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plot_manuscript_figures.m
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%% This code assumes same LBA2 for all Experiments -- vary b, not mean drift rates!
clear all; close all;
% base_folder = 'C:\Users\liu_s\policycompression_timememorycosts';
% cd(base_folder)
% addpath(genpath(base_folder))
% Figure and font default setting
set(0,'units','inches');
Inch_SS = get(0,'screensize');
set(0,'units','pixels');
figsize = get(0, 'ScreenSize');
Res = figsize(3)./Inch_SS(3);
set(groot, 'DefaultAxesTickDir', 'out', 'DefaultAxesTickDirMode', 'manual');
fontsize=12;
set(groot,'DefaultAxesFontName','Arial','DefaultAxesFontSize',fontsize);
set(groot,'DefaultLegendFontSize',fontsize-2,'DefaultLegendFontSizeMode','manual')
markersize = 10; linewidth=1.5;
% paths
figformat = "svg";
figpath = "figures\"; %"newplots\"
datapath = "data\";
lba_folder = "lba_models\";
png_dpi = 500;
% Color palettes
cmap = brewermap(9, 'Set1');
cmap(1:3,:) = cmap([1,3,2],:);
cmap(6,:) = [];
cmap_subj = brewermap(200, 'Set1');
cmap_exp3 = brewermap(12, 'Set2');
cmap_exp3 = cmap_exp3([2,1,3,4,5,6,9,7,8,10,11,12],:);
% Load data (test block data only)
load(datapath+"iti_bandit_data_exp1.mat");
data_exps.exp1 = datas.test;
survey_exps.exp1 = datas.survey;
load(datapath+"iti_bandit_data_exp2.mat");
data_exps.exp2 = datas.test;
survey_exps.exp2 = datas.survey;
load(datapath+"iti_bandit_data_exp3.mat");
[datas, exp3_correct_actions] = exp3_get_setsize_corresponding_actions(datas,[2,4,6]);
data_exps.exp3 = datas.test;
survey_exps.exp3 = datas.survey;
load(datapath+"iti_bandit_data_exp3_old2.mat");
data_exps.exp3_old2 = datas.test;
survey_exps.exp3_old2 = datas.survey;
clear data datas;
%% Parse data
experiment = "exp1";
[exp1.mturkIDs, exp1.optimal_sol, exp1.BehavioralStats, exp1.LME, exp1.TTests, exp1.EffectSizeCI, exp1.EffectSizes, exp1.WilcoxonTests] = parse_data(data_exps, survey_exps, experiment);
experiment = "exp2";
[exp2.mturkIDs, exp2.optimal_sol, exp2.BehavioralStats, exp2.LME, exp2.TTests, exp2.EffectSizeCI, exp2.EffectSizes, exp2.WilcoxonTests] = parse_data(data_exps, survey_exps, experiment);
experiment = "exp3";
[exp3.mturkIDs, exp3.optimal_sol, exp3.BehavioralStats, exp3.LME, exp3.TTests, exp3.EffectSizeCI, exp3.EffectSizes, exp3.WilcoxonTests] = parse_data(data_exps, survey_exps, experiment, exp3_correct_actions);
% Add in fake data generated from fitted LBAs
lba_models_visualized = [1,2,3,4];
[exp1,data_lba_exp1] = append_lba_preds("exp1", exp1, lba_folder, lba_models_visualized);
[exp2,data_lba_exp2] = append_lba_preds("exp2", exp2, lba_folder, lba_models_visualized, exp2.BehavioralStats.correct_actions);
[exp3,data_lba_exp3] = append_lba_preds("exp3", exp3, lba_folder, lba_models_visualized, exp3_correct_actions);
exps.exp1 = exp1; exps.exp2 = exp2; exps.exp3 = exp3;
% Store the predictive samples generated by fitted LBAs.
data_exps_lba.exp1 = data_lba_exp1;
data_exps_lba.exp2 = data_lba_exp2;
data_exps_lba.exp3 = data_lba_exp3;
%% 0) Compare I(S;A) of subjects in high ITI condition, and their optimal policy complexity in the low ITI condition.
figure("Position", [10,10,1280,500])
t=tiledlayout(1,3, 'Padding', 'compact', 'TileSpacing', 'compact');
for exp_idx=1:3
experiment_name = "exp"+exp_idx;
complexity = exps.(experiment_name).BehavioralStats.complexity;
complexity_rrmax = exps.(experiment_name).LME.complexity_rrmax;
leftward_subconds = find(complexity(:,1)<complexity_rrmax(:,1));
nexttile; hold on;
histogram(complexity(leftward_subconds,3) - complexity(leftward_subconds,1), -1:0.1:2, "FaceColor","k", "FaceAlpha",0.2)
[a,b,c,d] = ttest(complexity(leftward_subconds,3), complexity(leftward_subconds,1),"Tail","right");
[e,f,g] = signrank(complexity(leftward_subconds,3), complexity(leftward_subconds,1),"Tail","right");
effect=meanEffectSize(complexity(leftward_subconds,3), complexity(leftward_subconds,1));
title({experiment_name+", N="+length(leftward_subconds), "One-sided paired t-test: p="+round(b,3), "One-sided Wilcoxon signed-rank test: p="+round(e,3)})
end
xlabel(t,{"Human policy complexity in ITI=2s/Ns=6 - policy complexity in ITI=0s/Ns=2 (bits)","For subjects with leftward bias in ITI=0s/Ns=2 only"})
%% Fig. 1 (excluding Figure 1A)
figspecs = [0 0 figsize(3)*0.6 figsize(4)];
Figure1(exps, figspecs, cmap, cmap_exp3);
saveas(gca, figpath+'Fig1_partial.fig')
exportgraphics(gcf,figpath+'Fig1_partial.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig1_partial.pdf',"ContentType","vector");
%% Fig. 2 (only including Figure 2B)
figspecs = [0 0 figsize(4)*0.4 figsize(4)*0.4];
Figure2(exp1, figspecs);
saveas(gca, figpath+'Fig2_partial.fig')
exportgraphics(gcf,figpath+'Fig2_partial.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig2_partial.pdf',"ContentType","vector");
%% Fig. 3
figspecs = [0 100 figsize(3) figsize(3)*0.35];
Figure3(exp1,cmap, figspecs);
saveas(gca, figpath+'Fig3.fig')
exportgraphics(gcf,figpath+'Fig3.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig3.pdf',"ContentType","vector");
%% Fig. 4
figspecs = [0 0 figsize(3) figsize(4)];
Figure4(exp1, cmap, figspecs);
saveas(gca, figpath+'Fig4.fig')
exportgraphics(gcf,figpath+'Fig4.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig4.pdf',"ContentType","vector");
%% Fig. 5
figspecs = [0 0 min(figsize(3:4))*2 min(figsize(3:4))./2.5];
Figure5(exp2, cmap, figspecs)
saveas(gca, figpath+'Fig5_partial.fig')
exportgraphics(gcf,figpath+'Fig5_partial.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig5_partial.pdf',"ContentType","vector");
%% Fig. 6
figspecs = [0 100 figsize(3) figsize(3)*0.35];
Figure6(exp3,cmap_exp3, figspecs);
saveas(gca, figpath+'Fig6.fig')
exportgraphics(gcf,figpath+'Fig6.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig6.pdf',"ContentType","vector");
%% Fig. 7: LBA results for experiments.
