Main Analyses - Consistent sample

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Published

last rendered on: Aug 11, 2025

Show the code

# Change the following values depending on the session
date <- "2025-05-19"

# Load data file
All_Measures_Per_Trial <- utils::read.csv(paste("../preprocessed data/All_Measures_Per_Trial_", date, ".csv", sep=""))

#Filter consistent diet
All_Measures_Per_Trial <- All_Measures_Per_Trial %>%
  mutate(vegetarianism = case_when(
    vege == 1 & vege_Prolific == 1 ~ 1,
    vege == 0 & vege_Prolific == 0 ~ 0,
    TRUE ~ NA_real_
  ))

1 Descriptive statistics

Group Descriptive Statistics with t-test Results
Variable	Omnivore_Mean	Omnivore_SD	Vegetarian_Mean	Vegetarian_SD	t_value	p_value
Sample size	172	NA	196	NA	NA	NA
Age	40	10.569	38.398	11.573	1.388	0.166
Education	4.68	1.138	4.98	1.114	-2.543	0.011
Income	4.238	1.599	4.036	1.690	1.181	0.238

Gender Distribution by Group (Chi² p-value = 0.083)
	Omnivore	Vegetarian
W	80	110
M	92	86

Proportion of pro-environmental decisions
Variable	Omnivore_Mean	Omnivore_SD	Vegetarian_Mean	Vegetarian_SD
Decision	0.51	0.36	0.57	0.38

Number of participants consistently choosing the same option
Chosen.option	Omnivores	Vegetarians
Always pro-self	30	32
Always pro-environmental	23	45

Environmental attitude score and perceived efficacy of CO2 certificates
Variable	Omnivore_Mean	Omnivore_SD	Vegetarian_Mean	Vegetarian_SD	t_value	p_value
NEP score	54.808	9.434	56.694	9.291	-1.927	0.055
Certificates efficacy	3.326	1.081	3.653	1.004	-2.998	0.003

Process tracing measures
Variable	Omnivore_Mean	Omnivore_SD	Vegetarian_Mean	Vegetarian_SD
Delta duration on attributes	0.02	0.43	0.11	0.46
Delta duration on options	0.00	0.09	0.01	0.10
First acquisition on CO2	0.51	0.44	0.57	0.43
Last acquisition on CO2	0.46	0.34	0.52	0.35
Payne index	-0.53	0.34	-0.44	0.44

2 Preregistered main analyses

2.1 RQ1: diet predicts pro-environmental decision

2.1.1 Main models

Show the code

M1.1 <- glmer(
  formula = decision ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

M1.2 <- glmer(
  formula = decision ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

M1.3 <- glmer(
  formula = decision ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

To compare vegetarians and non-vegetarians in the proportion of pro-environmental decisions made in the carbon emission task (RQ1), we run mixed-effects logistic regressions with decision as the dependent variable and random intercepts for participants and trials.

In the first model (M1.1), we include vegetarianism (coded as 1 for vegetarians, 0 for non-vegetarians) as the main predictor of interest. Additionally, attribute position (coded as 1 if carbon emissions are displayed at the top of the matrix, 0 if at the bottom) and option position (coded as 1 if the pro-environmental option is on the left, 0 if on the right) are also included as fixed effects to account for potential display effects.
In the second model (M1.2), we test the sensitivity of results of M1.1 to the addition of control variables related to the task by adding fixed effects for percentage difference in carbon emissions (ranging from 1 [10%] to 5 [100%]), percentage difference in bonus payment (ranging from 1 [10%] to 5 [100%]) and sequential position of the trial (ranging from 1 to 25).
In the third model (M1.3), we test the sensitivity of results of M1.1 to the addition of demographic control variables by adding fixed effects for sex, age, education, income, environmental attitudes (assessed by the New Ecological Paradigm), and beliefs in the efficacy of European Union Emission Trading System (measured on a 5-point Likert scale from 1=not effective at all to 5=very effective).

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.39	0.13 – 1.20	0.099
vegetarianism	3.36	1.26 – 8.96	0.015
CB carbonUp	4.29	1.61 – 11.42	0.004
CB selfishLeft	0.99	0.85 – 1.14	0.840
Random Effects
σ²	3.29
τ₀₀ _subject	21.38
τ₀₀ _{trialNum_fixed}	3.09
ICC	0.88
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.030 / 0.885

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.72	0.24 – 2.19	0.565
vegetarianism	3.35	1.26 – 8.93	0.016
CB carbonUp	4.29	1.61 – 11.41	0.004
CB selfishLeft	0.99	0.85 – 1.14	0.846
carbon level	2.07	1.78 – 2.41	<0.001
bonus level	0.39	0.34 – 0.46	<0.001
trialNum centred	1.00	0.99 – 1.01	0.338
Random Effects
σ²	3.29
τ₀₀ _subject	21.36
τ₀₀ _{trialNum_fixed}	0.25
ICC	0.87
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.128 / 0.885

