Test for Individual Differences
Lesson
Elijah Galvan
September 1, 2023
12 min read
Goal During this Stage
We want to explicitly test whether or not people are different from each other, or if our findings indicate a tendency that is true of all people in the same way.
How to Achieve this Goal
Embodying No Individual Differences
We’ve already identified the best model and now we want to see if the instance that we proved was best - where we estimated Free Parameters for each Subjects - was justified in its complexity. Even if our best model captures ‘individual differences’ - i.e. multiple potential strategies - it does not necessarily mean that Subjects are different. Instead it indicates that this multinorm model is able to capture behavior that is not explained by any simplification of it. Testing for individual differences invovles training an instance of our model over data where we do not differentiate between Subjects and we then compare this model’s performance to a
result = fmincon(obj_function,x0 = initial_params, A = NULL, b = NULL, Aeq = NULL, beq = NULL,
lb = lower_bounds, ub = upper_bounds,
df = trialData)
trialData$PredictedNID = vector('numeric', length(trialData$SubjectID))
for (i in 1:length(trialData$IV)){
Utility = vector('numeric', length(Choices))
for (j in 1:length(Choices)){
Utility[j] = utility(parameter1 = results$par[1],
parameter2 = results$par[2],
construct1 = construct1(trialData$IV[k], trialData$Constant[k], Choices[n]),
construct2 = construct2(trialData$IV[k], trialData$Constant[k], Choices[n]),
construct3 = construct3(trialData$IV[k], trialData$Constant[k], Choices[n]))
}
trialData$PredictedNID[i] = Choices[which(Utility == max(Utility))]
}
subjectData$SS_NID = vector('numeric', length(subjectDatasubjectData$SubjectID))
for (i in 1:length(subjectData$SubjectID)){
trials = which(subjectData$SubjectID[i] == trialData$SubjectID)
subjectData$SS_NID[i] = sum((trialData$Decision[trials] - trialData$PredictedNID[trials])**2)
}
# number of parameter divided by the number of people (i.e. number of parameters for each person)
subjectData$AIC_NID = length(trialList$IV) * log(subjectData$SS_NID/length(trialList$IV)) + 2 * (2/length(subjectData$SubjectID))
t.test(subjectData$AIC_NID, subjectData$model_AIC, paired = T)
options = optimoptions('fmincon', 'Algorithm', 'interior-point');
result = fmincon(@(params) obj_function(params, trialData, 'OLS'), initial_params, [], [], [], [], lower_bounds, upper_bounds, [], options);
trialData.PredictedNID = zeros(length(trialData.SubjectID), 1);
for i = 1:length(trialData.IV)
Utility = zeros(length(Choices), 1);
for j = 1:length(Choices)
Utility(j) = utility(result(1), result(2), ...
construct1(trialData.IV(i), trialData.Constant(i), Choices(j)), ...
construct2(trialData.IV(i), trialData.Constant(i), Choices(j)), ...