lba_models_visualized = [1,2,3,4];
figspecs = [0 0 figsize(3).*0.85 figsize(4)];
%figspecs = figsize;
Figure7([1,2,3], exps, lba_models_visualized, cmap_exp3([1,2,3,4,5,6,11],:), cmap_exp3([1,2,3,4,5,6,11],:), figspecs, data_exps_lba)
saveas(gca, figpath+'Fig7.fig')
exportgraphics(gcf,figpath+'Fig7.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'Fig7.pdf',"ContentType","vector");
%% Figure S1: Subjects did not exploit the counterbalanced cycles
figspecs = [0 0 figsize(3)*0.37 figsize(4)];
experiment_names = ["exp1","exp2","exp3"];
FigureS1(exps, experiment_names, figspecs, cmap, cmap_exp3)
saveas(gca, figpath+'FigS1.fig')
exportgraphics(gcf,figpath+'FigS1.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'FigS1.pdf',"ContentType","vector");
%% Figure S2: even subject with low policy complexity are adjusting it across conditions
figspecs = [0 0 figsize(3) figsize(4)];
experiment_names = ["exp1","exp2","exp3"];
FigureS2(exps, experiment_names, figspecs)
saveas(gca, figpath+'FigS2.fig')
exportgraphics(gcf,figpath+'FigS2.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'FigS2.pdf',"ContentType","vector");
%% Figure S3: Complexity to RT relationship, and all LME fit plots.
figspecs = [0 0 figsize(3) figsize(4)*0.85];
FigureS3(exps, cmap, cmap_exp3, figspecs)
saveas(gca, figpath+'FigS3_partial.fig')
exportgraphics(gcf,figpath+'FigS3_partial.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'FigS3_partial.pdf',"ContentType","vector");
%% Figure S4: Empirical vs. reward-rate-maximizing (optimal) policy complexity
figspecs = [50,50,1000,350];
FigureS4(exps,figspecs,cmap,cmap_exp3);
saveas(gca, figpath+'FigS4.fig')
exportgraphics(gcf,figpath+'FigS4.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'FigS4.pdf',"ContentType","vector");
%% Figure S5: LBA model comparison
lba_models_visualized = [1,2,3,4];
figspecs = [50,50,1200,300];
[BIC_exps] = FigureS5(lba_models_visualized,lba_folder,figspecs);
saveas(gca, figpath+'FigS5.fig')
exportgraphics(gcf,figpath+'FigS5.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'FigS5.pdf',"ContentType","vector");
%% Figure S6: 5 set-size conditions
%figspecs = [0 0 min(figsize(3:4))*1.4 min(figsize(3:4))*0.8];
figspecs = [0 0 figsize(4)*1.25 figsize(4)];
[exp3_old2.mturkIDs, exp3_old2.optimal_sol, exp3_old2.BehavioralStats, exp3_old2.LME, exp3_old2.TTests, exp3_old2.WilcoxonTests] = FigureS6("exp3_old2", data_exps.exp3_old2, survey_exps.exp3_old2, cmap_exp3([4,1,5,2,3],:), figspecs);
saveas(gca, figpath+'FigS6.fig')
exportgraphics(gcf,figpath+'FigS6.png','Resolution',png_dpi);
exportgraphics(gcf,figpath+'FigS6.pdf',"ContentType","vector");
%% Experiment 2 P(a_perserv | s_suboptim) LME
SuboptimalA = exp2.BehavioralStats.SuboptimalA;
[n_subj,~]=size(SuboptimalA);
SuboptimalA_flat = SuboptimalA(:);
cond_flat = repmat([0,0.5,2], length(data_exps.exp2),1);
cond_flat = cond_flat(:);
subject_id = repmat(1:length(data_exps.exp2), 1, 3)';
tbl = table(subject_id,cond_flat,SuboptimalA_flat,'VariableNames',{'Subject','ITI','SuboptimalA'});
lme = fitlme(tbl,'SuboptimalA ~ ITI + (1|Subject) + (ITI-1|Subject)')
[~,~,stats] = randomEffects(lme,'Alpha',0.01);
q = dataset2cell(stats(1:n_subj,4));
w = dataset2cell(stats((n_subj+1):end,4));
random_effects_iti_std = std(cell2mat(w(2:end)))
%% Cohen's d helper function
extractFirstColumn(exp1.CohensD)
function outputStruct = extractFirstColumn(inputStruct)
% Initialize the output struct
outputStruct = struct();
% Get the fieldnames of the input struct
fields = fieldnames(inputStruct);
% Loop through each field
for i = 1:numel(fields)
fieldName = fields{i};
% Extract the first column of the 3x2 cell and convert it to a 1x3 vector
outputStruct.(fieldName) = cell2mat(inputStruct.(fieldName)(:, 1))';
end
end
%% Helper functions
function [mturkIDs, optimal_sol, BehavioralStats, LME, TTests, CohensD_CIs, CohensD, WilcoxonTests] = parse_data(data_exps, survey_exps, experiment,exp3_correct_actions)
if(nargin==3)
exp3_correct_actions = NaN;
end
TTests = struct();
CohensD = struct();
WilcoxonTests = struct();
data = data_exps.(experiment);
survey = survey_exps.(experiment);
feedback_duration = 0.3; % in seconds
switch experiment
case "exp1"
Q = eye(4).*0.5+0.25;
n_subj = length(data);
cond = unique(data(1).cond); % ITI conditions
case "exp2"
Q = [0.75 0.25 0.25 0.25; 0.75 0.25 0.25 0.25; 0.25 0.25 0.75 0.25; 0.25 0.25 0.25 0.75];
n_subj = length(data);
cond = unique(data(1).cond); % ITI conditions
case "exp3"
set_sizes = [2,4,6];
cond = [2000];
n_tasks = length(set_sizes);
task_names = "set_size_"+set_sizes;
datas = data;
n_subj = length(data.(task_names(1)));
end
reward_count = zeros(n_subj,3);
cond_entropy = zeros(n_subj,3); % H(A|S)
repeat_actions = zeros(n_subj,3); % Measure of perserverance
mturkIDs = [];
if(experiment ~= "exp3")
for s = 1:n_subj
mturkIDs = [mturkIDs; convertCharsToStrings(data(s).ID)];
for c = 1:length(cond)
idx = data(s).cond == cond(c);
state = data(s).s(idx);
action = data(s).a(idx);
acc = data(s).acc(idx);
r = data(s).r(idx);
rt = data(s).rt(idx);
tt = data(s).tt(idx); % total time of the block
n_trials(s,c) = length(state);
accuracy(s,c) = nanmean(acc);
reward(s,c) = nanmean(r);
reward_count(s,c) = sum(r);
reward_rate(s,c) = reward_count(s,c)/tt(end);
complexity(s,c) = mutual_information(round(state),round(action),0.1)./log(2);
response_time(s,c) = nanmean(rt./1000); % RT in seconds
cond_entropy(s,c) = condEntropy(round(action), round(state));
repeat_actions(s,c) = nanmean(action(1:end-1) == action(2:end));
first_cond(s) = data(s).first_cond;
end
if(experiment=="exp2") % Record which two states share the same correct action
correct_actions(s,:) = data(s).correct_action;
end
end
else % Experiment 3
for task = 1:n_tasks
task_name = task_names(task);
data = datas.(task_name);
for s = 1:n_subj
if(task==1)
mturkIDs = [mturkIDs; convertCharsToStrings(data(s).ID)];
end
iti_2_idx = data(s).cond == cond(end);
for c = 1:length(cond)
idx = data(s).cond == cond(c);
state = data(s).s(idx);
action = data(s).a(idx);
acc = data(s).acc(idx);
r = data(s).r(idx);
rt = data(s).rt(idx);
tt = data(s).tt(idx); % total time of the block
% Dimensions are: [subject, set size].