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.01	0.00 – 0.16	0.002
vegetarianism	1.72	0.63 – 4.65	0.289
CB carbonUp	4.27	1.61 – 11.33	0.004
CB selfishLeft	0.98	0.84 – 1.15	0.845
gender	2.32	0.82 – 6.54	0.112
age centred	1.01	0.97 – 1.05	0.697
education level	1.09	0.70 – 1.68	0.711
income	0.90	0.66 – 1.22	0.491
CertificatesEff	3.02	1.85 – 4.93	<0.001
NEP score centred	1.16	1.09 – 1.22	<0.001
Random Effects
σ²	3.29
τ₀₀ _subject	18.87
τ₀₀ _{trialNum_fixed}	3.10
ICC	0.87
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.150 / 0.889

Data: All_Measures_Per_Trial
Models:
M1.1: decision ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject) + (1 | trialNum_fixed)
M1.2: decision ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject) + (1 | trialNum_fixed)
M1.3: decision ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject) + (1 | trialNum_fixed)
     npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)    
M1.1    6 5737.1 5779.7 -2862.6   5725.1                         
M1.2    9 5683.7 5747.5 -2832.8   5665.7 59.413  3  7.846e-13 ***
M1.3   12 5694.6 5779.7 -2835.3   5670.6  0.000  3          1    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.1.2 Post Hoc analyses

If any control variables showed significant effects, we tested for potential interactions with vegetarianism.

Show the code

#Post hoc on significant covariates for M1.1
M1_CarbonUp <- glmer(
  formula = decision ~ vegetarianism * CB_carbonUp + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)

tab_model(M1_CarbonUp, transform = "exp")

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.45	0.13 – 1.60	0.218
vegetarianism	2.51	0.61 – 10.24	0.200
CB carbonUp	3.17	0.76 – 13.24	0.113
vegetarianism × CB carbonUp	1.77	0.25 – 12.53	0.569
Random Effects
σ²	3.29
τ₀₀ _subject	21.37
τ₀₀ _{trialNum_fixed}	3.09
ICC	0.88
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.031 / 0.885

Show the code

#Post hoc on significant covariates for M1.2
M1_Carbon <- glmer(
  formula = decision ~ vegetarianism * carbon_level + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
  
tab_model(M1_Carbon, transform = "exp")

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.08	0.02 – 0.34	0.001
vegetarianism	4.90	1.73 – 13.86	0.003
carbon level	2.24	1.50 – 3.35	<0.001
vegetarianism × carbon level	0.85	0.77 – 0.95	0.004
Random Effects
σ²	3.29
τ₀₀ _subject	21.85
τ₀₀ _{trialNum_fixed}	2.03
ICC	0.88
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.048 / 0.885

Simple slopes analyses were conducted to interpret the interactions.

Pairwise contrasts at each carbon difference
carbon_level	Contrast	Odds Ratio	95% CI		Signif.	p-value
1	vegetarianism0 - vegetarianism1	0.24	0.09	0.66	**	0.00558
2	vegetarianism0 - vegetarianism1	0.28	0.10	0.76	*	0.01226
3	vegetarianism0 - vegetarianism1	0.33	0.12	0.88	*	0.02763
4	vegetarianism0 - vegetarianism1	0.39	0.14	1.04		0.06087
5	vegetarianism0 - vegetarianism1	0.45	0.16	1.25		0.12528

Show the code

#Post hoc on significant covariates for M1.2
M1_Bonus <- glmer(
  formula = decision ~ vegetarianism * bonus_level + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
  
tab_model(M1_Bonus, transform = "exp")

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	20.00	5.39 – 74.27	<0.001
vegetarianism	1.51	0.53 – 4.32	0.441
bonus level	0.35	0.25 – 0.49	<0.001
vegetarianism × bonus level	1.25	1.12 – 1.41	<0.001
Random Effects
σ²	3.29
τ₀₀ _subject	21.80
τ₀₀ _{trialNum_fixed}	1.34
ICC	0.88
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.072 / 0.885

Simple slopes analyses were conducted to interpret the interactions.

Pairwise contrasts at each bonus percentage difference
bonus_level	Contrast	Odds Ratio	95% CI		Signif.	p-value
1	vegetarianism0 - vegetarianism1	0.53	0.19	1.46		0.21808
2	vegetarianism0 - vegetarianism1	0.42	0.16	1.14		0.08857
3	vegetarianism0 - vegetarianism1	0.34	0.12	0.90	*	0.03033
4	vegetarianism0 - vegetarianism1	0.27	0.10	0.72	**	0.00930
5	vegetarianism0 - vegetarianism1	0.21	0.08	0.59	**	0.00277

Show the code

#Post hoc on significant covariates for M1.3
M1_Certif <- glmer(
  formula = decision ~ vegetarianism * CertificatesEff + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
  
tab_model(M1_Certif, transform = "exp")

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.01	0.00 – 0.08	<0.001
vegetarianism	116.86	2.94 – 4641.44	0.011
CertificatesEff	4.53	2.18 – 9.40	<0.001
vegetarianism × CertificatesEff	0.33	0.12 – 0.90	0.030
Random Effects
σ²	3.29
τ₀₀ _subject	21.12
τ₀₀ _{trialNum_fixed}	3.09
ICC	0.88
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.057 / 0.887

Simple slopes analyses were conducted to interpret the interactions.