construct3(trialData.IV(i), trialData.Constant(i), Choices(j)));
end
[~, idx] = max(Utility);
trialData.PredictedNID(i) = Choices(idx);
end
subjectData.SS_NID = zeros(length(subjectData.SubjectID), 1);
for i = 1:length(subjectData.SubjectID)
trials = find(subjectData.SubjectID(i) == trialData.SubjectID);
subjectData.SS_NID(i) = sum((trialData.Decision(trials) - trialData.PredictedNID(trials)).^2);
end
subjectData.AIC_NID = length(trialList.IV) * log(subjectData.SS_NID / length(trialList.IV)) + 2 * (2 / length(subjectData.SubjectID));
ttest(subjectData.AIC_NID, subjectData.model_AIC, 'paired');
result = minimize(lambda params: obj_function(params, trialData, 'OLS'), initial_params, bounds=list(zip(lower_bounds, upper_bounds)))
trialData['PredictedNID'] = np.zeros(len(trialData['SubjectID']))
for i in range(len(trialData['IV'])):
Utility = np.zeros(len(Choices))
for j in range(len(Choices)):
Utility[j] = utility(result.x[0], result.x[1],
construct1(trialData['IV'].iloc[i], trialData['Constant'].iloc[i], Choices[j]),
construct2(trialData['IV'].iloc[i], trialData['Constant'].iloc[i], Choices[j]),
construct3(trialData['IV'].iloc[i], trialData['Constant'].iloc[i], Choices[j]))
trialData['PredictedNID'].iloc[i] = Choices[np.argmax(Utility)]
subjectData['SS_NID'] = np.zeros(len(subjectData['SubjectID']))
for i in range(len(subjectData['SubjectID'])):
trials = np.where(subjectData['SubjectID'].iloc[i] == trialData['SubjectID'])[0]
subjectData['SS_NID'].iloc[i] = np.sum((trialData['Decision'].iloc[trials] - trialData['PredictedNID'].iloc[trials]) ** 2)
subjectData['AIC_NID'] = len(trialList['IV']) * np.log(subjectData['SS_NID'] / len(trialList['IV'])) + 2 * (2 / len(subjectData['SubjectID']))
ttest_rel(subjectData['AIC_NID'], subjectData['model_AIC'])
Tutorials
Tutorial 1 - van Baar, Chang, & Sanfey, 2019
Embodying No Individual Differences
result = fmincon(obj_function,x0 = initial_params, A = NULL, b = NULL, Aeq = NULL, beq = NULL,
lb = lower_bounds, ub = upper_bounds,
df = trialData)
trialData$PredictedNID = vector('numeric', length(trialData$Subject))
for (i in 1:length(trialData$Subject)){
if (trialData$Investment[i] > 10) {
Choices = seq(0, (trialData$Investment[i] * trialData$Multiplier[i]), round((trialData$Investment[i]*trialData$Multiplier[i])/10))
} else {
Choices = seq(0, (trialData$Investment[i] * trialData$Multiplier[i]), 1)
}
Utility = vector('numeric', length(Choices))
for (n in 1:length(Choices)){
Utility[n] = utility(theta = result$par[1],
phi = result$par[2],
payout = payout_maximization(trialData$Investment[i], trialData$Multiplier[i], Choices[n]),
guilt = guilt(trialData$Investment[i], believed_multiplier = 4, Choices[n], trialData$Multiplier[i]),
inequity = inequity(trialData$Investment[i], trialData$Multiplier[i], Choices[n], endowment = 10))
}
trialData$PredictedNID[i] = Choices[which(Utility == max(Utility))]
}
subjectData$SS_NID = vector('numeric', length(subjectData$SubjectID))
for (i in 1:length(subjectData$SubjectID)){
trials = which(subjectData$SubjectID[i] == trialData$Subject)
subjectData$SS_NID[i] = sum((as.numeric(trialData$Returned[trials]) - trialData$PredictedNID[trials])**2)
}
# number of parameter divided by the number of people (i.e. number of parameters for each person)
subjectData$AIC_NID = length(df$Investment) * log(subjectData$SS_NID/length(df$Investment)) + 2 * (2/length(subjectData$SubjectID))
t.test(subjectData$modelAIC, subjectData$AIC_NID, paired = T)
summary(lm(data = trialData, as.numeric(Returned) ~ PredictedNID))
aic_id = c(mean(subjectData$modelAIC), mean(subjectData$AIC_NID))
qplot(y = aic_id,
x = as.factor(c('Individual Differences', 'No Individual Differences')),
fill = as.factor(c('Individual Differences', 'No Individual Differences')),
color = '',
geom = 'col') +
labs(x = 'Model', y = 'AIC', fill = NULL) + lims(y = c(-5, 155)) +
theme_minimal() +
geom_signif(comparisons = list(c('Individual Differences', 'No Individual Differences')), y_position = 135, textsize = 0, tip_length = 0.15)+
annotate("text", x = 1.5, y = 135,
label = "p = 0.18", vjust = -1, size = 4) +
scale_fill_manual(values = c(rgb(218, 165, 32, maxColorValue = 255), rgb(132.5, 132.5, 132.5, maxColorValue = 255))) +
scale_color_manual(values = c(rgb(0, 0, 0, maxColorValue = 255)))
result = fmincon(@(params) obj_function(params, trialData), initial_params, [], [], [], [], lower_bounds, upper_bounds);
trialData.PredictedNID = NaN(1, length(trialData.Subject));
for i = 1:length(trialData.Subject)
if trialData.Investment(i) > 10
Choices = 0:round((trialData.Investment(i) * trialData.Multiplier(i))/10):(trialData.Investment(i) * trialData.Multiplier(i));
else
Choices = 0:1:(trialData.Investment(i) * trialData.Multiplier(i));
end
Utility = NaN(1, length(Choices));
for n = 1:length(Choices)
Utility(n) = utility(result(1), result(2), ...