n_trials(s,task) = length(state);
accuracy(s,task) = nanmean(acc);
reward(s,task) = nanmean(r);
reward_count(s,task) = sum(r);
reward_rate(s,task) = reward_count(s,task)/tt(end);
complexity(s,task) = mutual_information(round(state),round(action),0.1)./log(2);
response_time(s,task) = nanmean(rt./1000); % RT in seconds
cond_entropy(s,task) = condEntropy(round(action), round(state));
repeat_actions(s,task) = nanmean(action(1:end-1) == action(2:end));
end
end
end
end
BehavioralStats.n_trials = n_trials;
BehavioralStats.accuracy=accuracy;
BehavioralStats.reward=reward;
BehavioralStats.reward_rate=reward_rate;
BehavioralStats.complexity=complexity;
BehavioralStats.response_time=response_time;
BehavioralStats.cond_entropy=cond_entropy;
BehavioralStats.repeat_actions=repeat_actions;
if(experiment=="exp2")
BehavioralStats.correct_actions = correct_actions;
end
% Compute Cohen's D
CohensD_complexity = cell(3,2); % ITI_cond
CohensD_response_time = cell(3,2); % ITI_cond
CohensD_perc_reward = cell(3,2); % ITI_cond
CohensD_reward_rate = cell(3,2); % ITI_cond
CohensD_cond_entropy = cell(3,2);
CohensD_repeat_actions = cell(3,2);
ITI_pairs = [1,2; 2,3; 1,3];
for iti_idx=1:length(ITI_pairs)
CohensD_complexity(iti_idx,:) = table2cell(meanEffectSize(complexity(:,ITI_pairs(iti_idx,1)),complexity(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_response_time(iti_idx,:) = table2cell(meanEffectSize(response_time(:,ITI_pairs(iti_idx,1)),response_time(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_reward_rate(iti_idx,:) = table2cell(meanEffectSize(reward_rate(:,ITI_pairs(iti_idx,1)),reward_rate(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_cond_entropy(iti_idx,:) = table2cell(meanEffectSize(cond_entropy(:,ITI_pairs(iti_idx,1)),cond_entropy(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_repeat_actions(iti_idx,:) = table2cell(meanEffectSize(repeat_actions(:,ITI_pairs(iti_idx,1)),repeat_actions(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
end
CohensD.complexity = CohensD_complexity;
CohensD.response_time = CohensD_response_time;
CohensD.cond_entropy = CohensD_cond_entropy;
CohensD.repeat_actions = CohensD_repeat_actions;
CohensD.reward_rate = CohensD_reward_rate;
[~,TTests.complexity(1),TTestsCI.complexity(:,1),~] = ttest(complexity(:,1), complexity(:,2), "Tail","left");
[~,TTests.complexity(2),TTestsCI.complexity(:,2),~] = ttest(complexity(:,2), complexity(:,3), "Tail","left");
[~,TTests.complexity(3),TTestsCI.complexity(:,3),~] = ttest(complexity(:,1), complexity(:,3), "Tail","left");
[~,TTests.response_time(1),TTestsCI.response_time(:,1),~] = ttest(response_time(:,1), response_time(:,2), "Tail","left");
[~,TTests.response_time(2),TTestsCI.response_time(:,2),~] = ttest(response_time(:,2), response_time(:,3), "Tail","left");
[~,TTests.response_time(3),TTestsCI.response_time(:,3),~] = ttest(response_time(:,1), response_time(:,3), "Tail","left");
[~,TTests.cond_entropy(1),TTestsCI.cond_entropy(:,1),~] = ttest(cond_entropy(:,2), cond_entropy(:,1), "Tail","left");
[~,TTests.cond_entropy(2),TTestsCI.cond_entropy(:,2),~] = ttest(cond_entropy(:,3), cond_entropy(:,2), "Tail","left");
[~,TTests.cond_entropy(3),TTestsCI.cond_entropy(:,3),~] = ttest(cond_entropy(:,3), cond_entropy(:,1), "Tail","left");
[~,TTests.repeat_actions(1),TTestsCI.repeat_actions(:,1),~] = ttest(repeat_actions(:,2), repeat_actions(:,1), "Tail","left");
[~,TTests.repeat_actions(2),TTestsCI.repeat_actions(:,2),~] = ttest(repeat_actions(:,3), repeat_actions(:,2), "Tail","left");
[~,TTests.repeat_actions(3),TTestsCI.repeat_actions(:,3),~] = ttest(repeat_actions(:,3), repeat_actions(:,1), "Tail","left");
[~,TTests.reward_rate(1),TTestsCI.reward_rate(:,1),~] = ttest(reward_rate(:,2), reward_rate(:,1), "Tail","left");
[~,TTests.reward_rate(2),TTestsCI.reward_rate(:,2),~] = ttest(reward_rate(:,3), reward_rate(:,2), "Tail","left");
[~,TTests.reward_rate(3),TTestsCI.reward_rate(:,3),~] = ttest(reward_rate(:,3), reward_rate(:,1), "Tail","left");
WilcoxonTests.complexity(1) = signrank(complexity(:,1), complexity(:,2), "Tail","left");
WilcoxonTests.complexity(2) = signrank(complexity(:,2), complexity(:,3), "Tail","left");
WilcoxonTests.complexity(3) = signrank(complexity(:,1), complexity(:,3), "Tail","left");
WilcoxonTests.response_time(1) = signrank(response_time(:,1), response_time(:,2), "Tail","left");
WilcoxonTests.response_time(2) = signrank(response_time(:,2), response_time(:,3), "Tail","left");
WilcoxonTests.response_time(3) = signrank(response_time(:,1), response_time(:,3), "Tail","left");
WilcoxonTests.cond_entropy(1) = signrank(cond_entropy(:,2), cond_entropy(:,1), "Tail","left");
WilcoxonTests.cond_entropy(2) = signrank(cond_entropy(:,3), cond_entropy(:,2), "Tail","left");
WilcoxonTests.cond_entropy(3) = signrank(cond_entropy(:,3), cond_entropy(:,1), "Tail","left");
WilcoxonTests.repeat_actions(1) = signrank(repeat_actions(:,2), repeat_actions(:,1), "Tail","left");
WilcoxonTests.repeat_actions(2) = signrank(repeat_actions(:,3), repeat_actions(:,2), "Tail","left");
WilcoxonTests.repeat_actions(3) = signrank(repeat_actions(:,3), repeat_actions(:,1), "Tail","left");
WilcoxonTests.reward_rate(1) = signrank(reward_rate(:,2), reward_rate(:,1), "Tail","left");
WilcoxonTests.reward_rate(2) = signrank(reward_rate(:,3), reward_rate(:,2), "Tail","left");
WilcoxonTests.reward_rate(3) = signrank(reward_rate(:,3), reward_rate(:,1), "Tail","left");
% Perceived difficulty
T0 = table(mturkIDs,complexity,'VariableNames',["ID","policy_complexity"]);
T1 = struct2table(survey);
T1 = table(table2array(T1(:,1)),table2array(T1(:,4)),'VariableNames',["ID","difficulty"]);
T = innerjoin(T0,T1);
if(experiment=="exp1")
difficulties = cell2mat(table2array(T(:,3)));
else
difficulties = table2array(T(:,3));
end
BehavioralStats.difficulties=difficulties;
[h,TTests.difficulty(1),TTestsCI.difficulty(:,1),~] = ttest(difficulties(:,1), difficulties(:,2), "Tail","left");
[h,TTests.difficulty(2),TTestsCI.difficulty(:,2),~] = ttest(difficulties(:,2), difficulties(:,3), "Tail","left");
[h,TTests.difficulty(3),TTestsCI.difficulty(:,3),~] = ttest(difficulties(:,1), difficulties(:,3), "Tail","left");