Pairwise contrasts at each perceived efficacy of CO2 certificates
CertificatesEff	Contrast	Odds Ratio	95% CI		Signif.	p-value
1	vegetarianism0 - vegetarianism1	0.03	0.00	0.40	**	0.00882
2	vegetarianism0 - vegetarianism1	0.08	0.01	0.50	**	0.00683
3	vegetarianism0 - vegetarianism1	0.24	0.08	0.76	*	0.01522
4	vegetarianism0 - vegetarianism1	0.74	0.24	2.29		0.59779
5	vegetarianism0 - vegetarianism1	2.25	0.37	13.74		0.38148

Show the code

#Post hoc on significant covariates for M1.3
M1_NEP <- glmer(
  formula = decision ~ vegetarianism * NEP_score_centred + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
  
tab_model(M1_NEP, transform = "exp")

	decision
Predictors	Odds Ratios	CI	p
(Intercept)	0.89	0.33 – 2.41	0.822
vegetarianism	2.33	0.86 – 6.32	0.096
NEP score centred	1.15	1.07 – 1.25	<0.001
vegetarianism × NEP score centred	1.04	0.93 – 1.16	0.493
Random Effects
σ²	3.29
τ₀₀ _subject	20.21
τ₀₀ _{trialNum_fixed}	3.09
ICC	0.88
N _subject	368
N _{trialNum_fixed}	25
Observations	8908
Marginal R² / Conditional R²	0.091 / 0.888

2.2 RQ2a - diet predicts ΔDuration on attributes

2.2.1 Main models

Show the code

M2a.1 <- lmer(
  formula = delta_duration_att ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject),
  data = All_Measures_Per_Trial
)

M2a.2 <- lmer(
  formula = delta_duration_att ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject),
  data = All_Measures_Per_Trial
)

M2a.3 <- lmer(
  formula = delta_duration_att ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject),
  data = All_Measures_Per_Trial
)

To compare vegetarians and non-vegetarians in the proportion of visiting time spent on carbon boxes compared to bonus boxes (RQ2a), we run mixed-effects models with ΔDuration on attributes as the dependent variable and random intercepts for participants and trials.

In the first model (M2A.1), we include vegetarianism (coded as 1 for vegetarians, 0 for non-vegetarians) as the main predictor of interest. Additionally, attribute position (coded as 1 if carbon emissions are displayed at the top of the matrix, 0 if at the bottom) and option position (coded as 1 if the pro-environmental option is on the left, 0 if on the right) are also included as fixed effects to account for potential display effects.
In the second model (M2A.2), we test the sensitivity of results of M2A.1 to the addition of control variables related to the task by adding fixed effects for percentage difference in carbon emissions (ranging from 1 [10%] to 5 [100%]), percentage difference in bonus payment (ranging from 1 [10%] to 5 [100%]) and sequential position of the trial (ranging from 1 to 25).
In the third model (M2A.3), we test the sensitivity of results of M2A.1 to the addition of demographic control variables by adding fixed effects for sex, age, education, income, environmental attitudes (assessed by the New Ecological Paradigm), and beliefs in the efficacy of European Union Emission Trading System (measured on a 5-point Likert scale from 1=not effective at all to 5=very effective).

	delta_duration_att
Predictors	Estimates	CI	p
(Intercept)	0.02	-0.07 – 0.10	0.715
vegetarianism	0.10	0.01 – 0.19	0.038
CB carbonUp	0.01	-0.08 – 0.10	0.889
CB selfishLeft	0.00	-0.01 – 0.01	0.958
Random Effects
σ²	0.06
τ₀₀ _subject	0.19
ICC	0.76
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.009 / 0.761

	delta_duration_att
Predictors	Estimates	CI	p
(Intercept)	0.01	-0.07 – 0.10	0.782
vegetarianism	0.10	0.01 – 0.19	0.038
CB carbonUp	0.01	-0.08 – 0.10	0.889
CB selfishLeft	0.00	-0.01 – 0.01	0.933
carbon level	-0.00	-0.00 – 0.00	0.701
bonus level	0.00	-0.00 – 0.01	0.317
trialNum centred	0.00	0.00 – 0.00	<0.001
Random Effects
σ²	0.06
τ₀₀ _subject	0.19
ICC	0.76
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.009 / 0.761