payout_maximization(trialData.Investment(i), trialData.Multiplier(i), Choices(n)), ...
guilt(trialData.Investment(i), 4, Choices(n), trialData.Multiplier(i)), ...
inequity(trialData.Investment(i), trialData.Multiplier(i), Choices(n), 10));
end
[~, maxIndex] = max(Utility);
trialData.PredictedNID(i) = Choices(maxIndex);
end
subjectData.SS_NID = NaN(1, length(subjectData.SubjectID));
for i = 1:length(subjectData.SubjectID)
trials = find(subjectData.SubjectID(i) == trialData.Subject);
subjectData.SS_NID(i) = sum((trialData.Returned(trials) - trialData.PredictedNID(trials)).^2);
end
subjectData.AIC_NID = length(df.Investment) * log(subjectData.SS_NID/length(df.Investment)) + 2 * (2/length(subjectData.SubjectID));
ttest(subjectData.modelAIC, subjectData.AIC_NID);
lm_result = fitlm(trialData, 'Returned ~ PredictedNID');
disp(lm_result);
aic_id = [mean(subjectData.modelAIC), mean(subjectData.AIC_NID)];
figure;
bar(categorical({'Individual Differences', 'No Individual Differences'}), aic_id, 'FaceColor', [0.85 0.85 0.85]);
ylabel('AIC');
ylim([-5 155]);
hold on;
sigstar({'Individual Differences', 'No Individual Differences'}, [0.15, 135, 1.5, 135], [0, 0, 0]);
text(1.5, 135, 'p = 0.18', 'VerticalAlignment', 'top', 'HorizontalAlignment', 'center', 'FontSize', 10);
hold off;
result = minimize(lambda params: obj_function(params, trialData), initial_params, bounds=list(zip(lower_bounds, upper_bounds)))
trialData['PredictedNID'] = np.nan
for i in range(1, len(trialData['Subject']) + 1):
if trialData['Investment'].iloc[i - 1] > 10:
Choices = np.arange(0, (trialData['Investment'].iloc[i - 1] * trialData['Multiplier'].iloc[i - 1]),
round((trialData['Investment'].iloc[i - 1] * trialData['Multiplier'].iloc[i - 1])/10))
else:
Choices = np.arange(0, (trialData['Investment'].iloc[i - 1] * trialData['Multiplier'].iloc[i - 1]), 1)
Utility = np.zeros(len(Choices))
for n in range(len(Choices)):
Utility[n] = utility(result.x[0], result.x[1],
payout_maximization(trialData['Investment'].iloc[i - 1], trialData['Multiplier'].iloc[i - 1], Choices[n]),
guilt(trialData['Investment'].iloc[i - 1], 4, Choices[n], trialData['Multiplier'].iloc[i - 1]),
inequity(trialData['Investment'].iloc[i - 1], trialData['Multiplier'].iloc[i - 1], Choices[n], 10))
correct_choice = Choices[np.argmax(Utility)]
trialData.at[i - 1, 'PredictedNID'] = correct_choice
subjectData['SS_NID'] = np.nan
for i in range(1, len(subjectData['SubjectID']) + 1):
trials = trialData[trialData['Subject'] == subjectData['SubjectID'].iloc[i - 1]]
subjectData.at[i - 1, 'SS_NID'] = np.sum((trials['Returned'].to_numpy() - trials['PredictedNID'].to_numpy())**2)
subjectData['AIC_NID'] = len(df['Investment']) * np.log(subjectData['SS_NID']/len(df['Investment'])) + 2 * (2/len(subjectData['SubjectID']))
ttest_rel(subjectData['modelAIC'], subjectData['AIC_NID'])
lm_result = sm.OLS(trialData['Returned'], sm.add_constant(trialData['PredictedNID'])).fit()