WilcoxonTests.difficulty(1) = signrank(difficulties(:,1), difficulties(:,2), "Tail","left");
WilcoxonTests.difficulty(2) = signrank(difficulties(:,2), difficulties(:,3), "Tail","left");
WilcoxonTests.difficulty(3) = signrank(difficulties(:,1), difficulties(:,3), "Tail","left");
for iti_idx=1:length(ITI_pairs)
CohensD_difficulties(iti_idx,:) = table2cell(meanEffectSize(difficulties(:,ITI_pairs(iti_idx,1)),difficulties(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
end
CohensD.difficulties=CohensD_difficulties;
% Theoretical curves assuming linear RTH
n_tot = 50;
beta_set = linspace(0.1,15,n_tot);
if(experiment ~= "exp3")
p_state = [0.25 0.25 0.25 0.25];
optimal_sol.Q = Q;
optimal_sol.p_state = p_state;
[optimal_sol.R, optimal_sol.V, optimal_sol.Pa, optimal_sol.optimal_policy] = blahut_arimoto(p_state,Q,beta_set);
R = optimal_sol.R; V=optimal_sol.V;
% P(A|S) for Experiment 2
P_a_given_s = zeros(n_subj,4,length(cond),4); % subj, states, conds, actions
for subj=1:n_subj
for state=1:4
s_idx = find(data(subj).s==state);
subj_thisstateoccurrences = data(subj).s(s_idx);
subj_actions_giventhisstate = data(subj).a(s_idx);
for c = 1:length(cond)
cond_idx = find(data(subj).cond(s_idx) == cond(c));
states = subj_thisstateoccurrences(cond_idx);
actions = subj_actions_giventhisstate(cond_idx);
[N,~] = histcounts(actions,0.5:1:4.5);
P_a_given_s(subj, state, c, :) = N./sum(N);
end
end
end
BehavioralStats.P_a_given_s = P_a_given_s;
else
P_a_given_s = nan(n_subj,max(set_sizes),length(cond),max(set_sizes)); % subj, states, conds, actions
Q_full = normalize(eye(max(set_sizes)), 'range', [0.25 0.75]);
for set_size_idx = 1:length(set_sizes)
set_size = set_sizes(set_size_idx);
task_name = task_names(set_size_idx);
p_state = ones(1,set_size)./set_size;
p_states.(task_name) = p_state;
Q = Q_full(1:set_size,:);
Qs.(task_name) = Q;
% initialize variables
[R.(task_name),V.(task_name),Pa.(task_name), optimal_policy.(task_name)] = blahut_arimoto(p_state,Q,beta_set);
% P(A|S) for Experiment 3
data = datas.(task_name);
for subj=1:n_subj
for state=1:set_size
s_idx = find(data(subj).s==state);
actions = data(subj).a(s_idx);
[N,~] = histcounts(actions,0.5:1:(max(set_sizes)+.5));
P_a_given_s(subj, state, set_size_idx, :) = N./sum(N);
end
end
end
optimal_sol.Q = Qs; optimal_sol.p_state = p_states; optimal_sol.R = R; optimal_sol.V = V; optimal_sol.Pa = Pa; optimal_sol.optimal_policy = optimal_policy;
BehavioralStats.P_a_given_s = P_a_given_s;
end
if(experiment=="exp2")
for s=1:n_subj
% [Subject, iti_condition].
a_perserv(s) = mode(data(s).correct_action, 2);
for c=1:length(cond)
% [Subject, iti_condition, the 2 states where a_perserv is suboptimal].
states_where_a_perserv_suboptimal(s,c,:) = find(data(s).correct_action~=a_perserv(s));
P_a_perserv_given_suboptimal_s(s,c,:) = P_a_given_s(s,states_where_a_perserv_suboptimal(s,c,:),c,a_perserv(s));
P_a_perserv_given_optimal_s(s,c,:) = P_a_given_s(s,setdiff(1:4, squeeze(states_where_a_perserv_suboptimal(s,c,:))),c,a_perserv(s));
end
end
% Average over p(a_perserv | s) for the two states s
% where a_perserv is suboptimal.
P_a_perserv_given_suboptimal_s_mean = mean(P_a_perserv_given_suboptimal_s,3);
BehavioralStats.SuboptimalA = P_a_perserv_given_suboptimal_s_mean;
for iti_idx=1:length(ITI_pairs)
CohensD_SuboptimalA(iti_idx,:) = table2cell(meanEffectSize(P_a_perserv_given_suboptimal_s_mean(:,ITI_pairs(iti_idx,1)), P_a_perserv_given_suboptimal_s_mean(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
end
CohensD.SuboptimalA = CohensD_SuboptimalA;
[~,TTests.SuboptimalA(1),TTestsCI.SuboptimalA(:,1),~] = ttest(P_a_perserv_given_suboptimal_s_mean(:,2), P_a_perserv_given_suboptimal_s_mean(:,1), "Tail","left");
[~,TTests.SuboptimalA(2),TTestsCI.SuboptimalA(:,2),~] = ttest(P_a_perserv_given_suboptimal_s_mean(:,3), P_a_perserv_given_suboptimal_s_mean(:,2), "Tail","left");
[~,TTests.SuboptimalA(3),TTestsCI.SuboptimalA(:,3),~] = ttest(P_a_perserv_given_suboptimal_s_mean(:,3), P_a_perserv_given_suboptimal_s_mean(:,1), "Tail","left");
WilcoxonTests.SuboptimalA(1) = signrank(P_a_perserv_given_suboptimal_s_mean(:,2),P_a_perserv_given_suboptimal_s_mean(:,1), "Tail","left");
WilcoxonTests.SuboptimalA(2) = signrank(P_a_perserv_given_suboptimal_s_mean(:,3),P_a_perserv_given_suboptimal_s_mean(:,2), "Tail","left");
WilcoxonTests.SuboptimalA(3) = signrank(P_a_perserv_given_suboptimal_s_mean(:,3),P_a_perserv_given_suboptimal_s_mean(:,1), "Tail","left");
end
%% Error probability analysis for Experiment 3;
if(experiment=="exp3")
BehavioralStats.correct_actions = exp3_correct_actions;
P_a_given_s = BehavioralStats.P_a_given_s; %[subj, state,cond,action]
n_subj = size(P_a_given_s,1);
n_actions = size(P_a_given_s,4);
n_states = size(P_a_given_s,2);
set_sizes = [2,4,6];
% Compute for Ns=2, p(a1|s2) vs. E[p(a|s2)] for all a except {a1,a2}.
mean_P_choosecorrectaction_givenstate = zeros(n_subj, length(set_sizes), n_states);
mean_P_choosecorrectaction_givenstate(:)=NaN;
mean_P_choosewrongbutpossibleaction_givenstate = zeros(n_subj, length(set_sizes), n_states);
mean_P_choosewrongbutpossibleaction_givenstate(:)=NaN;
mean_P_choosewrongandimpossibleaction_givenstate = zeros(n_subj, length(set_sizes), n_states);
mean_P_choosewrongandimpossibleaction_givenstate(:)=NaN;
for subj=1:n_subj
for c=1:3
P_a_give_s_Ns = squeeze((P_a_given_s(subj,:,c,:)));
possible_actions = unique(exp3_correct_actions(subj,c,:),'stable');
possible_actions(isnan(possible_actions))=[];
impossible_actions = setdiff(1:n_actions, possible_actions);
corresponding_states = 1:length(possible_actions);
for state=corresponding_states
P_choosewrongbutpossibleaction_giventhisstate = 0;
P_choosewrongandimpossibleaction_giventhisstate = 0;
for action_idx=1:length(possible_actions)
action = possible_actions(action_idx);
if(state==action_idx) %Skip p(a_i | s_i) for the same i.
mean_P_choosecorrectaction_givenstate(subj,c,state) = P_a_give_s_Ns(state,action);
else %if(ismember(action, possible_actions)) % a_i is an action optimal for one of the possible states in the cond, but not the correct action for the current state.
