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RandomWalkRounan.m
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%% Monte Carlo Simulation of Ambiguous Decision Making
% Produces estimate of response distribution during stochastic choices in ambiguous decision making task
% Indirect Method
% Initialize variables
tic
h = waitbar(0,'Simulating RandomWalk...');
probs = [.5]';
ambs = [.24 .5 .74 1.0]';
%vals = [5,6,7,8,10,12,14,16,19,23,27,31,37,44,52,61,73,86,101,120];
vals = [4,5,6,6,7,7,8,9,10,11,13,14,15,19,24,29,37,51,95,120];
valperms = 100; %up
for j=1:valperms;
for i=1:length(vals);
v1(i,j)=vals(i)*(1+.2*randn(1));
end;
v1 = round(v1);
end
n=1;
sortvals_rank = zeros(21,valperms);
while mean(sortvals_rank(1,valperms-5:valperms))<.8 && n<61 %Up
if n>1
v1 = round(repmat(monvals(:,1+size(monvals,2)/2:end),1,2).*(1+(1/(2*n))*randn(size(v1,1),size(v1,2))));
end
simnumbs = 1000; %up
for vals_index = 1:size(v1,2);
v = v1(:,vals_index)';
pr = probs;
a = ambs;
V = repmat(v,1,5)';
P_temp = ones(20,1)*pr;
P = [P_temp(:);.5*ones(80,1)];
A_temp = ones(20,1)*a';
A = [zeros(20,1);A_temp(:)];
trialnumber = length(V);
for sims = 1:simnumbs
Cresults = zeros(5,20);
while sum(sum(Cresults==1)) > 90 || sum(sum(Cresults==0)) > 90
Choices = zeros(trialnumber,1);
alpha = .1 + 1.9.*rand(1); %Gains Normal distribution of measured Risk Preferences
%alpha = .97 + .75*randn(1); %Loss
alpha(alpha<0) = 0;
beta = -1.5 + 3.*rand(1); %Gains Normal distribution of measured Ambiguity Preferences
%beta = -.48 + 1.01*randn(1); %Loss
noise = 0+.2*randn(1);
for i = 1:trialnumber;
if (5^alpha)*(1+noise*randn(1)) > (P(i)*(1-beta*(A(i)/2)))*(V(i)^alpha)*(1+noise*randn(1)); % Subjective Value under ambiguity model Gain
%if (-((5)^alpha))*(1+noise*randn(1)) > (P(i)*(1-beta*(A(i)/2)))*(-(V(i)^alpha))*(1+noise*randn(1)); % Subjective Value under ambiguity model Loss
Choices(i) = 0;
else
Choices(i) = 1;
end
end
%Risk = Choices(1:100);
%Ambiguity = Choices(101:160);
%Vresults = [mean(Risk(and(V(1:100)==5,P(1:100)==.13))),mean(Risk(V(1:100)==8)),mean(Risk(V(1:100)==20)),mean(Risk(V(1:100)==50)),mean(Risk(V(1:100)==125));...
%mean(Ambiguity(V(101:160)==5)),mean(Ambiguity(V(101:160)==8)),mean(Ambiguity(V(101:160)==20)),mean(Ambiguity(V(101:160)==50)),mean(Ambiguity(V(101:160)==125))];
%disp(Vresults)
Cresults = zeros(5,20);
for valindex = 1:20
for riskindex = 1
Cresults(riskindex,valindex) = mean(Choices(V==v(valindex) & P==pr(riskindex) & A==0));
end
for ambindex = 2:5
Cresults(ambindex,valindex) = mean(Choices(and(V==v(valindex),A==a(ambindex-1))));
end
end
end
MultiSubChoices(:,:,sims) = [V,P,A,Choices];
%MultiSubResults(:,:,sims) = Cresults;
MultiParams(sims,:) = [alpha,beta];
%MultiNoise(sims) = noise;
%MultiFOSD(sims) = sum(Cresults(:,1));
%waitbar(sims/simnumbs,h)
end
Subindex = 1:simnumbs;
%close(h)
%toc
%% Fit Model
%tic
base = 0;
model = 'ambigNrisk';
fixed_valueP = 5;
fixed_valueN = -5;
fixed_prob = 1;
% Initialize parameters (this could be smarter)
if strcmp(model,'ambiguity')
b0 = [-1 1]';
elseif strcmp(model,'power')
b0 = [-1 0.8];
elseif strcmp(model, 'ambigNrisk')
b0 = [-1 0.5 0.5]'; %slope, beta, alpha
elseif strcmp(model, 'ambigNriskFixSlope')
b0 = [0.5 0.5]'; %beta, alpha
end
parfor s = 1:length(Subindex)
%ACTUAL START
%MultiSubChoices(:,:,sims) = [V,P,A,Choices];
% get rid of no choice trials
choice = MultiSubChoices(:,4,s);
vA = MultiSubChoices(:,1,s); %Gains