print(lm_result.summary())
aic_id = [np.mean(subjectData['modelAIC']), np.mean(subjectData['AIC_NID'])]
plt.bar(['Individual Differences', 'No Individual Differences'], aic_id, color=[0.85, 0.85, 0.85])
plt.ylabel('AIC')
plt.ylim([-5, 155])
plt.xticks(rotation=45, ha='right')
plt.text(1.5, 135, 'p = 0.18', va='bottom', ha='center', fontsize=10)
plt.show()
Tutorial 2 - Galvan & Sanfey, 2024
Embodying No Individual Differences
trialData$PredictedNID = vector('numeric', length(trialData$SubjectID))
for (k in 1:length(conditions)){
z = which(trialData$condition == conditions[j])
df = trialData[z, c(6, 12:20, 2)]
result = fmincon(obj_function,x0 = initial_params, A = NULL, b = NULL, Aeq = NULL, beq = NULL,
lb = lower_bounds, ub = upper_bounds,
df = df)
for (i in 1:length(df)){
Utility = vector('numeric', length(Choices))
for (n in 1:length(Choices)){
Utility[n] = utility(theta = result$par[1],
phi = result$par[2],
Equity = equity(new_value(df[i, 1:10], choices[n]), df[i, 1:10], choices[n]),
Equality = equality(new_value(df[i, 1:10], choices[n]), df[i, 1:10], choices[n]),
Payout = payout(new_value(df[i, 1], choices[n]), df[i, 1], choices[n]))
}
trialData$PredictedNID[z[i]] = Choices[which(Utility == max(Utility))]
}
}
subjectData$SSNIDMerit = vector('numeric', length(subjectDatasubjectData$SubjectID))
subjectData$SSNIDEntitlement = vector('numeric', length(subjectDatasubjectData$SubjectID))
subjectData$SSNIDCorruption = vector('numeric', length(subjectDatasubjectData$SubjectID))
subjectData$SSNIDLuck = vector('numeric', length(subjectDatasubjectData$SubjectID))
for (i in 1:length(subjectData$SubjectID)){
trialsMerit = which(subjectData$SubjectID[i] == trialData$SubjectID && 'merit' == trialData$Condition)
trialsEntitlement = which(subjectData$SubjectID[i] == trialData$SubjectID && 'entitlement' == trialData$Condition)
trialsCorruption = which(subjectData$SubjectID[i] == trialData$SubjectID && 'corruption' == trialData$Condition)
trialsLuck = which(subjectData$SubjectID[i] == trialData$SubjectID && 'luck' == trialData$Condition)
subjectData$SSNIDMerit[i] = sum((trialData$observedTaxRate[trialsMerit] - trialData$PredictedNID[trialsMerit])**2)
subjectData$SSNIDEntitlement[i] = sum((trialData$observedTaxRate[trialsEntitlement] - trialData$PredictedNID[trialsEntitlement])**2)
subjectData$SSNIDCorruption[i] = sum((trialData$observedTaxRate[trialsCorruption] - trialData$PredictedNID[trialsCorruption])**2)
subjectData$SSNIDLuck[i] = sum((trialData$observedTaxRate[trialsLuck] - trialData$PredictedNID[trialsLuck])**2)
}
subjectData$AICNIDMerit = length(trialsMerit) * log(subjectData$SSNIDMerit/length(trialsMerit)) + 2 * (2/length(subjectData$SubjectID))
subjectData$AICNIDEntitlement = length(trialsEntitlement) * log(subjectData$SSNIDEntitlement/length(trialsEntitlement)) + 2 * (2/length(subjectData$SubjectID))