P_choosewrongbutpossibleaction_giventhisstate = P_choosewrongbutpossibleaction_giventhisstate + P_a_give_s_Ns(state,action);
end
end
for action_idx=1:length(impossible_actions) % a_i is not an optimal action for any of the possible states in this cond.
action = impossible_actions(action_idx);
P_choosewrongandimpossibleaction_giventhisstate = P_choosewrongandimpossibleaction_giventhisstate + P_a_give_s_Ns(state,action);
end
mean_P_choosewrongbutpossibleaction_givenstate(subj,c,state) = P_choosewrongbutpossibleaction_giventhisstate./(length(possible_actions)-1); %Average over the set of actions that are optimal for some state in the cond, but not the current state.
mean_P_choosewrongandimpossibleaction_givenstate(subj,c,state) = P_choosewrongandimpossibleaction_giventhisstate./(length(impossible_actions)); %Average over the set of actions that are never optimal for any possible state in the cond.
end
end
end
% Average over states
mean_P_choosecorrectaction = squeeze(nanmean(mean_P_choosecorrectaction_givenstate,3));
mean_P_choosewrongbutpossibleaction = squeeze(nanmean(mean_P_choosewrongbutpossibleaction_givenstate,3));
mean_P_choosewrongandimpossibleaction = squeeze(nanmean(mean_P_choosewrongandimpossibleaction_givenstate,3));
BehavioralStats.prob_choosewrongbutpossibleaction = mean_P_choosewrongbutpossibleaction;
[h,TTests.prob_choosewrongbutpossibleaction(1),TTestsCI.choosewrongbutpossibleaction(:,1),~] = ttest(mean_P_choosewrongbutpossibleaction(:,1), mean_P_choosewrongbutpossibleaction(:,2), "Tail","right");
[h,TTests.prob_choosewrongbutpossibleaction(2),TTestsCI.prob_choosewrongbutpossibleaction(:,2),~] = ttest(mean_P_choosewrongbutpossibleaction(:,2), mean_P_choosewrongbutpossibleaction(:,3), "Tail","right");
[h,TTests.prob_choosewrongbutpossibleaction(3),TTestsCI.prob_choosewrongbutpossibleaction(:,3),~] = ttest(mean_P_choosewrongbutpossibleaction(:,1), mean_P_choosewrongbutpossibleaction(:,3), "Tail","right");
WilcoxonTests.prob_choosewrongbutpossibleaction(1) = signrank(mean_P_choosewrongbutpossibleaction(:,1), mean_P_choosewrongbutpossibleaction(:,2), "Tail","right");
WilcoxonTests.prob_choosewrongbutpossibleaction(2) = signrank(mean_P_choosewrongbutpossibleaction(:,2), mean_P_choosewrongbutpossibleaction(:,3), "Tail","right");
WilcoxonTests.prob_choosewrongbutpossibleaction(3) = signrank(mean_P_choosewrongbutpossibleaction(:,1), mean_P_choosewrongbutpossibleaction(:,3), "Tail","right");
for iti_idx=1:length(ITI_pairs)
CohensD_prob_choosewrongbutpossibleaction(iti_idx,:) = table2cell(meanEffectSize(mean_P_choosewrongbutpossibleaction(:,ITI_pairs(iti_idx,1)),mean_P_choosewrongbutpossibleaction(:,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
end
CohensD.prob_choosewrongbutpossibleaction=CohensD_prob_choosewrongbutpossibleaction;
end
%% LME fitting
% Flattening arrays
complexity_flat = complexity(:);
response_time_flat = response_time(:);
[complexity_sorted, complexity_sorted_idx] = sort(complexity_flat);
response_time_sorted = response_time_flat(complexity_sorted_idx);
LME.complexity_sorted = complexity_sorted;
LME.response_time_sorted = response_time_sorted;
LME.complexity_sorted_idx = complexity_sorted_idx;
if(experiment~="exp3")
subject_id = repmat(1:n_subj, 1, length(cond))';
else
subject_id = repmat(1:n_subj, 1, length(set_sizes))';
end
tbl = table(subject_id,complexity_flat,response_time_flat,'VariableNames',{'Subject','PolicyComplexity','RT'});
lme = fitlme(tbl,'RT ~ PolicyComplexity + (1|Subject) + (PolicyComplexity-1|Subject)');
LME.lme = lme;
LME.tbl = tbl;
% STD of random effects
[~,~,stats] = randomEffects(lme,'Alpha',0.01);
q = dataset2cell(stats(1:n_subj,4));
w = dataset2cell(stats((n_subj+1):end,4));
LME.random_effects_intercept_std = std(cell2mat(q(2:end)));
LME.random_effects_complexity_std = std(cell2mat(w(2:end)));
% RT_predictions vs. RT_true
RT_lme = predict(lme); % Return 1SD, instead of 95% CI.
RT_lme_sorted = RT_lme(complexity_sorted_idx);
LME.RT_lme = RT_lme;
LME.RT_lme_sorted = RT_lme_sorted;
% Counterfactual RT at different policy complexity levels
if(experiment ~= "exp3")
complexity_rrmax = zeros(n_subj, length(cond));
RT_lme_theoretical = zeros(n_subj, length(R));
for subj=1:n_subj
tbl_new = table(repmat(subj,1,length(R))',R,'VariableNames',{'Subject','PolicyComplexity'});
rt_lme_theoretical = predict(lme, tbl_new);
RT_lme_theoretical(subj,:)=rt_lme_theoretical;
for c=1:length(cond)
rr = V ./ (rt_lme_theoretical + cond(c)/1000 + feedback_duration);
[max_rr, max_rr_complexity] = max(rr);
complexity_rrmax(subj,c) = R(max_rr_complexity);
end
end
LME.RT_lme_theoretical = RT_lme_theoretical;
else
complexity_rrmax = zeros(n_subj, length(set_sizes));
RT_lme_theoreticals = zeros(n_subj, length(R.(task_names(end))));
for subj=1:n_subj
for set_size_idx=1:length(set_sizes)
set_size = set_sizes(set_size_idx);
task_name = task_names(set_size_idx);
tbl_new = table(repmat(subj,1,length(R.(task_name)))',R.(task_name),'VariableNames',{'Subject','PolicyComplexity'});
RT_lme_theoretical = predict(lme, tbl_new);
if(set_size_idx == length(set_sizes))
RT_lme_theoreticals(subj,:)=RT_lme_theoretical;
end
rr = V.(task_name) ./ (RT_lme_theoretical + cond/1000 + feedback_duration);
[max_rr, max_rr_complexity] = max(rr);
complexity_rrmax(subj,set_size_idx) = R.(task_name)(max_rr_complexity);
end
end
LME.RT_lme_theoretical = RT_lme_theoreticals;
end
LME.complexity_rrmax = complexity_rrmax;
rhos_subj = zeros(n_subj,1);
difficulty_subj = 1;
for subj=1:n_subj
if(experiment=="exp1" && ~isempty(cell2mat(table2array(T(subj,3))))) % In Experiment 1, one subject did not have difficulty data.
