgartner2020(flag)
%
% EXP_BAUMGARTNER2020(flag) reproduces figures of the study from
% Baumgartner and Majdak (2020).
%
% The following flags can be specified
%
% fig2 shows cue-specific predictions, sensitivities, prediction errors,
% and optimal relative weights in order to best explain the actual
% externalization ratings. Oracle: prediction errors obtained with
% the oracle model.
%
% fig3 displays the prediction errors for all decision strategies,
% optimal cue weights and results for paired combinations.
%
% hartmann1996 models experiments from Hartmann & Wittenberg (1996; Fig.7-8)
% 1st panel: Synthesis of zero-ILD signals. Only the harmonics
% from 1 to nprime had zero interaural level difference;
% harmonics above nprime retained the amplitudes of the baseline
% synthesis. Externalization scores as a function of the boundary
% harmonic number nprime. Fundamental frequency of 125 Hz.
% 2nd panel: Synthesis of signals to test the ISLD hypothesis.
% Harmonics at and below the boundary retained only the interaural
% spectral level differences of the baseline synthesis. Higher
% harmonics retained left and right baseline harmonic levels.
% Externalization scores as a function of the boundary
% frequency.
%
% hassager2016 models experiments from Hassager et al. (2016; Fig.6).
% The mean of the seven listeners perceived sound source
% location (black) as a function of the bandwidth factor
% and the corresponding model predictions (colored).
% The model predictions have been shifted slightly to the right
% for a better visual interpretation. The error bars are one
% standard error of the mean.
%
% baumgartner2017 models experiments from Baumgartner et al. (2017).
% Effect of HRTF spectral contrast manipulations on sound externalization.
% Externalization scores were derived from paired comparisons via
% Bradley-Terry-Luce modeling.
%
% boyd2012 models experiments from Boyd et al. (2012; Fig.1, top).
% Average externalization ratings of 1 talker for NH participants
% against mix point as a function of microphone position (ITE/BTE)
% and frequency response (BB/LP). The reference condition (ref) is
% the same as ITE/BB. Error bars show SEM.
%
% Requirements:
% -------------
%
% 1) SOFA API v0.4.3 or higher from http://sourceforge.net/projects/sofacoustics for Matlab (in e.g. thirdparty/SOFA)
%
% 2) Data in hrtf/baumgartner2017
%
% 3) Statistics Toolbox for Matlab (for some of the figures)
%
% Examples:
% ---------
%
% To display indivdual predictions for all experiments use :
%
% exp_baumgartner2020('fig2');
%
% To display results for different decision strategies use :
%
% exp_baumgartner2020('fig3');
%
% References:
% R. Baumgartner and P. Majdak. Decision making in auditory
% externalization perception. bioRxiv, 2020.
%
% A. W. Boyd, W. M. Whitmer, J. J. Soraghan, and M. A. Akeroyd. Auditory
% externalization in hearing-impaired listeners: The effect of pinna cues
% and number of talkers. J. Acoust. Soc. Am., 131(3):EL268--EL274, 2012.
% [1]arXiv | [2]www: ]
%
% W. M. Hartmann and A. Wittenberg. On the externalization of sound
% images. J. Acoust. Soc. Am., 99(6):3678--88, June 1996.
%
% References
%
% 1. http://arxiv.org/abs/ http://dx.doi.org/10.1121/1.3687015
% 2. http://dx.doi.org/10.1121/1.3687015
%
% hassager2016 baumgartner2017looming
%
% Url: http://amtoolbox.sourceforge.net/amt-0.10.0/doc/experiments/exp_baumgartner2020.php
% Copyright (C) 2009-2020 Piotr Majdak and the AMT team.
% This file is part of Auditory Modeling Toolbox (AMT) version 0.10.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% AUTHOR: Robert Baumgartner, Acoustics Research Institute, Vienna, Austria
definput.import={'amt_cache','baumgartner2020'};
definput.flags.type = {'all','fig2','fig3','hartmann1996','hassager2016','baumgartner2017','boyd2012','pairs','figStrat','tab2','tab3'};
definput.flags.gradients={'positive','negative','both'};
definput.flags.quickCheck = {'','quickCheck'};
definput.flags.disp = {'progress','silent'};
definput.keyvals.Sintra = 2;
definput.keyvals.Sinter = 2;
definput.keyvals.numCue = 2;
definput.keyvals.ignore = {'ITSD'};
[flags,kv] = ltfatarghelper({},definput,varargin);
Ncues = 8;
% Normalized externalization rating scale
Erange = 1;
Eoffset = 0;
% For cue combination analysis
% Sfix = [.16,.40,nan,.45,.70,.37,nan,nan]; % obtained from tab2
cueSelLbl = {{'MSS','ISS','MSSD','ISSD','ITIT','IC','MI'};...
{'MSS','ISS','MSSD','ISSD','ITIT','IC'};...
{'MSS','ISS','ISSD','ITIT','IC'};...
{'MSS','ISS','ISSD','ITIT'};...
{'MSS','ISSD','ITIT'};...
{'MSS','ITIT'};...
{'MSS'};...
};
cueSelLblTxt = {'MSS, ISS, MSSD, ISSD, ITIT, IC, MI';...
'MSS, ISS, MSSD, ISSD, ITIT, IC';...
'MSS, ISS, ISSD, ITIT, IC';...
'MSS, ISS, ISSD, ITIT';...
'MSS, ISSD, ITIT';...
'MSS, ITIT';...