	delta_duration_att
Predictors	Estimates	CI	p
(Intercept)	-0.17	-0.44 – 0.10	0.230
vegetarianism	0.05	-0.04 – 0.15	0.242
CB carbonUp	-0.00	-0.09 – 0.08	0.931
CB selfishLeft	0.00	-0.01 – 0.01	0.953
gender	0.05	-0.04 – 0.14	0.304
age centred	0.00	-0.00 – 0.01	0.180
education level	0.00	-0.04 – 0.04	0.875
income	-0.01	-0.03 – 0.02	0.618
CertificatesEff	0.05	0.01 – 0.10	0.013
NEP score centred	0.01	0.01 – 0.02	<0.001
Random Effects
σ²	0.06
τ₀₀ _subject	0.18
ICC	0.74
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.073 / 0.763

Data: All_Measures_Per_Trial
Models:
M2a.1: delta_duration_att ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject)
M2a.2: delta_duration_att ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject)
M2a.3: delta_duration_att ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject)
      npar    AIC    BIC   logLik deviance  Chisq Df Pr(>Chisq)    
M2a.1    6 2036.5 2079.1 -1012.26   2024.5                         
M2a.2    9 2026.0 2089.8 -1003.98   2008.0 16.563  3  0.0008692 ***
M2a.3   12 2015.5 2100.7  -995.78   1991.5 16.414  3  0.0009327 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.2.2 Post Hoc analyses

If any control variables showed significant effects, we tested for potential interactions with vegetarianism.

Show the code

#Post hoc on significant covariates for M2a.2
M2a_trialNum <- lmer(
  formula = delta_duration_att ~ vegetarianism * trialNum_centred + (1 | subject),
  data = All_Measures_Per_Trial
)
  
tab_model(M2a_trialNum, transform = NULL)

	delta_duration_att
Predictors	Estimates	CI	p
(Intercept)	0.02	-0.05 – 0.09	0.573
vegetarianism	0.10	0.01 – 0.19	0.038
trialNum centred	0.00	-0.00 – 0.00	0.428
vegetarianism × trialNum centred	0.00	0.00 – 0.00	0.009
Random Effects
σ²	0.06
τ₀₀ _subject	0.19
ICC	0.76
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.009 / 0.761

Simple slopes analyses were conducted to interpret the interactions.

Pairwise contrasts at specific trial number
trialNum	Contrast	Estimate	95% CI		Signif.	p-value
1	vegetarianism1 - vegetarianism0	0.07	-0.02	0.16		0.1229
5	vegetarianism1 - vegetarianism0	0.08	-0.01	0.17		0.0850
10	vegetarianism1 - vegetarianism0	0.09	0.00	0.18		0.0522
15	vegetarianism1 - vegetarianism0	0.10	0.01	0.19	*	0.0316
20	vegetarianism1 - vegetarianism0	0.11	0.02	0.20	*	0.0191
25	vegetarianism1 - vegetarianism0	0.12	0.03	0.21	*	0.0117

Show the code

#Post hoc on significant covariates for M2a.3
M2a_Certif <- lmer(
  formula = delta_duration_att ~ vegetarianism * CertificatesEff + (1 | subject),
  data = All_Measures_Per_Trial
)
  
tab_model(M2a_Certif, transform = NULL)

	delta_duration_att
Predictors	Estimates	CI	p
(Intercept)	-0.27	-0.49 – -0.06	0.011
vegetarianism	0.37	0.06 – 0.69	0.020
CertificatesEff	0.09	0.03 – 0.15	0.004
vegetarianism × CertificatesEff	-0.08	-0.17 – 0.00	0.057
Random Effects
σ²	0.06
τ₀₀ _subject	0.19
ICC	0.76
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.025 / 0.761

Show the code

#Post hoc on significant covariates for M2a.3
M2a_NEP <- lmer(
  formula = delta_duration_att ~ vegetarianism * NEP_score_centred + (1 | subject),
  data = All_Measures_Per_Trial
)
  
tab_model(M2a_NEP, transform = NULL)

	delta_duration_att
Predictors	Estimates	CI	p
(Intercept)	0.02	-0.04 – 0.09	0.470
vegetarianism	0.07	-0.02 – 0.16	0.106
NEP score centred	0.01	0.00 – 0.02	0.001
vegetarianism × NEP score centred	0.00	-0.01 – 0.01	0.869
Random Effects
σ²	0.06
τ₀₀ _subject	0.18
ICC	0.75
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.057 / 0.761

2.3 RQ2b - diet predicts ΔDuration on options

2.3.1 Main models

Show the code

M2b.1 <- lmer(
  formula = delta_duration_opt ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject),
  data = All_Measures_Per_Trial
)

M2b.2 <- lmer(
  formula = delta_duration_opt ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject),
  data = All_Measures_Per_Trial
)

M2b.3 <- lmer(
  formula = delta_duration_opt ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject),
  data = All_Measures_Per_Trial
)

To compare vegetarians and non-vegetarians in the proportion of visiting time spent on the pro-environmental option compared to pro-self option (RQ2b), we run mixed-effects models with ΔDuration on options as the dependent variable and random intercepts for participants and trials.