rhos_subj(subj) = corr(complexity(subj,:)', difficulties(difficulty_subj,:)',"Type", "Spearman");
difficulty_subj = difficulty_subj + 1;
else
rhos_subj(subj) = corr(complexity(subj,:)', difficulties(subj,:)',"Type", "Spearman");
end
end
BehavioralStats.complexity_difficulty_spearman = rhos_subj;
CohensD.complexity_difficulty_spearman_ispositive = table2cell(meanEffectSize(rhos_subj,Effect="cohen"));
[~,TTests.complexity_difficulty_spearman_ispositive,TTestsCI.complexity_difficulty_spearman_ispositive,~] = ttest(rhos_subj,0, "Tail","right");
WilcoxonTests.complexity_difficulty_spearman_ispositive = signrank(rhos_subj,0, "Tail","right");
% Leftward complexity bias
complexity_diff_from_rrmax = complexity-complexity_rrmax;
LME.complexity_diff_from_rrmax=complexity_diff_from_rrmax;
for c=1:3
%CohensD_complexity_lessthan_rrmax(c,:) = table2cell(meanEffectSize(complexity(:,c),complexity_rrmax(:,c),Effect="cohen", Paired=true)); % cliff's delta instead of Cohen's d, because we will use nonparametric test
CohensD_complexity_lessthan_rrmax(c,:) = table2cell(meanEffectSize(complexity(:,c),complexity_rrmax(:,c),Effect="cliff", Paired=true)); % cliff's delta instead of Cohen's d, because we will use nonparametric test
end
CohensD.complexity_lessthan_rrmax = CohensD_complexity_lessthan_rrmax;
[~,TTests.complexity_lessthan_rrmax(1),TTestsCI.complexity_lessthan_rrmax(:,1)] = ttest(complexity(:,1), complexity_rrmax(:,1), "Tail","left");
[~,TTests.complexity_lessthan_rrmax(2),TTestsCI.complexity_lessthan_rrmax(:,2)] = ttest(complexity(:,2), complexity_rrmax(:,2), "Tail","left");
[~,TTests.complexity_lessthan_rrmax(3),TTestsCI.complexity_lessthan_rrmax(:,3)] = ttest(complexity(:,3), complexity_rrmax(:,3), "Tail","left");
WilcoxonTests.complexity_lessthan_rrmax(1) = signrank(complexity(:,1), complexity_rrmax(:,1),"Tail","left");
WilcoxonTests.complexity_lessthan_rrmax(2) = signrank(complexity(:,2), complexity_rrmax(:,2),"Tail","left");
WilcoxonTests.complexity_lessthan_rrmax(3) = signrank(complexity(:,3), complexity_rrmax(:,3),"Tail","left");
% Two subgroups analysis of RT and policy complexity
switch experiment
case "exp1"
thres = -1;
% Use ITI=2 to separate into 2 groups
lowcomplexity_group_subjidx = find(squeeze(complexity(:,3)-complexity_rrmax(:,3))<thres);
highcomplexity_group_subjidx = find(squeeze(complexity(:,3)-complexity_rrmax(:,3))>=thres);
case "exp2"
thres = 0.25;
% Use ITI=9.5 to separate into 2 groups
lowcomplexity_group_subjidx = find(squeeze(complexity(:,2)-complexity_rrmax(:,2))<thres);
highcomplexity_group_subjidx = find(squeeze(complexity(:,2)-complexity_rrmax(:,2))>=thres);
case "exp3"
thres = -0.9;
% Use ITI=9.5 to separate into 2 groups
lowcomplexity_group_subjidx = find(squeeze(complexity(:,3)-complexity_rrmax(:,3))<thres);
highcomplexity_group_subjidx = find(squeeze(complexity(:,3)-complexity_rrmax(:,3))>=thres);
end
complexity_group_subjidx = {lowcomplexity_group_subjidx, highcomplexity_group_subjidx};
for iti_idx=1:length(ITI_pairs)
CohensD_complexity_low_complexity(iti_idx,:) = table2cell(meanEffectSize(complexity(lowcomplexity_group_subjidx,ITI_pairs(iti_idx,1)),complexity(lowcomplexity_group_subjidx,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_response_time_low_complexity(iti_idx,:) = table2cell(meanEffectSize(response_time(lowcomplexity_group_subjidx,ITI_pairs(iti_idx,1)),response_time(lowcomplexity_group_subjidx,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_complexity_high_complexity(iti_idx,:) = table2cell(meanEffectSize(complexity(highcomplexity_group_subjidx,ITI_pairs(iti_idx,1)),complexity(highcomplexity_group_subjidx,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
CohensD_response_time_high_complexity(iti_idx,:) = table2cell(meanEffectSize(response_time(highcomplexity_group_subjidx,ITI_pairs(iti_idx,1)),response_time(highcomplexity_group_subjidx,ITI_pairs(iti_idx,2)),Effect="cohen", Paired=true));
end
CohensD.complexity_low_complexity = CohensD_complexity_low_complexity;
CohensD.response_time_low_complexity = CohensD_response_time_low_complexity;
CohensD.complexity_high_complexity = CohensD_complexity_high_complexity;
CohensD.response_time_high_complexity = CohensD_response_time_high_complexity;
[~,TTests.complexity_lowcomplexity(1),TTestsCI.complexity_lowcomplexity(:,1)] = ttest(complexity(lowcomplexity_group_subjidx,1), complexity(lowcomplexity_group_subjidx,2),"Tail","left");
[~,TTests.complexity_lowcomplexity(2),TTestsCI.complexity_lowcomplexity(:,2)] = ttest(complexity(lowcomplexity_group_subjidx,2), complexity(lowcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.complexity_lowcomplexity(3),TTestsCI.complexity_lowcomplexity(:,3)] = ttest(complexity(lowcomplexity_group_subjidx,1), complexity(lowcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.response_time_lowcomplexity(1),TTestsCI.response_time_lowcomplexity(:,1)] = ttest(response_time(lowcomplexity_group_subjidx,1), response_time(lowcomplexity_group_subjidx,2),"Tail","left");
[~,TTests.response_time_lowcomplexity(2),TTestsCI.response_time_lowcomplexity(:,2)] = ttest(response_time(lowcomplexity_group_subjidx,2), response_time(lowcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.response_time_lowcomplexity(3),TTestsCI.response_time_lowcomplexity(:,3)] = ttest(response_time(lowcomplexity_group_subjidx,1), response_time(lowcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.complexity_lowcomplexity(1) = signrank(complexity(lowcomplexity_group_subjidx,1), complexity(lowcomplexity_group_subjidx,2),"Tail","left");
WilcoxonTests.complexity_lowcomplexity(2) = signrank(complexity(lowcomplexity_group_subjidx,2), complexity(lowcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.complexity_lowcomplexity(3) = signrank(complexity(lowcomplexity_group_subjidx,1), complexity(lowcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.response_time_lowcomplexity(1) = signrank(response_time(lowcomplexity_group_subjidx,1), response_time(lowcomplexity_group_subjidx,2),"Tail","left");
WilcoxonTests.response_time_lowcomplexity(2) = signrank(response_time(lowcomplexity_group_subjidx,2), response_time(lowcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.response_time_lowcomplexity(3) = signrank(response_time(lowcomplexity_group_subjidx,1), response_time(lowcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.complexity_highcomplexity(1),TTestsCI.complexity_highcomplexity(:,1)] = ttest(complexity(highcomplexity_group_subjidx,1), complexity(highcomplexity_group_subjidx,2),"Tail","left");