'MSS'};
strategies = {'Oracle','WSM','LTA','MTA','WTA'};
% Symbol order for plotting
symb = {'-o','-s','-h','-d','-<','->','-^','-x','-p',':*','--+',':v'};
colors = 0.8*[zeros(1,3);jet(Ncues);lines(3)];
%% Hartmann & Wittenberg (1996)
if flags.do_hartmann1996
cond = {'ILD','ISLD'};
% condPlotLbl = {'ILD to 0','ILD const.'};
nprime = [0,1,8,14,19,22,25,38];
f0 = 125; %Hz
fncache = flags.type;%['hartmann1996'];
if not(flags.do_positive)
fncache = [fncache,'_',flags.gradients,'Grad'];
end
[Pext,cues,cueLbl] = amt_cache('get',fncache,flags.cachemode);
if isempty(Pext)
azi = -37;
data = data_baumgartner2017;
if flags.do_quickCheck
data = data(1:5);
end
Pext = repmat({nan(length(data),length(nprime))},2,2);
cues = repmat({nan(length(data),length(nprime),Ncues)},2,1);
for isub = 1:length(data)
Obj = data(isub).Obj;
template = sig_hartmann1996(0,'Obj',Obj,'dur',0.1);
for ee = 1:length(cond)
for nn = 1:length(nprime)
target = sig_hartmann1996(nprime(nn),'Obj',Obj,'dur',0.1,cond{ee});
[~,cues{ee}(isub,nn,:),cueLbl] = baumgartner2020(target,template,'flow',100,'fhigh',5000,'lat',azi,flags.gradients);
end
end
amt_disp([num2str(isub),' of ',num2str(length(data)),' subjects completed.'],'progress')
end
if not(flags.do_quickCheck)
amt_cache('set',fncache,Pext,cues,cueLbl);
end
end
%% Cue weighting optimization procedure
% Erange = 1; % original: 3
% Eoffset = 0;
Pext = cell(Ncues-length(kv.ignore),length(cond));
PextNumCue = cell(length(strategies),length(cond));
figure
hax{1} = tight_subplot(1,2,0,[.15,.1],[.1,.05]);
figure;
hax{2} = tight_subplot(1,2,0,[.15,.1],[.1,.05]);
for ee = 1:length(cond)
act = data_hartmann1996(cond{ee});
actual = act.avg.Escore(:)/3; % normalized response scale
% align actual and simulated data format
tmp = permute(cues{ee},[2,1,3]);
tmp = interp1(nprime,tmp,act.avg.nprime);
predCue = squeeze(num2cell(tmp,1:2));
fncache2 = [fncache,'_exp',num2str(ee)];
amt_disp([flags.type,', Exp. ',num2str(ee)],'progress')
amt_cache('set',[fncache2,'_fitting'],predCue,actual);
% cue analysis: first optimal then fixed sensitivities
[Pext(:,ee),PextNumCue(:,ee),cueTab{ee},cueSelTab{ee}] = cueAnalysis(...
cueLbl,cueSelLbl,cueSelLblTxt,predCue,actual,Erange,Eoffset,fncache2,kv);
%% Plot
dataLbl = [{'Actual'};cueTab{ee}.Properties.RowNames];
Nsubj = size(Pext{1},2);
act = data_hartmann1996(cond{ee});
x = 1e-3*f0*act.avg.nprime;
yall = {Pext,PextNumCue};
for iy = 1:length(yall)
axes(hax{iy}(ee)); clear h
y = yall{iy};
for cc = 1:size(y,1)
dx = 0.025*(cc - size(y,1)/2);
h(cc+1) = errorbar(x+dx,mean(y{cc,ee},2),std(y{cc,ee},0,2)/sqrt(Nsubj),...
symb{cc+1},'Color',colors(cc+1,:));
hold on
end
h(1) = plot(x,act.avg.Escore/3,symb{1},'Color',colors(1,:));
set(h(2:end),'MarkerFaceColor','w')
set(h(1),'MarkerFaceColor','k')
if ee == 1
xlabel('Highest frequency altered in kHz') %n^{\prime}
ylabel('Externalization')
else
% xlabel('Highest frequency altered in kHz')
set(gca,'YTickLabel',{})
end
axis([x(1)-.5,x(end)+.5,Eoffset-0.1*Erange,Eoffset+1.1*Erange])
box off
if ee == 1
if iy == 1
leg= [{'Actual'};cueTab{ee}.Properties.RowNames];
legend(h,leg(1:end-1),'Location','southwest','box','off');
else
leg= [{'Actual'};strategies(:)];
legend(h,leg,'Location','southwest','box','off');
end
end
end
end
end
%% Hassager et al. (2016)
if flags.do_hassager2016
azi = [0,50];
flp = 6000; % lowpass filtered noise stimuli
Pext_A = data_hassager2016;
B = Pext_A.B;
fncache = flags.type;
if not(flags.do_positive)
fncache = [fncache,'_',flags.gradients,'Grad'];
end
[Pext,cues,cueLbl] = amt_cache('get',fncache,flags.cachemode);
if isempty(cues)
data = data_baumgartner2017;
if flags.do_quickCheck
data = data(1:5);
end
cues = nan(length(B),length(azi),length(data),Ncues);
for isubj = 1:length(data)
Obj = data(isubj).Obj;
for iazi = 1:length(azi)
idazi = Obj.SourcePosition(:,1) == azi(iazi) & Obj.SourcePosition(:,2) == 0;
template = squeeze(shiftdim(Obj.Data.IR(idazi,:,:),2));
for iB = 1:length(B)
amt_disp(num2str(iB),'volatile');
if isnan(B(iB))
target = template;
else
Obj_tar = sig_hassager2016(Obj,B(iB));
target = squeeze(shiftdim(Obj_tar.Data.IR(idazi,:,:),2));
end
[~,cues(iB,iazi,isubj,:),cueLbl] = baumgartner2020(target,template,'flow',100,'fhigh',flp,'lat',azi(iazi),flags.gradients);
end
end
amt_disp([num2str(isubj),' of ',num2str(length(data)),' subjects completed.'],'progress')
end
if not(flags.do_quickCheck)
amt_cache('set',fncache,Pext,cues,cueLbl);
end
end
%% Cue weighting optimization procedure
dimSubj = 3;
% dimCues = 4;
Nsubj = size(cues,dimSubj);
predCue = squeeze(num2cell(reshape(cues,[],Nsubj,Ncues),1:2));
% optimize sensitivities
actual = Pext_A.rating(:);%repmat(Pext_A.rating(:),Nsubj,1);
actual = (actual-1)/4; % normalized response scale
% Erange = 1; % original: 4
% Eoffset = 0; % original: 1
amt_disp(flags.type)
amt_cache('set',[fncache,'_fitting'],predCue,actual);
% cue analysis
[Pext,PextNumCue,cueTab,cueSelTab] = cueAnalysis(...
cueLbl,cueSelLbl,cueSelLblTxt,predCue,actual,Erange,Eoffset,fncache,kv);
%% Plot
BplotTicks = logspace(log10(1),log10(64),3);
BplotTicks = round(BplotTicks*100)/100;
BplotStr = ['Ref.';[repmat(' ',3,1),num2str(BplotTicks(:)),repmat(' ',3,1)]];
BplotTicks = [0.25/2,BplotTicks];
B(1) = B(2)/2;
yall = {Pext,PextNumCue};
for iy = 1:length(yall)
y = yall{iy};
figure
hax = tight_subplot(1,2,0,[.15,.1],[.1,.05]);
for iazi = 1:length(azi)
axes(hax(iazi)); clear h
h(1) = plot(B,(Pext_A.rating(:,iazi)-1)/4,symb{1},'Color',colors(1,:));
hold on
for m = 1:length(y)
dx = 1+0.01*(m - (Ncues+1)/2);
pred = reshape(y{m},length(B),[],Nsubj);
h(m+1) = errorbar(dx*B,mean(pred(:,iazi,:),dimSubj),std(pred(:,iazi,:),0,dimSubj)/sqrt(Nsubj),...