subjectData$AICNIDCorruption = length(trialsCorruption) * log(subjectData$SSNIDCorruption/length(trialsCorruption)) + 2 * (2/length(subjectData$SubjectID))
subjectData$AICNIDLuck = length(trialsLuck) * log(subjectData$SSNIDLuck/length(trialsLuck)) + 2 * (2/length(subjectData$SubjectID))
t.test(subjectData$AICMerit, subjectData$AICNIDMerit, paired = T, alternative = 'less', conf.int = (1 - alpha))
t.test(subjectData$AICEntitlement, subjectData$AICNIDEntitlement, paired = T, alternative = 'less', conf.int = (1 - alpha))
t.test(subjectData$AICCorruption, subjectData$AICNIDCorruption, paired = T, alternative = 'less', conf.int = (1 - alpha))
t.test(subjectData$AICLuck, subjectData$AICNIDLuck, paired = T, alternative = 'less', conf.int = (1 - alpha))
trialData.PredictedNID = zeros(1, length(trialData.SubjectID));
for j = 1:length(conditions)
z = find(trialData.condition == conditions(j));
df = trialData(z, [6, 12:20, 2]);
result = fmincon(@(params) obj_function(params, df), initial_params, [], [], [], [], lower_bounds, upper_bounds);
for i = 1:length(df)
Utility = zeros(1, length(Choices));
for n = 1:length(Choices)
Utility(n) = utility(result(1), result(2), ...
equity(new_value(df(i, 1:10), Choices(n)), df(i, 1:10), Choices(n)), ...
equality(new_value(df(i, 1:10), Choices(n)), df(i, 1:10), Choices(n)), ...
payout(new_value(df(i, 1), Choices(n)), df(i, 1), Choices(n)));
end
trialData.PredictedNID(z(i)) = Choices(Utility == max(Utility));
end
end
subjectData.SSNIDMerit = zeros(1, length(subjectData.SubjectID));
subjectData.SSNIDEntitlement = zeros(1, length(subjectData.SubjectID));
subjectData.SSNIDCorruption = zeros(1, length(subjectData.SubjectID));
subjectData.SSNIDLuck = zeros(1, length(subjectData.SubjectID));
for i = 1:length(subjectData.SubjectID)
trialsMerit = find(subjectData.SubjectID(i) == trialData.SubjectID & strcmp('merit', trialData.Condition));
trialsEntitlement = find(subjectData.SubjectID(i) == trialData.SubjectID & strcmp('entitlement', trialData.Condition));
trialsCorruption = find(subjectData.SubjectID(i) == trialData.SubjectID & strcmp('corruption', trialData.Condition));
trialsLuck = find(subjectData.SubjectID(i) == trialData.SubjectID & strcmp('luck', trialData.Condition));
subjectData.SSNIDMerit(i) = sum((trialData.observedTaxRate(trialsMerit) - trialData.PredictedNID(trialsMerit)).^2);
subjectData.SSNIDEntitlement(i) = sum((trialData.observedTaxRate(trialsEntitlement) - trialData.PredictedNID(trialsEntitlement)).^2);
subjectData.SSNIDCorruption(i) = sum((trialData.observedTaxRate(trialsCorruption) - trialData.PredictedNID(trialsCorruption)).^2);
subjectData.SSNIDLuck(i) = sum((trialData.observedTaxRate(trialsLuck) - trialData.PredictedNID(trialsLuck)).^2);
end
subjectData.AICNIDMerit = length(trialsMerit) * log(subjectData.SSNIDMerit/length(trialsMerit)) + 2 * (2/length(subjectData.SubjectID));