[~,TTests.complexity_highcomplexity(2),TTestsCI.complexity_highcomplexity(:,2)] = ttest(complexity(highcomplexity_group_subjidx,2), complexity(highcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.complexity_highcomplexity(3),TTestsCI.complexity_highcomplexity(:,3)] = ttest(complexity(highcomplexity_group_subjidx,1), complexity(highcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.response_time_highcomplexity(1),TTestsCI.response_time_highcomplexity(:,1)] = ttest(response_time(highcomplexity_group_subjidx,1), response_time(highcomplexity_group_subjidx,2),"Tail","left");
[~,TTests.response_time_highcomplexity(2),TTestsCI.response_time_highcomplexity(:,2)] = ttest(response_time(highcomplexity_group_subjidx,2), response_time(highcomplexity_group_subjidx,3),"Tail","left");
[~,TTests.response_time_highcomplexity(3),TTestsCI.response_time_highcomplexity(:,3)] = ttest(response_time(highcomplexity_group_subjidx,1), response_time(highcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.complexity_highcomplexity(1) = signrank(complexity(highcomplexity_group_subjidx,1), complexity(highcomplexity_group_subjidx,2),"Tail","left");
WilcoxonTests.complexity_highcomplexity(2) = signrank(complexity(highcomplexity_group_subjidx,2), complexity(highcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.complexity_highcomplexity(3) = signrank(complexity(highcomplexity_group_subjidx,1), complexity(highcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.response_time_highcomplexity(1) = signrank(response_time(highcomplexity_group_subjidx,1), response_time(highcomplexity_group_subjidx,2),"Tail","left");
WilcoxonTests.response_time_highcomplexity(2) = signrank(response_time(highcomplexity_group_subjidx,2), response_time(highcomplexity_group_subjidx,3),"Tail","left");
WilcoxonTests.response_time_highcomplexity(3) = signrank(response_time(highcomplexity_group_subjidx,1), response_time(highcomplexity_group_subjidx,3),"Tail","left");
LME.complexity_group_subjidx=complexity_group_subjidx;
% Counterbalanced trial design
if(experiment ~= "exp3")
rewards_phase = cell(length(cond),1);
for c=1:length(cond)
for phase=1:8
for subj=1:n_subj
idx = find(data(subj).cond==cond(c));
subj_r = data(subj).r(idx);
reward_phase(subj,phase) = mean(subj_r(phase:8:end));
end
end
rewards_phase{c} = reward_phase;
CohensD.undesired_cycle_effects = table2cell(meanEffectSize(reward_phase(:,1), reward_phase(:,end), Effect="cohen", Paired=true));
[~,TTests.undesired_cycle_effects,TTestsCI.undesired_cycle_effects] = ttest(reward_phase(:,1), reward_phase(:,end), "Tail","left");
WilcoxonTests.undesired_cycle_effects = signrank(reward_phase(:,1), reward_phase(:,end), "Tail","left");
end
else
rewards_phase = cell(length(set_sizes),1);
periods = [2*4,4*2,6*2];
for set_size_idx = 1:length(set_sizes)
period = periods(set_size_idx);
data = datas.(task_names(set_size_idx));
for phase=1:period
for subj=1:n_subj
subj_r = data(subj).r;
reward_phase(subj,phase) = mean(subj_r(phase:period:end));
end
end
rewards_phase{set_size_idx} = reward_phase;
CohensD.undesired_cycle_effects = table2cell(meanEffectSize(reward_phase(:,1), reward_phase(:,end), Effect="cohen", Paired=true));
[~,TTests.undesired_cycle_effects(set_size_idx),TTestsCI.undesired_cycle_effects(:,set_size_idx)] = ttest(reward_phase(:,1), reward_phase(:,end), "Tail","left");
WilcoxonTests.undesired_cycle_effects(set_size_idx) = signrank(reward_phase(:,1), reward_phase(:,end), "Tail","left");
end
end
BehavioralStats.rewards_phase = rewards_phase;
% Cohen's d--only return the point estimate
CohensD_new = struct();
CohensD_CIs = struct();
fields = fieldnames(CohensD);
for i = 1:numel(fields)
fieldName = fields{i};
% Extract the first column of the 3x2 cell and convert it to a 1x3 vector
CohensD_new.(fieldName) = cell2mat(CohensD.(fieldName)(:, 1))';
CohensD_CIs.(fieldName) = cell2mat(CohensD.(fieldName)(:, 2))';
end
CohensD = CohensD_new;
end
%% Figure 1 partial
function [] = Figure1(exps, figspecs, cmap, cmap_exp3)
exp1 = exps.exp1; exp3 = exps.exp3;
markersize = 20; linewidth=1.5;
feedback_duration = 0.3;
cond = [0,500,2000];
exp1_R = exps.exp1.optimal_sol.R;
exp1_V = exps.exp1.optimal_sol.V;
RT_intercept = 0.3; RT_slope = 0.45;
exp1_RT = exp1_R .* RT_slope + RT_intercept;
exp1_rewardrate = zeros(length(exp1_R), length(cond));
for c=1:length(cond)
exp1_rewardrate(:,c) = exp1_V ./ (exp1_RT + feedback_duration + cond(c)./1000);
end
exp3_R = exps.exp3.optimal_sol.R;
exp3_V = exps.exp3.optimal_sol.V;
set_sizes = [2,4,6];
task_names = convertCharsToStrings(fieldnames(exps.exp3.optimal_sol.R));
exp3_rewardrate = zeros(length(exp3_R.(task_names(1))), length(task_names));
for task = 1:length(task_names)
task_name = task_names(task);
exp3_RT.(task_name) = exp3_R.(task_name) .* RT_slope + RT_intercept;
exp3_rewardrate(:,task) = exp3_V.(task_name) ./ (exp3_RT.(task_name) + feedback_duration + 2);
end
% Figures
figure("Position", figspecs)
tiledlayout(6,2, 'Padding', 'loose', 'TileSpacing', 'compact');
ttl_position_shift = -0.18;
ttl_fontsize = 10;
nexttile(1,[2,1]); hold on;
plot(exp1_R, exp1_V, "k-","MarkerSize", markersize, "LineWidth", linewidth)
xlabel("Policy complexity (bits)")
ylabel("Trial-averaged reward")
xticks(0:0.5:log2(6))
xlim([0 log2(6)])
yticks(0.3:0.2:1)
ylim([0.3,0.8])
ttl = title('D', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_shift-0.02; % use negative values (ie, -0.1) to move further left
ttl.Position(2) = 1.05; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
nexttile(5,[2,1]); hold on;
plot(exp3_R.(task_names(end)), exp3_RT.(task_names(end)), "k-","MarkerSize", markersize, "LineWidth", linewidth)
xlabel("Policy complexity (bits)")
ylabel("RT (s)")
xticks(0:0.5:log2(6))
xlim([0 log2(6)])
yticks(0:0.5:1.5)
ylim([0,Inf])
ttl = title('E', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_shift-0.02; % use negative values (ie, -0.1) to move further left
ttl.Position(2) = 1.05; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
nexttile(9,[2,1]); hold on;
for task=1:length(task_names)