In the first model (M2B.1), we include vegetarianism (coded as 1 for vegetarians, 0 for non-vegetarians) as the main predictor of interest. Additionally, attribute position (coded as 1 if carbon emissions are displayed at the top of the matrix, 0 if at the bottom) and option position (coded as 1 if the pro-environmental option is on the left, 0 if on the right) are also included as fixed effects to account for potential display effects.
In the second model (M2B.2), we test the sensitivity of results of M2B.1 to the addition of control variables related to the task by adding fixed effects for percentage difference in carbon emissions (ranging from 1 [10%] to 5 [100%]), percentage difference in bonus payment (ranging from 1 [10%] to 5 [100%]) and sequential position of the trial (ranging from 1 to 25).
In the third model (M2B.3), we test the sensitivity of results of M2B.1 to the addition of demographic control variables by adding fixed effects for sex, age, education, income, environmental attitudes (assessed by the New Ecological Paradigm), and beliefs in the efficacy of European Union Emission Trading System (measured on a 5-point Likert scale from 1=not effective at all to 5=very effective).

	delta_duration_opt
Predictors	Estimates	CI	p
(Intercept)	-0.02	-0.04 – -0.00	0.044
vegetarianism	0.02	-0.00 – 0.04	0.071
CB carbonUp	0.03	0.01 – 0.05	0.002
CB selfishLeft	-0.00	-0.01 – 0.01	0.886
Random Effects
σ²	0.04
τ₀₀ _subject	0.01
ICC	0.14
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.006 / 0.143

	delta_duration_opt
Predictors	Estimates	CI	p
(Intercept)	-0.00	-0.03 – 0.02	0.699
vegetarianism	0.02	-0.00 – 0.04	0.073
CB carbonUp	0.03	0.01 – 0.05	0.002
CB selfishLeft	-0.00	-0.01 – 0.01	0.895
carbon level	0.01	0.01 – 0.01	<0.001
bonus level	-0.01	-0.02 – -0.01	<0.001
trialNum centred	-0.00	-0.00 – -0.00	0.030
Random Effects
σ²	0.04
τ₀₀ _subject	0.01
ICC	0.14
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.017 / 0.155

	delta_duration_opt
Predictors	Estimates	CI	p
(Intercept)	-0.05	-0.11 – 0.01	0.088
vegetarianism	0.01	-0.01 – 0.03	0.347
CB carbonUp	0.03	0.01 – 0.05	0.002
CB selfishLeft	-0.00	-0.01 – 0.01	0.901
gender	0.02	-0.00 – 0.04	0.109
age centred	0.00	-0.00 – 0.00	0.291
education level	-0.00	-0.01 – 0.01	0.834
income	-0.00	-0.01 – 0.00	0.283
CertificatesEff	0.01	0.00 – 0.02	0.006
NEP score centred	0.00	0.00 – 0.00	0.006
Random Effects
σ²	0.04
τ₀₀ _subject	0.01
ICC	0.13
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.017 / 0.145

Data: All_Measures_Per_Trial
Models:
M2b.1: delta_duration_opt ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject)
M2b.2: delta_duration_opt ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject)
M2b.3: delta_duration_opt ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject)
      npar     AIC     BIC logLik deviance  Chisq Df Pr(>Chisq)    
M2b.1    6 -1800.0 -1757.5 906.02  -1812.0                         
M2b.2    9 -1913.6 -1849.7 965.79  -1931.6 119.54  3     <2e-16 ***
M2b.3   12 -1812.8 -1727.7 918.42  -1836.8   0.00  3          1    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.4 RQ2c - diet predicts first visit

2.4.1 Main models

Show the code

M2c.1 <- glmer(
  formula = first_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

M2c.2 <- glmer(
  formula = first_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

M2c.3 <- glmer(
  formula = first_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

To compare vegetarians and non-vegetarians on the likelihood of performing their first visit on a carbon box (RQ2c), we run mixed-effects models with first visit as the dependent variable and random intercepts for participants and trials.