symb{m+1},'Color',colors(m+1,:));
end
set(h,'MarkerFaceColor','w')
set(h(1),'MarkerFaceColor','k')
set(gca,'XTick',BplotTicks,'XTickLabel',BplotStr,'XScale','log')
axis([BplotTicks(1)/1.5,BplotTicks(end)*1.5,Eoffset-0.1*Erange,Eoffset+1.1*Erange])
xlabel('Bandwidth Factor [ERB]')
if iazi==1
ylabel('Externalization')
else
set(gca,'YTickLabel',{})
end
text(0.125,Eoffset,[num2str(azi(iazi)),'\circ'])
end
if iy == 1
leg=[{'Actual'};cueTab.Properties.RowNames];
leg = legend(h,leg(1:end-1),'Location','southwest');
else
leg = legend(h,[{'Actual'};strategies(:)],'Location','southwest');
end
set(leg,'Box','off')
end
end
%% Baumgartner et al. (2017) ----------------------------------------------
if flags.do_baumgartner2017
% Behavioral results
fncache = [flags.type,'_actual'];%'baumgartner2017_E_BTL';
data = amt_cache('get',fncache,flags.cachemode);
if isempty(data)
exp2 = data_baumgartner2017looming('exp2');
Nsubj = length(exp2.meta.subject);
iISI = exp2.meta.ISI == 0.1;
iresp = strcmp(exp2.meta.response,'approaching');
data.C = 0:0.5:1;
data.subj = [];%exp2.meta.subject;
data.Escore = [];%nan(Nsubj,length(A));
data.azi = [exp2.rawData.azimuth];
M = zeros(3,3);
iM = [7,4,8,3,2,6]; % indices to map judgements to preference matrix (
iss = 0;
for ss = 1:Nsubj
M(iM) = exp2.data(ss,1:6,iresp,iISI)+eps;
Ns = 200; % max # hits
E = nansum(M,2)/Ns;
E = E/E(3);
if E(1)<=1 % if C = 0 is more externalized than the reference (C = 1) either the subject misunderstood the task or something was wrong with the reference
iss = iss+1;
data.subj{iss} = exp2.meta.subject{ss};
data.Escore(iss,:) = E;
end
end
amt_cache('set',fncache,data)
end
Nsubj = length(data.subj);
hrtf = data_baumgartner2017looming('exp2','hrtf');
% Modeling
fncache = flags.type;
if not(flags.do_positive)
fncache = [fncache,'_',flags.gradients,'Grad'];
end
[Pext,cues,cueLbl] = amt_cache('get',fncache,flags.cachemode);
if isempty(cues)
Pext = nan(length(data.C),Nsubj);
cues = nan(length(data.C),Nsubj,Ncues);
for isubj = 1:Nsubj
template = hrtf(ismember({hrtf.id},data.subj(isubj))).Obj;
for iC = 1:length(data.C)
target = sig_baumgartner2017looming(template,data.C(iC));
[Pext(iC,isubj),cues(iC,isubj,:),cueLbl] = baumgartner2020(target,template,...
'lat',data.azi(isubj),'flow',1000,'fhigh',18e3,flags.gradients);
end
amt_disp([num2str(isubj),' of ',num2str(Nsubj),' subjects completed.'],'progress')
end
amt_cache('set',fncache,Pext,cues,cueLbl);
end
%% Cue weighting optimization procedure
dimSubj = 2;
dimCues = 3;
% Erange = 1;
% Eoffset = 0;
Nsubj = size(cues,dimSubj);
actual = permute(data.Escore,[2,1]);
predCue = squeeze(num2cell(cues,1:dimCues-1));
amt_disp(flags.type)
amt_cache('set',[fncache,'_fitting'],predCue,actual);
[Pext,PextNumCue,cueTab,cueSelTab] = cueAnalysis(...
cueLbl,cueSelLbl,cueSelLblTxt,predCue,actual,Erange,Eoffset,fncache,kv);
%% Figure
flags.do_plot_individual = false;
yall = {[{data.Escore'};Pext],[{data.Escore'};PextNumCue]};
for iy = 1:length(yall)
y = yall{iy};
figure; clear h;
if not(flags.do_plot_individual)
for iE = 1:length(y)
dx = .005*(iE - length(y)/2);
h(iE) = errorbar(data.C+dx,mean(y{iE},2),std(y{iE},0,2)/sqrt(Nsubj),...
symb{iE},'Color',colors(iE,:));
set(h,'MarkerFaceColor','w')
hold on
end
set(h(1),'MarkerFaceColor','k')
set(gca,'XTick',data.C)
axis([-0.2,1.2,Eoffset-0.1*Erange,Eoffset+1.1*Erange])
ylabel('Externalization')
xlabel('Spectral contrast, C')
else % flags.do_plot_individual
for isubj = 1:Nsubj
subplot(3,ceil(Nsubj/3),isubj); clear h;
for iE = 1:length(y)
dx = .005*(iE - length(y)/2);
h(iE) = plot(data.C+dx,y{iE}(:,isubj),...
symb{iE},'Color',colors(iE,:));
set(h,'MarkerFaceColor','w')
hold on
end
set(h(1),'MarkerFaceColor','k')
set(gca,'XTick',data.C)
axis([-0.2,1.2,Eoffset-0.1*Erange,Eoffset+1.1*Erange])
ylabel('Externalization')
xlabel('Spectral contrast, C')
end
end
if iy == 1
leg=[{'Actual'};cueTab.Properties.RowNames];
legend(h,leg(1:end-1),'Location','EastOutside','box','off')
else
leg=[{'Actual'};strategies(:)];
legend(h,leg,'Location','EastOutside','box','off')
end
end
end
%% Boyd et al. (2012) -----------------------------------------------------
if flags.do_boyd2012
flags.do_BRIR = true; % directly based on BRIRs
flags.do_noise = false; % or based on BRIR-convoluted noise
% otherwise: original speech samples
flp = [nan,6500]; % Low-pass cut-off frequency
azi = -30;
subjects = data_boyd2012;
if flags.do_noise || flags.do_BRIR
subjects = subjects([3,6,7]); % only the ones with BRIRs
else
subjects = subjects([1,3,4,6,7]); % only the ones with stimuli
end
mix = subjects(1).Resp.mix/100;
idn = not(isnan(mix));
mix = mix(idn); % omit reference
% determine cache name
fncache = flags.type;%['boyd2012'];
if not(flags.do_positive)
fncache = [fncache,'_',flags.gradients,'Grad'];
end
if flags.do_noise
fncache = [fncache,'_noise'];
elseif flags.do_BRIR
% standard
else
fncache = [fncache,'_speech'];
end
[E,cues,cueLbl] = amt_cache('get',fncache,flags.cachemode);
if isempty(cues)
if flags.do_noise || flags.do_BRIR
sig = noise(50e3,1,'pink');
fs = subjects(1).BRIR.fs;
[b,a]=butter(10,2*flp(2)/fs,'low');
end
E.all = repmat({nan([length(mix),2,2,length(subjects)])},1,1);
cues = nan(length(mix),2,2,length(subjects),Ncues);
for isub = 1:length(subjects)
E.all{1}(:,:,:,isub) = cat(3,...