plot(exp3_R.(task_names(task)), exp3_V.(task_names(task)), "-","Color", cmap_exp3(task,:), "MarkerSize", markersize, "LineWidth", linewidth)
end
xlabel("Policy complexity (bits)")
ylabel("Trial-averaged reward")
xticks(0:0.5:log2(6))
xlim([0 log2(6)])
yticks(0:0.25:1)
ylim([0,1])
h_leg = legend("Set size = 2","Set size = 4", "Set size = 6", "location","southeast");
h_leg.BoxFace.ColorType='truecoloralpha';
h_leg.BoxFace.ColorData=uint8(255*[1 1 1 0.75]');
ttl = title('G', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_shift-0.02; % use negative values (ie, -0.1) to move further left
ttl.Position(2) = 1.05; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
nexttile(2, [3,1]); hold on;
for c=1:length(cond)
plot(exp1_R, normalize(exp1_rewardrate(:,c),"range",[0,1]),"-","Color", cmap(c,:), "MarkerSize", markersize, "LineWidth", linewidth)
[max_rr, max_rr_idx] = max(exp1_rewardrate(:,c));
max_rr_complexity = exp1_R(max_rr_idx);
plot([max_rr_complexity,max_rr_complexity],[0,1], "-","Color", [cmap(c,:),0.3], "MarkerSize", markersize, "LineWidth", linewidth,"HandleVisibility","off")
end
xlabel("Policy complexity (bits)")
ylabel({" ","Time-averaged reward (/s), ","normalized"})
xticks(0:0.5:log2(6))
xlim([0 log2(6)])
yticks(0:0.25:1)
ylim([0,1])
ttl = title('F', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_shift-0.07; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
h_leg = legend("ITI = 0s","ITI = 0.5s","ITI = 2s", "location","south");
h_leg.BoxFace.ColorType='truecoloralpha';
h_leg.BoxFace.ColorData=uint8(255*[1 1 1 0.75]');
nexttile(8, [3,1]); hold on;
for task=1:length(task_names)
plot(exp3_R.(task_names(task)), normalize(exp3_rewardrate(:,task),"range",[0,1]),"-","Color", cmap_exp3(task,:), "MarkerSize", markersize, "LineWidth", linewidth)
[max_rr, max_rr_idx] = max(exp3_rewardrate(:,task));
max_rr_complexity = exp3_R.(task_names(task))(max_rr_idx);
plot([max_rr_complexity,max_rr_complexity],[0,1], "-","Color", [cmap_exp3(task,:),0.3], "MarkerSize", markersize, "LineWidth", linewidth, "HandleVisibility","off")
end
xlabel("Policy complexity (bits)")
ylabel({" ","Time-averaged reward (/s), ","normalized"})
xticks(0:0.5:log2(6))
xlim([0 log2(6)])
yticks(0:0.25:1)
ylim([0,1])
ttl = title('H', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_shift-0.07; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
h_leg = legend("Set size = 2","Set size = 4", "Set size = 6", "location","south");
h_leg.BoxFace.ColorType='truecoloralpha';
h_leg.BoxFace.ColorData=uint8(255*[1 1 1 0.75]');
end
%% Figure 2 partial
function [] = Figure2(exp, figspecs)
Q = exp.optimal_sol.Q;
num_states=length(Q);
Q_transpose = Q';
figure('Position', figspecs);
tiledlayout(1,1, 'Padding', 'compact', 'TileSpacing', 'tight');
reward_mat_fontsize=12;
ax=nexttile(1,[1,1]); hold on;
ax.XAxis.FontSize = reward_mat_fontsize; ax.YAxis.FontSize = reward_mat_fontsize;
[X Y]=meshgrid(1:num_states,1:num_states);
string = mat2cell(num2str(Q_transpose(:)),ones(num_states*num_states,1));
imagesc(zeros(num_states),'AlphaData',0)
text(Y(:)-0.33,flipud(X(:)),string,'HorizontalAlignment','left', 'fontsize',reward_mat_fontsize+3)
grid = .5:1:(num_states+0.5);
grid1 = [grid;grid];
grid2 = repmat([.5;(num_states+0.5)],1,length(grid));
plot(grid1,grid2,'k')
plot(grid2,grid1,'k')
set(gca,'TickLength',[0,0])
set(gca,'xaxisLocation','top')
xlim([0.5, num_states+0.5])
ylim([0.5, num_states+0.5])
xticks(1:num_states)
yticks(1:num_states)
xticklabels("A_"+[1:4])
yticklabels("S_"+[4:-1:1])
end
%% Figure 3
function [] = Figure3(experiment_stats, cmap, figspecs)
markersize = 20; linewidth=1.5;
cond = [0,500,2000];
% Parse participant behavioral stats
accuracy = experiment_stats.BehavioralStats.accuracy;
reward = experiment_stats.BehavioralStats.reward;
complexity = experiment_stats.BehavioralStats.complexity;
response_time = experiment_stats.BehavioralStats.response_time;
cond_entropy = experiment_stats.BehavioralStats.cond_entropy;
repeat_actions = experiment_stats.BehavioralStats.repeat_actions;
reward_rate = experiment_stats.BehavioralStats.reward_rate;
difficulties = experiment_stats.BehavioralStats.difficulties;
V = experiment_stats.optimal_sol.V;
R = experiment_stats.optimal_sol.R;
% Figure 1: policy complexity, reward rate, RT
figure('Position', figspecs);
tiledlayout(2,10, 'Padding', 'loose', 'TileSpacing', 'tight');
ttl_fontsize = 10; ttl_position_xshift = -0.27; ttl_position_yshift=1.08;
% reward vs complexity
ax=nexttile(1,[2,4]);
hold on; colororder(cmap)
plot(ax,complexity,reward,'.','MarkerSize',markersize-5)
plot(ax,R, V,'k', 'LineWidth', linewidth);
xticks(0:0.5:2)
xticklabels(0:0.5:2)
yticks(0:0.25:1)
xlim([0,2])
ylim([0,1])
ylabel('Trial-averaged reward')
xlabel('Policy complexity (bits)')
h_leg = legend('ITI = 0s','ITI = 0.5s','ITI = 2s', 'Location', "northwest");
h_leg.BoxFace.ColorType='truecoloralpha';
h_leg.BoxFace.ColorData=uint8(255*[1 1 1 0.75]');
ttl = title('A', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_xshift+0.13; % use negative values (ie, -0.1) to move further left
ttl.Position(2) = ttl_position_yshift-0.05; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
% optimal complexity vs ITI
[n_subj,~] = size(response_time);
ax=nexttile([1,2]); hold on;
[se,m] = wse(complexity);
errorbar(ax,cond/1000,m,se,'.-','MarkerSize',markersize,'LineWidth',linewidth,'Color','k')
xlabel('ITI (s)')
xticks(cond/1000)
xticklabels(cond/1000)
ylabel('Policy complexity (bits)')
yticks(0.2:0.2:0.8)
ylim([0.2 0.8])
xlim([-0.25 2.25])
ttl = title('B', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_xshift; % use negative values (ie, -0.1) to move further left
ttl.Position(2) = ttl_position_yshift; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';
% optimal RT vs ITI
ax=nexttile([1,2]); hold on;
[se,m] = wse(response_time);
errorbar(ax,cond/1000,m,se,'.-','MarkerSize',markersize,'LineWidth',linewidth,'Color','k')
xlabel('ITI (s)')
xticks(cond/1000)
xticklabels(cond/1000)
ylabel('RT (s)')
yticks(0.2:0.2:0.8)
xlim([-0.25 2.25])
ylim([0.2 0.8])
ttl = title('C', "Fontsize", ttl_fontsize);
ttl.Units = 'Normalize';
ttl.Position(1) = ttl_position_xshift; % use negative values (ie, -0.1) to move further left
ttl.Position(2) = ttl_position_yshift; % use negative values (ie, -0.1) to move further left
ttl.HorizontalAlignment = 'left';