In the first model (M2C.1), we include vegetarianism (coded as 1 for vegetarians, 0 for non-vegetarians) as the main predictor of interest. Additionally, attribute position (coded as 1 if carbon emissions are displayed at the top of the matrix, 0 if at the bottom) and option position (coded as 1 if the pro-environmental option is on the left, 0 if on the right) are also included as fixed effects to account for potential display effects.
In the second model (M2C.2), we test the sensitivity of results of M2C.1 to the addition of control variables related to the task by adding fixed effects for percentage difference in carbon emissions (ranging from 1 [10%] to 5 [100%]), percentage difference in bonus payment (ranging from 1 [10%] to 5 [100%]) and sequential position of the trial (ranging from 1 to 25).
In the third model (M2C.3), we test the sensitivity of results of M2C.1 to the addition of demographic control variables by adding fixed effects for sex, age, education, income, environmental attitudes (assessed by the New Ecological Paradigm), and beliefs in the efficacy of European Union Emission Trading System (measured on a 5-point Likert scale from 1=not effective at all to 5=very effective).

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	0.03	0.01 – 0.07	<0.001
vegetarianism	3.06	1.34 – 6.97	0.008
CB carbonUp	598.45	240.17 – 1491.20	<0.001
CB selfishLeft	1.05	0.89 – 1.24	0.548
Random Effects
σ²	3.29
τ₀₀ _subject	12.18
ICC	0.79
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.401 / 0.873

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	0.04	0.02 – 0.08	<0.001
vegetarianism	3.07	1.34 – 7.03	0.008
CB carbonUp	617.41	246.52 – 1546.34	<0.001
CB selfishLeft	1.06	0.90 – 1.25	0.508
carbon level	0.95	0.90 – 1.01	0.095
bonus level	1.00	0.94 – 1.06	0.981
trialNum centred	1.02	1.01 – 1.03	<0.001
Random Effects
σ²	3.29
τ₀₀ _subject	12.29
ICC	0.79
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.402 / 0.874

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	0.00	0.00 – 0.04	<0.001
vegetarianism	2.30	1.00 – 5.25	0.049
CB carbonUp	543.24	224.35 – 1315.42	<0.001
CB selfishLeft	1.05	0.89 – 1.24	0.546
gender	2.56	1.08 – 6.07	0.032
age centred	1.01	0.98 – 1.05	0.455
education level	1.07	0.74 – 1.55	0.701
income	1.08	0.85 – 1.39	0.527
CertificatesEff	1.41	0.95 – 2.09	0.086
NEP score centred	1.06	1.01 – 1.11	0.015
Random Effects
σ²	3.29
τ₀₀ _subject	11.45
ICC	0.78
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.428 / 0.872

Data: All_Measures_Per_Trial
Models:
M2c.1: first_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject)
M2c.2: first_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject)
M2c.3: first_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject)
      npar    AIC    BIC  logLik deviance   Chisq Df Pr(>Chisq)    
M2c.1    5 4735.9 4771.4 -2363.0   4725.9                          
M2c.2    8 4723.8 4780.6 -2353.9   4707.8 18.1426  3   0.000411 ***
M2c.3   11 4728.8 4806.9 -2353.4   4706.8  0.9994  3   0.801396    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

2.4.2 Post Hoc analyses

If any control variables showed significant effects, we tested for potential interactions with vegetarianism.

Show the code

#Post hoc on significant covariates for M2c.1
M2c_CarbonUp <- glmer(
  formula = first_visit ~ vegetarianism * CB_carbonUp + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
  
tab_model(M2c_CarbonUp, transform = "exp")

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	0.02	0.01 – 0.06	<0.001
vegetarianism	6.23	1.92 – 20.22	0.002
CB carbonUp	1286.58	347.47 – 4763.84	<0.001
vegetarianism × CB carbonUp	0.24	0.05 – 1.27	0.094
Random Effects
σ²	3.29
τ₀₀ _subject	12.15
ICC	0.79
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.405 / 0.873

Show the code

#Post hoc on significant covariates for M2c.2
M2c_trialNum <- glmer(
  formula = first_visit ~ vegetarianism * trialNum_centred + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
  
tab_model(M2c_trialNum, transform = "exp")

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	1.02	0.49 – 2.14	0.956
vegetarianism	2.15	0.78 – 5.93	0.139
trialNum centred	1.00	0.99 – 1.02	0.809
vegetarianism × trialNum centred	1.04	1.02 – 1.06	<0.001
Random Effects
σ²	3.29
τ₀₀ _subject	22.68
ICC	0.87
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.007 / 0.874

Simple slopes analyses were conducted to interpret the interactions.