[subjects(isub).Resp.ITE_BB_1T(idn),subjects(isub).Resp.BTE_BB_1T(idn)],...
[subjects(isub).Resp.ITE_LP_1T(idn),subjects(isub).Resp.BTE_LP_1T(idn)]);
if flags.do_noise
stim{1} = lconv(sig,subjects(isub).BRIR.ITE(:,:,1));
stim{2} = lconv(sig,subjects(isub).BRIR.BTE(:,:,1));
stim{3} = lconv(sig,subjects(isub).BRIR.noHead(:,:,1));
template = stim{1};
targetSet = cell(length(mix),2,2);
elseif flags.do_BRIR
template = subjects(isub).BRIR.ITE(:,:,1);
stim{1} = subjects(isub).BRIR.ITE(:,:,1);
stim{2} = subjects(isub).BRIR.BTE(:,:,1);
stim{3} = subjects(isub).BRIR.noHead(:,:,1);
targetSet = cell(length(mix),2,2);
else % speech samples
template = subjects(isub).Reference_1T;
targetSet = cat(3,...
[subjects(isub).Target.ITE_BB_1T(:),subjects(isub).Target.BTE_BB_1T(:)],...
[subjects(isub).Target.ITE_LP_1T(:),subjects(isub).Target.BTE_LP_1T(:)]);
end
%% Model simulations
flow = 100;
fhigh = [16e3,16e3]; % set fhigh(2) to flp(2) for manual bandwidth adjustment
for c = 1:2
for lp = 1:2
for m = 1:length(mix)
% mixing
if flags.do_noise || flags.do_BRIR
targetSet{m,c,lp} = mix(m)*stim{c} + (1-mix(m))*stim{3};
% low-pass filtering
if lp == 2
targetSet{m,c,lp} = filter(b,a,targetSet{m,c,lp});
end
end
target = targetSet{m,c,lp};
[~,cues(m,c,lp,isub,:),cueLbl] = baumgartner2020(target,template...
,'argimport',flags,kv,'flow',flow,'fhigh',fhigh(lp),'lat',azi,flags.gradients);%,'reflectionOnsetTime',5e-3);
end
end
end
amt_disp([num2str(isub),' of ',num2str(length(subjects)),' subjects completed.'],'progress')
end
if not(flags.do_quickCheck)
amt_cache('set',fncache,E,cues,cueLbl);
end
end
%% Cue weighting optimization procedure
dimSubj = 4;
% Erange = 1; % original: 100
% Eoffset = 0;
Nsubj = size(cues,dimSubj);
if flags.do_BRIR % comparison on individual basis
actual = E.all{1};
actual = reshape(actual,[],Nsubj);
else % average comparison
actual = mean(E.all{1},4);
actual = actual(:);
end
actual = actual/100; % normalized response range
E.all{1} = E.all{1}/100;
predCue = squeeze(num2cell(reshape(cues,[],Nsubj,Ncues),1:2));
amt_disp(flags.type)
amt_cache('set',[fncache,'_fitting'],predCue,actual);
[Pext,PextNumCue,cueTab,cueSelTab] = cueAnalysis(...
cueLbl,cueSelLbl,cueSelLblTxt,predCue,actual,Erange,Eoffset,fncache,kv);
dims = [length(mix),size(cues,2),size(cues,3),size(cues,4)];
for ii = 1:length(Pext)
E.all{ii+1} = reshape(Pext{ii},dims);
end
EnumCue = E.all(1);
for ii = 1:length(PextNumCue)
EnumCue{ii+1} = reshape(PextNumCue{ii},dims);
end
%% Plot
flags.do_plot_individual = false;
condLbl = {'ITE | BB','BTE | BB','ITE | LP','BTE | LP'};
mix = mix*100;
if not(flags.do_plot_individual)
yall = {E.all,EnumCue};
for iy = 1:length(yall)
y = yall{iy};
figure
hax = tight_subplot(2,2,0,[.15,.1],[.1,.05]);
for cc = 1:length(condLbl)
axes(hax(cc))
for ee = 1:length(y)
dx = 0.5*(ee - length(y)/2);
m = mean(y{ee},4);
s = std(y{ee},0,4);
h = errorbar(mix+dx,m(:,cc),s(:,cc),...
symb{ee},'Color',colors(ee,:));
if ee == 1
set(h,'MarkerFaceColor','k')
else
set(h,'MarkerFaceColor','w')
end
hold on
end
set(gca,'XDir','reverse')
if cc == 3 || cc == 4
xlabel('Mix (%)')
else
set(gca,'XTickLabel',[])
end
if cc == 1 || cc == 3
ylabel('Externalization')
else
set(gca,'YTickLabel',[])
end
text(110,0,condLbl{cc},'HorizontalAlignment','left')
axis([-20,120,Eoffset-0.1*Erange,Eoffset+1.1*Erange])
if cc == 4
end
end
end
else % flags.do_plot_individual
for isub = 1:size(E.all{1},4)
figure
hax = tight_subplot(1,4,0,[.15,.1],[.1,.05]);
for cc = 1:length(condLbl)
axes(hax(cc))
for ee = 1:Nee
Eisub = E.all{ee}(:,:,:,isub);
h = plot(mix,Eisub(2:end,cc),symb{ee},'Color',colors(ee,:));
set(h,'MarkerFaceColor','w')
hold on
end
set(gca,'XDir','reverse')
xlabel('Mix (%)')
if cc == 1
ylabel('Externalization')
else
set(gca,'YTickLabel',[])
end
title(condLbl{cc})
axis([-20,120,Eoffset-0.1*Erange,Eoffset+1.1*Erange])
if cc == 4
leg = legend(dataLbl);
set(leg,'Box','off','Location','north')
end
end
end
end
%% Output
Pext = E;
end
if flags.do_all
exp = {'hartmann1996','hassager2016','baumgartner2017','boyd2012'};
for ii = 1:length(exp)
exp_baumgartner2020(exp{ii},flags.cachemode);
end
elseif flags.do_fig3 || flags.do_pairs
exp = {'hartmann1996_exp1','hartmann1996_exp2','hassager2016','baumgartner2017','boyd2012'};
Nexp = length(exp);
[~,~,cueLbl] = amt_cache('get','hassager2016');
predCue = [];
actual = [];
for ii = 1:Nexp
if flags.do_positive
fn = [exp{ii},'_fitting'];
else
if ii <=2
fn = [exp{ii}(1:12),'_',flags.gradients,'Grad',exp{ii}(13:end),'_fitting'];
else
fn = [exp{ii},'_',flags.gradients,'Grad','_fitting'];
end
end
[p,a] = amt_cache('get',fn);
if isempty(p)
amt_disp('Execution stopped because cached data not found. Please run calculations for fig2 first.')