subjectData.AICNIDEntitlement = length(trialsEntitlement) * log(subjectData.SSNIDEntitlement/length(trialsEntitlement)) + 2 * (2/length(subjectData.SubjectID));
subjectData.AICNIDCorruption = length(trialsCorruption) * log(subjectData.SSNIDCorruption/length(trialsCorruption)) + 2 * (2/length(subjectData.SubjectID));
subjectData.AICNIDLuck = length(trialsLuck) * log(subjectData.SSNIDLuck/length(trialsLuck)) + 2 * (2/length(subjectData.SubjectID));
alpha = 0.05;
ttest(subjectData.AICMerit, subjectData.AICNIDMerit, 'Tail', 'left', 'Alpha', alpha);
ttest(subjectData.AICEntitlement, subjectData.AICNIDEntitlement, 'Tail', 'left', 'Alpha', alpha);
ttest(subjectData.AICCorruption, subjectData.AICNIDCorruption, 'Tail', 'left', 'Alpha', alpha);
ttest(subjectData.AICLuck, subjectData.AICNIDLuck, 'Tail', 'left', 'Alpha', alpha);
trialData['PredictedNID'] = np.zeros(len(trialData['SubjectID']))
for j in range(len(conditions)):
z = np.where(trialData['condition'] == conditions[j])[0]
df = trialData.iloc[z, [5, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1]]
result = minimize(lambda params: obj_function(params, df), initial_params, bounds=list(zip(lower_bounds, upper_bounds)))
for i in range(len(df)):
Utility = np.zeros(len(Choices))
for n in range(len(Choices)):
Utility[n] = utility(result.x[0], result.x[1],
equity(new_value(df.iloc[i, 0:9], Choices[n]), df.iloc[i, 0:9], Choices[n]),
equality(new_value(df.iloc[i, 0:9], Choices[n]), df.iloc[i, 0:9], Choices[n]),
payout(new_value(df.iloc[i, 0], Choices[n]), df.iloc[i, 0], Choices[n]))
trialData.at[z[i], 'PredictedNID'] = Choices[np.argmax(Utility)]
subjectData['SSNIDMerit'] = np.zeros(len(subjectData['SubjectID']))
subjectData['SSNIDEntitlement'] = np.zeros(len(subjectData['SubjectID']))
subjectData['SSNIDCorruption'] = np.zeros(len(subjectData['SubjectID']))
subjectData['SSNIDLuck'] = np.zeros(len(subjectData['SubjectID']))
for i in range(len(subjectData['SubjectID'])):
trialsMerit = np.where((subjectData['SubjectID'][i] == trialData['SubjectID']) & (trialData['Condition'] == 'merit'))[0]
trialsEntitlement = np.where((subjectData['SubjectID'][i] == trialData['SubjectID']) & (trialData['Condition'] == 'entitlement'))[0]
trialsCorruption = np.where((subjectData['SubjectID'][i] == trialData['SubjectID']) & (trialData['Condition'] == 'corruption'))[0]
trialsLuck = np.where((subjectData['SubjectID'][i] == trialData['SubjectID']) & (trialData['Condition'] == 'luck'))[0]
subjectData.at[i, 'SSNIDMerit'] = np.sum((trialData['observedTaxRate'][trialsMerit] - trialData['PredictedNID'][trialsMerit])**2)
subjectData.at[i, 'SSNIDEntitlement'] = np.sum((trialData['observedTaxRate'][trialsEntitlement] - trialData['PredictedNID'][trialsEntitlement])**2)
subjectData.at[i, 'SSNIDCorruption'] = np.sum((trialData['observedTaxRate'][trialsCorruption] - trialData['PredictedNID'][trialsCorruption])**2)
