PMB -> PEB: Batch 1 through 3

Dataset preperation

Manipulation and attention checks

table(data_combined$Condition_eco, data_combined$cond.eco_flag) #Eco conditions 1:EEF, 2:EEC, 3:EEF+EEC

   
    FALSE TRUE
  1    44   14
  2    28   26
  3    65    5

table(data_combined$Condition_reward, data_combined$cond.reward_flag) #Reward 1: Control, 2:Process, 3: Performance

   
    FALSE TRUE
  1    68    0
  2    45    8
  3    47   14

table(data_combined$att_flag) #Attention check

FALSE  TRUE 
  180     2 

table(data_combined$prescreener_flag) # Failed pre-screener validation questions

< table of extent 0 >

####Converting groups to factors
#| echo: false
#| include: false
data_combined$Condition_reward <- as.factor(data_combined$Condition_reward)
data_combined$Condition_eco <- as.factor(data_combined$Condition_eco)

Filtering out bad participants

data_combined$prescreener_flag <- (
  (data_combined$prescreener_employment_work_role == 7 | 
     data_combined$prescreener_employment_work_role == 8 | 
     data_combined$prescreener_company_size != 1) &
    !is.na(data_combined$prescreener_employment_work_role) &
    !is.na(data_combined$prescreener_company_size)
  )

prescreener_flag_subset <- subset(data_combined, prescreener_flag == TRUE)
excluded <- subset(data_combined, cond.eco_flag == TRUE | cond.reward_flag == TRUE | att_flag == TRUE | prescreener_flag == TRUE)
data_filtered <- data_combined %>%
  filter(!Prolific.id %in% excluded$Prolific.id)

Descriptive

 all good 
 182  107 

     vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
S1      1 107 5.05 1.43      5    5.18 1.48   1   7     6 -0.91     0.52 0.14
S2      2 107 4.84 1.52      5    4.97 1.48   1   7     6 -0.79     0.04 0.15
S3      3 107 5.07 1.41      5    5.20 1.48   1   7     6 -0.92     0.81 0.14
IM1     4 107 5.16 1.57      5    5.37 1.48   1   7     6 -1.05     0.75 0.15
IM2     5 107 5.65 1.29      6    5.84 1.48   1   7     6 -1.60     3.45 0.12
IM3     6 107 5.60 1.32      6    5.77 1.48   1   7     6 -1.43     2.52 0.13
INR1    7 107 4.93 1.54      5    5.09 1.48   1   7     6 -0.88     0.24 0.15
INR2    8 107 4.50 1.81      5    4.60 1.48   1   7     6 -0.40    -0.89 0.18
INR3    9 107 4.30 1.82      5    4.37 1.48   1   7     6 -0.32    -1.01 0.18
IDR1   10 107 6.19 1.06      6    6.36 1.48   1   7     6 -1.99     5.81 0.10
IDR2   11 107 6.26 1.01      6    6.44 1.48   1   7     6 -2.32     7.81 0.10
IDR3   12 107 6.31 1.01      7    6.48 0.00   1   7     6 -2.09     6.32 0.10
EEF1   13 107 5.18 1.53      6    5.37 1.48   1   7     6 -1.00     0.55 0.15
EEF2   14 107 5.47 1.51      6    5.69 1.48   1   7     6 -1.19     1.23 0.15
EEF3   15 107 5.42 1.50      6    5.63 1.48   1   7     6 -1.13     1.07 0.14
EEC1   16 107 4.31 1.60      4    4.39 1.48   1   7     6 -0.44    -0.44 0.15
EEC2   17 107 4.30 1.69      5    4.33 1.48   1   7     6 -0.24    -0.87 0.16
EEC3   18 107 4.31 1.71      4    4.37 1.48   1   7     6 -0.31    -0.70 0.17
TR1    19 107 3.36 1.61      3    3.30 1.48   1   7     6  0.19    -0.80 0.16
TR2    20 107 3.42 1.61      3    3.40 1.48   1   7     6  0.03    -0.88 0.16
TR3    21 107 2.96 1.58      3    2.90 1.48   1   7     6  0.34    -0.94 0.15
BV1    22 107 6.83 1.90      7    7.02 1.48   2   9     7 -0.73    -0.35 0.18
BV2    23 107 7.23 1.79      8    7.46 1.48   3   9     6 -0.75    -0.44 0.17
BV3    24 107 7.37 1.75      8    7.62 1.48   3   9     6 -0.90    -0.18 0.17

Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = only_scales_good)
Overall MSA =  0.92
MSA for each item = 
  S1   S2   S3  IM1  IM2  IM3 INR1 INR2 INR3 IDR1 IDR2 IDR3 EEF1 EEF2 EEF3 EEC1 
0.91 0.89 0.93 0.96 0.96 0.94 0.93 0.93 0.91 0.92 0.93 0.92 0.93 0.90 0.93 0.96 
EEC2 EEC3  TR1  TR2  TR3  BV1  BV2  BV3 
0.91 0.89 0.94 0.76 0.82 0.96 0.90 0.91 

Non-normality test across all scales

$S1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89194, p-value = 2.883e-07


$S2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89739, p-value = 5.206e-07


$S3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89177, p-value = 2.831e-07


$IM1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.86544, p-value = 2.04e-08


$IM2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.79853, p-value = 8.519e-11