return
end
p = mean(cat(3,p{:}),2);
predCue = cat(1,predCue,p);
actual = cat(1,actual,mean(a,2));
end
predCue = squeeze(num2cell(predCue,1:2));
Pext = cell(length(cueSelLbl),1);
Nstrat = length(strategies)-1; % no Oracle
Wsel = nan(length(cueSelLbl),length(cueSelLbl{1}),Nstrat);
RMSE = nan(length(cueSelLbl),Nstrat);
RMSE_CI = nan(length(cueSelLbl),Nstrat,2);
BIC = RMSE;
for ics = 1:length(cueSelLbl)
cueSelId = ismember(cueLbl(:,1),cueSelLbl{ics});
[Pext{ics},S{ics},Wtmp,MSEtmp,BICtmp] = mapAndDecide(...
predCue(cueSelId),actual,Erange,Eoffset);
Wsel(ics , ismember(cueSelLbl{1},cueSelLbl{ics}),:) = Wtmp(:,2:end);
RMSE(ics,:) = sqrt(MSEtmp.m(end-Nstrat+1:end));
RMSE_CI(ics,:,:) = sqrt(MSEtmp.ci(end-Nstrat+1:end,:));
BIC(ics,:) = BICtmp(end-Nstrat+1:end);
end
cueSelTab{1} = table(RMSE(:,1),RMSE(:,2),RMSE(:,3),RMSE(:,4),...
BIC(:,1),BIC(:,2),BIC(:,3),BIC(:,4),...
'RowNames',cueSelLblTxt,...
'VariableNames',...
{'RMSE_WSM','RMSE_LTA','RMSE_MTA','RMSE_WTA',...
'BIC_WSM','BIC_LTA','BIC_MTA','BIC_WTA'});
amt_disp('Prediciton errors for tested decisions:');
amt_disp(cueSelTab{1});
for ss = 1:Nstrat
amt_disp([strategies{1+ss} ' weights/percentages'])
cueSelTab{1+ss} = array2table([squeeze(Wsel(:,:,ss)),RMSE(:,ss),BIC(:,ss)],...
'VariableNames',[cueSelLbl{1},{'RMSE','BIC'}],...
'RowNames',cueSelLblTxt);
amt_disp(cueSelTab{1+ss});
end
figure;
colors = [0.8500 0.3250 0.0980;... % red
0.9290 0.6940 0.1250;... % yellow
0.4940 0.1840 0.5560;... % purple
0.4660 0.6740 0.1880]; % green
x = length(cueSelLbl{1}):-1:1;
b = bar(x,RMSE);
for i = 1:length(b)
b(i).FaceColor = colors(i,:);
end
hold on
ngroups = size(RMSE, 1);
nbars = size(RMSE, 2);
% Calculating the width for each bar group
groupwidth = min(0.8, nbars/(nbars + 1.5));
errlow = RMSE-RMSE_CI(:,:,1);
errhigh = RMSE_CI(:,:,2)-RMSE;
for i = 1:nbars
x = (1:ngroups) - groupwidth/2 + (2*i-1) * groupwidth / (2*nbars);
errorbar(fliplr(x), RMSE(:,i), errlow(:,i), errhigh(:,i), 'k.');
end
hold off
leg = legend(strategies(2:end),'Location','northwest');
leg.Box = 'off';
xlabel('Number of cues')
ylabel('Mean squared prediction error')
%% only plot results for 7 cues
figure
for ii = 1:4
b(ii) = bar(ii,RMSE(1,ii));
b(ii).FaceColor = colors(ii,:);
hold on
errorbar(ii, RMSE(1,ii), errlow(1,ii), errhigh(1,ii), 'k.');
end
hold off
set(gca,'XLim',[.4,4.6],'XTick',1:4,'XTickLabel',strategies(2:end))
set(gca,'XTickLabelRotation',45)
xlabel('Strategy')
ylabel('RMS prediction error')
box off
% RB_print(gcf,[3.5,8],'exp_baumgartner2020_tab1_MSEallCues',10,2,'-r1000',1)
%%
figure
x = 1:length(cueSelLbl{1});
Wsel(:,:,1) = 100*Wsel(:,:,1); % also weights in percent
b = barh(fliplr(x),squeeze(Wsel(1,:,:)));
for i = 1:length(b)
b(i).FaceColor = colors(i,:);
end
set(gca,'YTick',x,'YTickLabel',fliplr(cueSelLbl{1}))
% xlabel('Cue')
xlabel('Weight or selection rate in %')
box off
% RB_print(gcf,[5.5,8],'exp_baumgartner2020_tab1_weights',10,2,'-r1000',1)
Ncues = length(cueSelLbl{1});
combs = nchoosek(1:Ncues,2);
Ncombs = size(combs,1);
Pext = cell(Ncombs,1);
Wsel = nan(Ncombs,Ncues);
S = nan(Ncombs,Ncues);
Nstrat = length(strategies)-1; % no Oracle
RMSE = nan(Ncombs,Nstrat);
RMSE_CI = nan(Ncombs,Nstrat,2);
BIC = RMSE;
for ics = 1:Ncombs
cueSelId = false(length(predCue),1);
cueSelId(combs(ics,:)) = true;
[Pext{ics},Stmp,Wtmp,MSEtmp,BICtmp] = mapAndDecide(...
predCue(cueSelId),actual,Erange,Eoffset);
Wsel(ics , cueSelId(1:Ncues)) = Wtmp(:,2);
S(ics , cueSelId(1:Ncues)) = Stmp;
RMSE(ics,:) = sqrt(MSEtmp.m(end-Nstrat+1:end));
RMSE_CI(ics,:,:) = sqrt(MSEtmp.ci(end-Nstrat+1:end,:));
BIC(ics,:) = BICtmp(end-Nstrat+1:end);
end
Stab = array2table(S,'VariableNames',cueSelLbl{1});
data = array2table(cat(2,Wsel,RMSE(:,1),squeeze(RMSE_CI(:,1,:))),...