Pairwise contrasts at specific trial number
trialNum	Contrast	Odds Ratio	95% CI		Signif.	p-value
1	vegetarianism1 - vegetarianism0	1.35	0.47	3.82		0.5781
5	vegetarianism1 - vegetarianism0	1.57	0.56	4.39		0.3897
10	vegetarianism1 - vegetarianism0	1.90	0.69	5.26		0.2139
15	vegetarianism1 - vegetarianism0	2.31	0.84	6.37		0.1058
20	vegetarianism1 - vegetarianism0	2.80	1.01	7.80	*	0.0487
25	vegetarianism1 - vegetarianism0	3.40	1.20	9.66	*	0.0218

Show the code

#Post hoc on significant covariates for M2c.3
M2c_gender <- glmer(
  formula = first_visit ~ vegetarianism * gender + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
 
tab_model(M2c_gender, transform = "exp")

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	0.69	0.26 – 1.89	0.476
vegetarianism	1.29	0.31 – 5.42	0.729
gender	2.26	0.52 – 9.76	0.276
vegetarianism × gender	2.17	0.29 – 16.16	0.451
Random Effects
σ²	3.29
τ₀₀ _subject	22.01
ICC	0.87
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.021 / 0.873

Show the code

#Post hoc on significant covariates for M2c.3
M2c_NEP <- glmer(
  formula = first_visit ~ vegetarianism * NEP_score_centred + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 2e5))
)
 
tab_model(M2c_NEP, transform = "exp")

	first_visit
Predictors	Odds Ratios	CI	p
(Intercept)	1.04	0.48 – 2.27	0.920
vegetarianism	1.92	0.66 – 5.58	0.231
NEP score centred	1.08	0.99 – 1.18	0.066
vegetarianism × NEP score centred	1.04	0.93 – 1.17	0.483
Random Effects
σ²	3.29
τ₀₀ _subject	21.82
ICC	0.87
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.041 / 0.874

2.5 RQ2d - diet predicts last visit

2.5.1 Main models

Show the code

M2d.1 <- glmer(
  formula = last_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

M2d.2 <- glmer(
  formula = last_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

M2d.3 <- glmer(
  formula = last_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

To compare vegetarians and non-vegetarians on the likelihood of performing their last visit on a carbon box (RQ2c), we run mixed-effects models with first visit as the dependent variable and random intercepts for participants and trials.

In the first model (M2D.1), we include vegetarianism (coded as 1 for vegetarians, 0 for non-vegetarians) as the main predictor of interest. Additionally, attribute position (coded as 1 if carbon emissions are displayed at the top of the matrix, 0 if at the bottom) and option position (coded as 1 if the pro-environmental option is on the left, 0 if on the right) are also included as fixed effects to account for potential display effects.
In the second model (M2D.2), we test the sensitivity of results of M2D.1 to the addition of control variables related to the task by adding fixed effects for percentage difference in carbon emissions (ranging from 1 [10%] to 5 [100%]), percentage difference in bonus payment (ranging from 1 [10%] to 5 [100%]) and sequential position of the trial (ranging from 1 to 25).
In the third model (M2D.3), we test the sensitivity of results of M2D.1 to the addition of demographic control variables by adding fixed effects for sex, age, education, income, environmental attitudes (assessed by the New Ecological Paradigm), and beliefs in the efficacy of European Union Emission Trading System (measured on a 5-point Likert scale from 1=not effective at all to 5=very effective).

	last_visit
Predictors	Odds Ratios	CI	p
(Intercept)	3.99	2.85 – 5.59	<0.001
vegetarianism	1.40	0.97 – 2.02	0.075
CB carbonUp	0.05	0.03 – 0.07	<0.001
CB selfishLeft	0.82	0.74 – 0.92	0.001
Random Effects
σ²	3.29
τ₀₀ _subject	2.79
ICC	0.46
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.278 / 0.609

	last_visit
Predictors	Odds Ratios	CI	p
(Intercept)	3.47	2.38 – 5.06	<0.001
vegetarianism	1.40	0.97 – 2.02	0.076
CB carbonUp	0.05	0.03 – 0.07	<0.001
CB selfishLeft	0.82	0.74 – 0.92	0.001
carbon level	1.03	0.99 – 1.07	0.167
bonus level	1.02	0.98 – 1.06	0.306
trialNum centred	1.02	1.01 – 1.03	<0.001
Random Effects
σ²	3.29
τ₀₀ _subject	2.81
ICC	0.46
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.281 / 0.612

	last_visit
Predictors	Odds Ratios	CI	p
(Intercept)	2.71	0.89 – 8.26	0.080
vegetarianism	1.25	0.86 – 1.81	0.246
CB carbonUp	0.05	0.03 – 0.07	<0.001
CB selfishLeft	0.82	0.74 – 0.92	0.001
gender	1.13	0.77 – 1.66	0.543
age centred	1.01	0.99 – 1.03	0.274
education level	0.99	0.84 – 1.17	0.908
income	0.99	0.88 – 1.11	0.810
CertificatesEff	1.15	0.96 – 1.37	0.121
NEP score centred	1.04	1.02 – 1.06	0.001
Random Effects
σ²	3.29
τ₀₀ _subject	2.64
ICC	0.44
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.297 / 0.610