subjectData.at[i, 'SSNIDLuck'] = np.sum((trialData['observedTaxRate'][trialsLuck] - trialData['PredictedNID'][trialsLuck])**2)
subjectData['AICNIDMerit'] = len(trialsMerit) * np.log(subjectData['SSNIDMerit'] / len(trialsMerit)) + 2 * (2 / len(subjectData['SubjectID']))
subjectData['AICNIDEntitlement'] = len(trialsEntitlement) * np.log(subjectData['SSNIDEntitlement'] / len(trialsEntitlement)) + 2 * (2 / len(subjectData['SubjectID']))
subjectData['AICNIDCorruption'] = len(trialsCorruption) * np.log(subjectData['SSNIDCorruption'] / len(trialsCorruption)) + 2 * (2 / len(subjectData['SubjectID']))
subjectData['AICNIDLuck'] = len(trialsLuck) * np.log(subjectData['SSNIDLuck'] / len(trialsLuck)) + 2 * (2 / len(subjectData['SubjectID']))
alpha = 0.05
ttest_rel(subjectData['AICMerit'], subjectData['AICNIDMerit'], alternative='less', nan_policy='omit')
ttest_rel(subjectData['AICEntitlement'], subjectData['AICNIDEntitlement'], alternative='less', nan_policy='omit')
ttest_rel(subjectData['AICCorruption'], subjectData['AICNIDCorruption'], alternative='less', nan_policy='omit')
ttest_rel(subjectData['AICLuck'], subjectData['AICNIDLuck'], alternative='less', nan_policy='omit')
Tutorial 3 - Crockett et al., 2014
Embodying No Individual Differences
resultNID = fmincon(obj_function, x0 = initial_params, lb = lower_bounds, ub = upper_bounds, df = trialData, optimMethod = "OLS")
dfNID = generate_predictions(trialData, resultNID)
sum(dfNID$choseHarm == round(dfNID$ProbHarm))/nrow(dfNID)
altSubjectData$Deviance_NID = 0
for (i in 1:length(included_subjects)){
df = grab_data(included_subjects[i]); if (is.character(df)){next} else {trials = which(included_subjects[i] == dfNID$SubjectID)}
df = dfNID[trials, ]
altSubjectData$Deviance_NID[i] = -2*sum(df$choseHarm * log(df$ProbHarm) + (1 - df$choseHarm) * log(1 - df$ProbHarm))
}
altSubjectData$BIC_NID = as.numeric(altSubjectData$Deviance_NID) + log(152) * 6/(nrow(dfNID))
t.test(subjectData$BIC[-20], altSubjectData$BIC_NID[-20], paired = T)
which(modelBIC > sum(altSubjectData$BIC_NID))
Tutorial 4 - Li et al., 2022
Embodying No Individual Differences
resultNID = fmincon(of_ar, x0 = initial_params[c(1,3:6)], lb = lower_bounds[c(1,3:6)], ub = upper_bounds[c(1,3:6)], df = trialData[2:8], optimMethod = "MLE")
pars = c(resultNID$par[1], 0, resultNID$par[2:5])
trialData$Prob1_NID = generatePredictions(pars, trialData)
sum(trialData$Chose1 == round(trialData$Prob1_NID))/nrow(trialData)
altSubjectData$Deviance_NID = 0
for (i in 1:length(included_subjects)){
trials = which(included_subjects[i] == trialData$SubjectID)
df = trialData[trials, ]
altSubjectData$Deviance_NID[i] = -2*sum(df$Chose1 * log(df$Prob1_NID) + (1 - df$Chose1) * log(1 - df$Prob1_NID))
}
altSubjectData$BIC_NID = as.numeric(altSubjectData$Deviance_NID) + log(65) * 6/(length(included_subjects))
t.test(altSubjectData$BIC_M5, altSubjectData$BIC_NID, paired = T)
which(modelBIC > sum(altSubjectData$BIC_NID))