'VariableNames',cat(2,cueSelLbl{1},{'WSM_RMSE','CI_low','CI_high'}));
[data,isort]=sortrows(data,8);
Stab = Stab(isort,:);
amt_disp('Contributions and Prediction errors:');
amt_disp(data)
amt_disp('Sensitivities:')
amt_disp(Stab)
%%
figure
ha = tight_subplot(2,1,0,[.12 .03],[.15 .22]);
axes(ha(1))
x = 1:length(isort);
xlim = [x(1)-.5,x(end)+.5];
y = RMSE(isort,1);
try
h = errorbar(x,y,y-RMSE_CI(isort,1,1),RMSE_CI(isort,1,2)-y,'k.','CapSize',0);
catch
h = errorbar(x,y,y-RMSE_CI(isort,1,1),RMSE_CI(isort,1,2)-y,'k.');
end
hold on
plot(xlim,ones(2,1)*RMSE_CI(isort(1),1,2),'k--')
ylabel('Error')
axis([xlim,.01,.5])
box off
set(gca,'XTickLabel',{},'XTick',x)
axes(ha(2))
imagesc(Wsel(isort,:)')
colormap(flipud(hot(100)));
c = colorbar('eastoutside');
c.Position(1) = c.Position(1)+.1;
c.Label.String = 'Weight';
c.Box = 'off';
XTickLabel = num2cell(x);
XTickLabel(2:2:end) = repmat({[]},floor(length(x)/2),1);
set(gca,'YTick',1:length(cueSelLbl{1}),'YTickLabel',cueSelLbl{1},'XTick',x,'XTickLabel',XTickLabel)
xlabel('Error rank')
box off
% RB_print(gcf,[8,8],'exp_baumgartner2020_pairs',10,10,'-r1000',1)
elseif flags.do_tab2 || flags.do_fig2
exp = {'hartmann1996_exp1','hartmann1996_exp2','hassager2016','baumgartner2017','boyd2012'};
Nexp = length(exp);
for ii = 1:Nexp
if flags.do_positive
fn = [exp{ii},'_tab2'];
else
if ii <=2
fn = [exp{ii}(1:12),'_',flags.gradients,'Grad',exp{ii}(13:end),'_tab2'];
else
fn = [exp{ii},'_',flags.gradients,'Grad','_tab2'];
end
end
tab = amt_cache('get',fn,flags.cachemode);
% amt_disp(['Collecting data for ' exp{ii}],'progress');
if isempty(tab)
if ii == 1
exp{ii} = 'hartmann1996';
end
if ii == 2
tab = amt_cache('get',[exp{ii},'_tab2'],'localonly'); % has been (re)computed together with exp. 1
else
data = exp_baumgartner2020(exp{ii},flags.cachemode);
if ii < 3
tab = data{1}{2};
else
tab = data{1};
end
end
end
tabT = array2table(transpose(table2array(tab(:,1:3))));
for rr = 1:3
tabT.Properties.RowNames{rr} = ['Exp',num2str(ii),'_',tab.Properties.VariableNames{rr}];
end
tab.Properties.RowNames = strrep(tab.Properties.RowNames,'Oracle','Oracle');
tabT.Properties.VariableNames = tab.Properties.RowNames;
if ii == 1
tab2 = tabT;
else
tab2 = [tab2;tabT];
end
end
Error = tab2{2:3:end,:};
Sensitivity = tab2{1:3:end,:};
Weight = tab2{3:3:end,:};
MeanError = mean(Error);
WavgS_cue = sum(Sensitivity.*Error.^-2./repmat(sum(Error.^-2),5,1));
MeanWeight = mean(Weight);
sumTab = array2table([WavgS_cue;MeanError;MeanWeight]);
sumTab.Properties.VariableNames = tab2.Properties.VariableNames;
sumTab.Properties.RowNames = {'W. Avg. S_cue','Mean Error','Mean Weight'};
tab2 = [tab2;sumTab];
% disp('here we want to display Tab2');
if ~flags.do_fig2, amt_disp(tab2,flags.disp); end
% Output
data = tab2;
if flags.do_fig2
exp_baumgartner2020('all')
figure
x = 1:5;
imagesc(Error(:,1:7)')
colormap(flipud(copper(100)));
c = colorbar('eastoutside');
c.Label.String = 'Error';
c.Box = 'off';
c.Limits = round(c.Limits*10)/10;
c.Ticks = c.Limits(1):.1:c.Limits(2);
XTickLabel = {'I','II','III','IV','V'};
set(gca,'YTick',1:length(cueSelLbl{1}),'YTickLabel',cueSelLbl{1},'XTick',x,'XTickLabel',XTickLabel)
xlabel('Experiment')
box off
% RB_print(gcf,[6,5],'exp_baumgartner2020_singleCueErr',10,10,'-r1000',1)
figure
imagesc(log10(1./Sensitivity(:,1:7)'))
colormap(flipud(summer(100)));
c = colorbar('eastoutside');
c.Label.String = 'Log Sensitivity';
c.Box = 'off';
% set(gca,'ColorScale','log')
XTickLabel = {'I','II','III','IV','V'};
set(gca,'YTick',1:length(cueSelLbl{1}),'YTickLabel',cueSelLbl{1},'XTick',x,'XTickLabel',XTickLabel)
xlabel('Experiment')
box off
% RB_print(gcf,[6,5],'exp_baumgartner2020_singleCueS',10,10,'-r1000',1)
end
elseif flags.do_tab3 || flags.do_figStrat
experiments = {'Exp.I','Exp.II','Exp.III','Exp.IV','Exp.V'};
exp = {'hartmann1996_exp1','hartmann1996_exp2','hassager2016','baumgartner2017','boyd2012'};
Nexp = length(exp);
MSE = [];
BIC = [];
for ii = 1:Nexp
if flags.do_positive
fn = [exp{ii},'_tab3'];
else
if ii <=2
fn = [exp{ii}(1:12),'_',flags.gradients,'Grad',exp{ii}(13:end),'_tab3'];
else
fn = [exp{ii},'_',flags.gradients,'Grad','_tab3'];
end
end
tab = amt_cache('get',fn,flags.cachemode);
if isempty(tab)
if ii == 1
exp{ii} = 'hartmann1996';
end
if ii == 2
tab = amt_cache('get',[exp{ii},'_tab3']); % has been (re)computed together with exp. 1
else
data = exp_baumgartner2020(exp{ii},flags.cachemode);
if ii < 3
tab = data{2}{2};
else
tab = data{2};
end
end
end
if ii == 1
meanTab = tab;
else
meanTab{:,:} = meanTab{:,:} + tab{:,:};
end
MSE(:,:,ii) = tab{:,7+(1:length(strategies))};