Data: All_Measures_Per_Trial
Models:
M2d.1: last_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject)
M2d.2: last_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + carbon_level + bonus_level + trialNum_centred + (1 | subject)
M2d.3: last_visit ~ vegetarianism + CB_carbonUp + CB_selfishLeft + gender + age_centred + education_level + income + CertificatesEff + NEP_score_centred + (1 | subject)
      npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)    
M2d.1    5 8236.2 8271.7 -4113.1   8226.2                         
M2d.2    8 8218.3 8275.0 -4101.1   8202.3 23.915  3  2.603e-05 ***
M2d.3   11 8229.5 8307.6 -4103.8   8207.5  0.000  3          1    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

3 Preregistered exploratory analyses

3.1 EX1 - diet predicts total visiting time

Show the code

M_TVT1 <- lmer(
  formula = t_total_scaled ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject),
  data = All_Measures_Per_Trial
)

	t_total_scaled
Predictors	Estimates	CI	p
(Intercept)	0.72	0.64 – 0.79	<0.001
vegetarianism	0.01	-0.08 – 0.09	0.886
CB carbonUp	-0.01	-0.09 – 0.08	0.850
CB selfishLeft	0.00	-0.02 – 0.02	0.966
Random Effects
σ²	0.16
τ₀₀ _subject	0.16
ICC	0.49
N _subject	368
Observations	8931
Marginal R² / Conditional R²	0.000 / 0.493

3.2 EX2 - diet predicts Payne index

Show the code

M_PI1 <- lmer(
  formula = payne_index ~ vegetarianism + CB_carbonUp + CB_selfishLeft + (1 | subject),
  data = All_Measures_Per_Trial
)

	payne_index
Predictors	Estimates	CI	p
(Intercept)	-0.52	-0.59 – -0.44	<0.001
vegetarianism	0.09	0.01 – 0.17	0.034
CB carbonUp	-0.04	-0.12 – 0.05	0.374
CB selfishLeft	0.01	-0.00 – 0.03	0.132
Random Effects
σ²	0.13
τ₀₀ _subject	0.16
ICC	0.56
N _subject	368
Observations	8893
Marginal R² / Conditional R²	0.009 / 0.560

3.3 EX3 - Attention predicts decision

Show the code

Mex3a <- glmer(
  formula = decision ~ delta_duration_att + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

Mex3b <- glmer(
  formula = decision ~ delta_duration_opt + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

Mex3c <- glmer(
  formula = decision ~ first_visit + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

Mex3d <- glmer(
  formula = decision ~ last_visit + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

Mex3e <- glmer(
  formula = decision ~ t_total_scaled + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

Mex3f <- glmer(
  formula = decision ~ payne_index + (1 | subject) + (1 | trialNum_fixed),
  data = All_Measures_Per_Trial,
  family = binomial(link = "logit"),
  control = glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun = 5e5))
)

	decision			decision
Predictors	Odds Ratios	CI	p	Odds Ratios	CI	p
(Intercept)	1.50	0.71 – 3.17	0.283	1.69	0.80 – 3.56	0.171
delta duration att	5.26	4.06 – 6.80	<0.001
delta duration opt				37.04	26.44 – 51.88	<0.001
Random Effects
σ²	3.29			3.29
τ₀₀	15.51 _subject			18.79 _subject
	2.74 _{trialNum_fixed}			2.59 _{trialNum_fixed}
ICC	0.85			0.87
N	481 _subject			481 _subject
	25 _{trialNum_fixed}			25 _{trialNum_fixed}
Observations	11626			11626
Marginal R² / Conditional R²	0.031 / 0.852			0.028 / 0.870

	decision			decision
Predictors	Odds Ratios	CI	p	Odds Ratios	CI	p
(Intercept)	1.26	0.58 – 2.70	0.561	1.39	0.65 – 2.98	0.399
first visit	1.75	1.37 – 2.22	<0.001
last visit				1.53	1.30 – 1.80	<0.001
Random Effects
σ²	3.29			3.29
τ₀₀	18.89 _subject			19.51 _subject
	2.66 _{trialNum_fixed}			2.67 _{trialNum_fixed}
ICC	0.87			0.87
N	481 _subject			481 _subject
	25 _{trialNum_fixed}			25 _{trialNum_fixed}
Observations	11626			11626
Marginal R² / Conditional R²	0.003 / 0.868			0.002 / 0.871

	decision			decision
Predictors	Odds Ratios	CI	p	Odds Ratios	CI	p
(Intercept)	1.85	0.86 – 3.98	0.115	1.70	0.78 – 3.69	0.181
t total scaled	0.91	0.81 – 1.01	0.069
payne index				1.00	0.84 – 1.19	0.999
Random Effects
σ²	3.29			3.29
τ₀₀	19.93 _subject			20.41 _subject
	2.67 _{trialNum_fixed}			2.74 _{trialNum_fixed}
ICC	0.87			0.88
N	481 _subject			480 _subject
	25 _{trialNum_fixed}			25 _{trialNum_fixed}
Observations	11626			11548
Marginal R² / Conditional R²	0.000 / 0.873			0.000 / 0.876