%vA = -1*MultiSubChoices(:,1,s); %Loss
AL = MultiSubChoices(:,3,s);
pA = MultiSubChoices(:,2,s);
% separate fit for pos
choiceP = choice(find(vA>0));
vP = vA(find(vA>0));
pP = pA(find(vA>0));
AP = AL(find(vA>0));
vFP = fixed_valueP * ones(length(choiceP),1);
pFP = fixed_prob * ones(length(choiceP),1);
[info,p] = fit_ambigNrisk_model_Constrained(choiceP,vFP,vP,pFP,pP,AP,model,b0,base);
if strcmp(model,'ambigNrisk')
slopeP = info.b(1);
aP = info.b(3);
bP = info.b(2);
elseif strcmp(model,'ambigNriskFixSlope')
slopeP = -1;
aP = info.b(2);
bP = info.b(1);
end
r2P = info.r2;
% % separate fit for neg
% choiceN = choice(find(vA<0));
% vN = vA(find(vA<0));
% pN = pA(find(vA<0));
% AN = AL(find(vA<0));
% vFN = fixed_valueN * ones(length(choiceN),1);
% pFN = fixed_prob * ones(length(choiceN),1);
%
% [info,p] = fit_ambigNrisk_model_Constrained(~choiceN,-vFN,-vN,pFN,pN,AN,model,b0,base);
%
% if strcmp(model,'ambigNrisk')
% slopeN = info.b(1);
% aN = info.b(3);
% bN = info.b(2);
% elseif strcmp(model,'ambigNriskFixSlope')
% slopeN = -1;
% aN = info.b(2);
% bN = info.b(1);
% end
% r2N = info.r2;
ParamsResults(s,:) = [aP,bP,slopeP,r2P];
%ParamsResults(s,:) = [aN,bN,slopeN,r2N];
%waitbar(s/length(Subindex),h,'Fitting...')
end
r = corr(MultiParams,ParamsResults);
%
%
ralpha(vals_index) = r(1,1);
rbeta(vals_index) = r(2,2);
%
% rcross(probs_index,ambs_index) = abs(r(1,2))+abs(r(2,1));
%
% mean_r2(probs_index,ambs_index) = mean(ParamsResults(:,4));
% min_r2(probs_index,ambs_index) = min(ParamsResults(:,4));
% lower05_r2(probs_index,ambs_index) = quantile(ParamsResults(:,4),.05);
%
% reps = (ambs_index+(probs_index-1)*length(ambs));
%
% Choice4d(:,:,:,reps) = MultiSubChoices;
% SubResults4d(:,:,:,reps) = MultiSubResults;
% gParams4d(:,:,reps) = MultiParams;
% Noise4d(:,reps) = MultiNoise;
% fosd4d(:,reps) = MultiFOSD;
% fitParams4d(:,:,reps) = ParamsResults;
%
% disp(ambs_index+(probs_index-1)*length(ambs))
waitbar(vals_index/(size(v1,2)),h,['Simulating RandomWalk... Loop: ' num2str(n)]);
end
rsqprd = (ralpha.^2).*(rbeta.^2);
topval = max(v1);
expense_constant = .001;
expense = (120-topval).*expense_constant;
costfunc = reshape(rsqprd,[size(rsqprd,2),1])+expense';
tempX = [costfunc reshape(rsqprd,[size(rsqprd,2),1]) reshape(ralpha,[size(rsqprd,2),1]) reshape(rbeta,[size(rsqprd,2),1]) v1'];
sortvals_rank = sortrows(tempX,1)';
sortvals = sortvals_rank(5:end,:);
splitvals = [mean(tempX(1:(size(tempX,1)/2),2:size(tempX,2)))' mean(tempX((1+size(tempX,1)/2):size(tempX,1),2:size(tempX,2)))'];
monvals = sort(sortvals);
sortvalsrank_multi(:,:,n) = sortvals_rank;
n=n+1;
disp(n)
end
converge = reshape(mean(sortvalsrank_multi(1:2,(1+size(tempX,1)/2):size(tempX,1),:),2),[2,size(sortvalsrank_multi,3)])';
alphabeta = reshape(mean(sortvalsrank_multi(3:4,(1+size(tempX,1)/2):size(tempX,1),:),2),[2,size(sortvalsrank_multi,3)])';
drift = reshape(mean(sort(sortvalsrank_multi(5:end,:,:)),2),[20,size(sortvalsrank_multi,3)]);
figure;
plot(1:length(converge),converge(:,1))
hold on
plot(1:length(converge),converge(:,2),'r')
legend('costfunction','sqrprd');
figure;
plot(1:size(sortvalsrank_multi,3),drift);
figure;
plot(1:length(alphabeta),alphabeta(:,1));
title('Alpha');
figure
plot(1:length(alphabeta),alphabeta(:,2));
title('Beta');
close(h)
clearvars -except MultiSubChoices Cresults rsqprd ralpha rbeta r v1 vals ambs probs splitvals sortvals sortvals_rank monvals n sortvalsrank_multi converge drift alphabeta
toc