BIC(:,:,ii) = tab{:,8+length(strategies):end};
end
meanTab{:,:} = 1/Nexp * meanTab{:,:};
if flags.do_tab3
% disp('Here we want to display Tab 3');
amt_disp(meanTab,flags.disp);
% Output
data = meanTab;
else % flags.do_figStrat
dBIC = BIC-repmat(BIC(:,1,:),1,length(strategies),1);
y = {MSE,dBIC};
ylbl = {'Mean squared prediction error','BIC'};
for yy = 1:length(y)
figure
Ncues = size(y{yy},1):-1:1;
b = bar(Ncues,mean(y{yy},3));
% set(gca,'XDir','reverse')
hold on
symbols = {'o','s','<','p','h'};
hleg = nan(Nexp,1);
for ii = 1:Nexp
for jj = 1:length(strategies)
h = plot(Ncues+ .9*(jj/(1+length(strategies))-0.5),y{yy}(:,jj,ii),['k',symbols{ii}]);
set(h,'MarkerFaceColor',b(jj).FaceColor)
end
hleg(ii) = h(1);
end
xlabel('Number of cues')
ylabel(ylbl{yy})
l = legend([b';hleg],[strategies,experiments]);
% l = legend([flipud(b');hleg],[fliplr(strategies),experiments]);
set(l,'Box','off','Location','eastoutside')
box off
end
end
else
%% Output
data = {cueTab,cueSelTab,Pext};
end
end
%%%%%%%%%%%%%%%%%%%% INTERNAL FUNCTIONS %%%%%%%%%%%%%%%%%%%%
function ha = tight_subplot(Nh, Nw, gap, marg_h, marg_w)
% tight_subplot creates "subplot" axes with adjustable gaps and margins
%
% ha = tight_subplot(Nh, Nw, gap, marg_h, marg_w)
%
% in: Nh number of axes in hight (vertical direction)
% Nw number of axes in width (horizontaldirection)
% gap gaps between the axes in normalized units (0...1)
% or [gap_h gap_w] for different gaps in height and width
% marg_h margins in height in normalized units (0...1)
% or [lower upper] for different lower and upper margins
% marg_w margins in width in normalized units (0...1)
% or [left right] for different left and right margins
%
% out: ha array of handles of the axes objects
% starting from upper left corner, going row-wise as in
% going row-wise as in
%
% Example: ha = tight_subplot(3,2,[.01 .03],[.1 .1],[.1 .1])
% for ii = 1:6; axes(ha(ii)); plot(randn(10,ii)); end
% set(ha(1:4),'XTickLabel',''); set(ha,'YTickLabel','')
% Pekka Kumpulainen 20.6.2010 @tut.fi
% Tampere University of Technology / Automation Science and Engineering
if nargin<3; gap = .02; end
if nargin<4 || isempty(marg_h); marg_h = .05; end
if nargin<5; marg_w = .05; end
if numel(gap)==1;
gap = [gap gap];
end
if numel(marg_w)==1;
marg_w = [marg_w marg_w];
end
if numel(marg_h)==1;
marg_h = [marg_h marg_h];
end
axh = (1-sum(marg_h)-(Nh-1)*gap(1))/Nh;
axw = (1-sum(marg_w)-(Nw-1)*gap(2))/Nw;
py = 1-marg_h(2)-axh;
ha = zeros(Nh*Nw,1);
ii = 0;
for ih = 1:Nh
px = marg_w(1);
for ix = 1:Nw
ii = ii+1;
ha(ii) = axes('Units','normalized', ...
'Position',[px py axw axh], ...
'XTickLabel','', ...
'YTickLabel','');
px = px+axw+gap(2);
end
py = py-axh-gap(1);
end
end
function [Pext,PextNumCue,cueTab,cueSelTab] = cueAnalysis(cueLbl,cueSelLbl,cueSelLblTxt,predCue,actual,Erange,Eoffset,fncache,kv)
% remove to be ignored cues
idkeep = not(ismember(cueLbl(:,1),kv.ignore));
cueLbl = cueLbl(idkeep,:);
predCue = predCue(idkeep);
[Pext,S,W,MSE] = mapAndDecide(predCue,actual,Erange,Eoffset);
PextLbl = [cueLbl(:,1);{'Oracle'}];
cueTab = table([S;nan],MSE.m(1:length(S)+1),[W(:,1);nan],...
[cueLbl(:,2);...
{'Weighted combination'}],...
'RowNames',PextLbl,...
'VariableNames',{'S_cue','Error','Weight','Description'});
flags=amt_flags;
if strcmp(flags.disp,'verbose'),
amt_disp(['Showing modelling details for ' fncache]);
amt_disp(cueTab);
end
amt_cache('set',[fncache,'_tab2'],cueTab);
try
tab2 = exp_baumgartner2020('tab2','cached','silent');
catch
amt_disp('Table 2 cannot be created. Re-run individual experiments.')
end
if exist('tab2','var') && not(isempty(tab2))
Sfix = tab2{16,:};
MSE = nan(length(cueSelLbl),5);
BIC = nan(length(cueSelLbl),5);
Wsel = nan(length(cueSelLbl),length(cueSelLbl{1}));
try
tab3 = exp_baumgartner2020('tab3','cached','silent');
catch
tab3 = array2table(nan(length(cueSelLbl),length(cueSelLbl{1})));
amt_disp('Re-run to calculate WSM')
end
PextNumCue = cell(length(cueSelLbl),1);
for ics = 1:length(cueSelLbl)
Wfix = tab3{ics,ismember(cueSelLbl{1},cueSelLbl{ics})};
cueSelId = find(ismember(cueLbl(:,1),cueSelLbl{ics}));
[PextNumCue{ics},~,Wtmp,MSEtmp,BICtmp] = mapAndDecide(...
predCue(cueSelId),actual,Erange,Eoffset,Sfix(cueSelId),Wfix);
Wsel(ics , ismember(cueSelLbl{1},cueSelLbl{ics})) = Wtmp(:,1);
MSE(ics,:) = MSEtmp.m(end-4:end);
BIC(ics,:) = BICtmp(end-4:end);
end
cueSelTab = [array2table(Wsel,'VariableNames',cueSelLbl{1}),...
table(MSE(:,1),MSE(:,2),MSE(:,3),MSE(:,4),MSE(:,5),...
BIC(:,1),BIC(:,2),BIC(:,3),BIC(:,4),BIC(:,5),...
'RowNames',cueSelLblTxt,...
'VariableNames',...
{'Error_Oracle','Error_WSM','Error_LTA','Error_MTA','Error_WTA',...
'BIC_Oracle','BIC_WSM','BIC_LTA','BIC_MTA','BIC_WTA'})];
if strcmp(flags.disp,'verbose'),
amt_disp(['Showing cue contributions for ' fncache]);
amt_disp(cueSelTab)
end
amt_cache('set',[fncache,'_tab3'],cueSelTab);
else
cueSelTab = nan;
end
% only output to be plotted data
Pext = Pext(1:length(S)); % only single-cue predictions
if exist('PextNumCue','var')
PextNumCue = PextNumCue{end-kv.numCue+1}; % only specific # cues
PextNumCue = PextNumCue(kv.numCue+1:end); % only combination strategies
else
PextNumCue = Pext(kv.numCue+1:end);
amt_disp('Warning: Used *Pext* instead of *PextNumCue*.')
end
end
function [Pext,S,W,MSE,BIC] = mapAndDecide(predCue,actual,Erange,Eoffset,S,Wfix)
% [Pext,S,W,MSE,BIC] = mapAndDecide(predCue,actual,Erange,Eoffset,S,Wfix)
%
% Input parameters:
% predCue ... cue-specific deviation metrics;
% matrix dimensions: conditions x listeners
% actual ... listeners' externalization scores; matrix dimensions must
% match *predCue*
% Erange ... range of externalization rating scale, typically 1
% Eoffset ... offset of externalization rating scale, typically 0
% S ... sensitivity parameters, one for each cue [optional, otherwise optimized]
% Wfix ... fixed weights for cues [optional, otherwise optimized]
%
% Output parameters:
% Pext ... predicted externalization scores (first) for individual cues and
% (then) for cue combinations (see decision strategies)
% S ... sensitivity parameters, one for each cue
% W ... weights to combine selected cues and percentages of cue selection
% for optimally predicting *actual*
% MSE ... mean squared error
% BIC ... Bayesian information criterion
%
% Decision strategies:
% 1) optimal weighting ("oracle")
% 2) fixed weighting ("weighted sum model")
% 3) minimum externalization selection ("loser takes all")
% 4) median externalization selection ("median takes all")
% 5) maximum externalization selection ("winner takes all")
% Definitions of error functions
f_cue2E = @(cue,s) baumgartner2020_mapping(cue,s,Erange,Eoffset);
if size(actual,2) > 1 % Individual data
f_predErr = @(p) nanmean((p(:)-actual(:)).^2);%nanrms(p(:)-actual(:)) / (Erange-Eoffset);
f_predErrA = @(p,a) nanmean((p(:)-a(:)).^2); % used for bootstrapping
else % Average data
f_predErr = @(p) nanmean((mean(p,2) - actual).^2);%nanrms(p(:)-actual(:)) / (Erange-Eoffset);
f_predErrA = @(p,a) nanmean((mean(p,2) - a).^2);
end
Ncues = length(predCue);
% Optimize sensitivities
if not(exist('S','var'))
S = ones(Ncues,1); % sensitivity to cue
for cc = 1:Ncues
S(cc) = fminsearch(@(s) f_predErr(f_cue2E(predCue{cc},s)),S(cc));
end
end
% Compute externalization scores
predExtSingle = nan([size(predCue{1}),Ncues]);
for cc = 1:Ncues
if all(isnan(predCue{cc}(:)))
predExtSingle(:,:,cc) = zeros(size(predCue{cc}));
else
predExtSingle(:,:,cc) = f_cue2E(predCue{cc},S(cc));
end
% MSE.m(cc) = f_predErr(predExtSingle(:,:,cc)); % mean(abs( predE(:,cc) - actual )) / (Erange-Eoffset);
end
% Optimize weights
W = 1/Ncues*ones(size(S)); % weighting of cue
f_weight = @(p,w) reshape( reshape(p,[],length(w))*w(:) ,size(p,1),[]);
f_opt = @(p,w) f_predErr( f_weight(p,abs(w)./sum(abs(w))) );
o = optimset('Display','off');
W = fminsearch(@(w) f_opt(predExtSingle,w) , W,o);
W = abs( W );
W = W/sum(W);
W(W<.005) = 0; % threshold the weights
W = W/sum(W);
if not(exist('Wfix','var'))
Wfix = W;
end
if sum(isnan(Wfix))>0, Wfix=W; end
% Decision strategies
function [E,cueStat] = f_select(cue,s,type)
Eall = reshape(...
f_cue2E(cue(:),repmat(s(:),length(cue(:))/length(s(:)),1)),...
size(cue,1),size(cue,2),size(cue,3));
switch type
case 'LTA'
[E,iCue] = nanmin(Eall,[],3);
case 'MTA'
E = median(Eall,3,'omitnan');
[~,iCue] = nanmin((Eall-repmat(E,1,1,size(Eall,3))).^2,[],3);
case 'WTA'
[E,iCue] = nanmax(Eall,[],3);
otherwise
error('Undefined type of decision strategy')
end
cueStat = 100*histcounts(iCue,1:Ncues+1)/length(iCue);
end
predExtComb(:,:,1) = f_weight(predExtSingle,W); % Oracle
predExtComb(:,:,2) = f_weight(predExtSingle,Wfix); % WSM
predCueMtx = cat(3,predCue{:});
cueStat = nan(Ncues,3);
o = optimset('MaxFunEvals',300*length(S),'Display','off');
S_LTA=fminsearch(@(s) f_predErr(f_select(predCueMtx,s,'LTA')),S,o);
[predExtComb(:,:,3),cueStat(:,1)] = f_select(predCueMtx,S_LTA,'LTA');
S_MTA=fminsearch(@(s) f_predErr(f_select(predCueMtx,s,'MTA')),S,o);
[predExtComb(:,:,4),cueStat(:,2)] = f_select(predCueMtx,S_MTA,'MTA');
S_WTA=fminsearch(@(s) f_predErr(f_select(predCueMtx,s,'WTA')),S,o);
[predExtComb(:,:,5),cueStat(:,3)] = f_select(predCueMtx,S_WTA,'WTA');
predExt = cat(3,predExtSingle,predExtComb);
Pext = squeeze(num2cell(predExt,1:2));
% Mean squared errors
Nstrat = 5;
MSE.m = nan(Ncues+Nstrat,1);
MSE.ci = nan(Ncues+Nstrat,2);
for ii = 1:Ncues+Nstrat
if ii <= Ncues
p = predExtSingle(:,:,ii);
else
p = predExtComb(:,:,ii-Ncues);
end
MSE.m(ii) = f_predErr(p);
MSE.ci(ii,:) = bootci(1000,f_predErrA,p,actual);
end
% Bayesian Information Criteria
n = size(actual,1); % # conditions (no individual parameters for # listeners)
mc = ones(size(MSE.m)); % model complexity = # parameters; 1 sensitivity parameter per cue
mc(Ncues+1:end) = Ncues; % combinations -> all sensitivity parameters
mc(Ncues+(1:2)) = 2*Ncues; % weighted combinations -> all sensitivity parameters + weights
BIC = n*log(MSE.m) + mc*log(n);
W = [W(:),Wfix(:),cueStat];
end
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