$IM3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.82534, p-value = 6.476e-10


$INR1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.8897, p-value = 2.273e-07


$INR2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92122, p-value = 8.727e-06


$INR3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92476, p-value = 1.376e-05


$IDR1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.72996, p-value = 9.739e-13


$IDR2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.69119, p-value = 1.093e-13


$IDR3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.69579, p-value = 1.402e-13


$EEF1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.87429, p-value = 4.758e-08


$EEF2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.84305, p-value = 2.772e-09


$EEF3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.85428, p-value = 7.367e-09


$EEC1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92479, p-value = 1.383e-05


$EEC2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.93936, p-value = 0.0001026


$EEC3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.93763, p-value = 7.997e-05


$TR1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.93297, p-value = 4.15e-05


$TR2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.923, p-value = 1.096e-05


$TR3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89942, p-value = 6.522e-07


$BV1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89299, p-value = 3.228e-07


$BV2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.85849, p-value = 1.075e-08


$BV3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.84027, p-value = 2.191e-09

Analysing dependent variables

Descriptive on EEF composite

hist(data_reduced_good$EEF_composite, main = "Histogram of EEF composite")

boxplot(data_reduced_good$EEF_composite, main = "Boxplot of EEF composite")

qqnorm(data_reduced_good$EEF_composite)
qqline(data_reduced_good$EEF_composite, col = "red")

shapiro.test(data_reduced_good$EEF_composite)

    Shapiro-Wilk normality test

data:  data_reduced_good$EEF_composite
W = 0.8819, p-value = 1.014e-07

Descriptive on EEC composite

hist(data_reduced_good$EEC_composite, main = "Histogram of EEC composite")

boxplot(data_reduced_good$EEC_composite, main = "Boxplot of EEC composite")

qqnorm(data_reduced_good$EEC_composite)
qqline(data_reduced_good$EEC_composite, col = "red")

shapiro.test(data_reduced_good$EEC_composite)

    Shapiro-Wilk normality test

data:  data_reduced_good$EEC_composite
W = 0.96693, p-value = 0.009084

Descriptive on Groupwise

data_reduced_good %>%
  group_by(Condition_reward, Condition_eco) %>%
  summarise(
    n = n(),
    shapiro_p = shapiro.test(EEF_composite)$p.value
  )

`summarise()` has grouped output by 'Condition_reward'. You can override using
the `.groups` argument.

# A tibble: 9 × 4
# Groups:   Condition_reward [3]
  Condition_reward Condition_eco     n shapiro_p
  <fct>            <fct>         <int>     <dbl>
1 1                1                11    0.0360
2 1                2                10    0.543 
3 1                3                24    0.0206
4 2                1                16    0.0987
5 2                2                 8    0.201 
6 2                3                12    0.0243
7 3                1                 6    0.339 
8 3                2                 6    0.0598
9 3                3                14    0.0636

data_reduced_good %>%
  group_by(Condition_reward, Condition_eco) %>%
  summarise(
    n = n(),
    shapiro_p = shapiro.test(EEC_composite)$p.value
  )

`summarise()` has grouped output by 'Condition_reward'. You can override using
the `.groups` argument.

# A tibble: 9 × 4
# Groups:   Condition_reward [3]
  Condition_reward Condition_eco     n shapiro_p
  <fct>            <fct>         <int>     <dbl>
1 1                1                11     0.869
2 1                2                10     0.978
3 1                3                24     0.604
4 2                1                16     0.238
5 2                2                 8     0.912
6 2                3                12     0.605
7 3                1                 6     0.168
8 3                2                 6     0.674
9 3                3                14     0.293

Motivation variables

data_reduced_good$IM_composite <- rowMeans(data_reduced_good[, c("IM1", "IM2", "IM3")], na.rm = TRUE)  # Calculate composite scores using the mean of the indicators - motivation
data_reduced_good$IDR_composite <- rowMeans(data_reduced_good[, c("IDR1", "IDR2", "IDR3")], na.rm = TRUE)
data_reduced_good$INR_composite <- rowMeans(data_reduced_good[, c("INR1", "INR2", "INR3")], na.rm = TRUE)

Descriptive on IM composite

hist(data_reduced_good$IM_composite, main = "Histogram of IM composite")

boxplot(data_reduced_good$IM_composite, main = "Boxplot of IM composite")

qqnorm(data_reduced_good$IM_composite)
qqline(data_reduced_good$IM_composite, col = "red")

shapiro.test(data_reduced_good$IM_composite)

    Shapiro-Wilk normality test

data:  data_reduced_good$IM_composite
W = 0.86986, p-value = 3.1e-08

Descriptive on IDR composite

hist(data_reduced_good$IDR_composite, main = "Histogram of IDR composite")

boxplot(data_reduced_good$IDR_composite, main = "Boxplot of IDR composite")

qqnorm(data_reduced_good$IDR_composite)
qqline(data_reduced_good$IDR_composite, col = "red")

shapiro.test(data_reduced_good$IDR_composite)

    Shapiro-Wilk normality test

data:  data_reduced_good$IDR_composite
W = 0.73978, p-value = 1.754e-12

Descriptive on INR composite

hist(data_reduced_good$INR_composite, main = "Histogram of INR composite")

boxplot(data_reduced_good$INR_composite, main = "Boxplot of INR composite")

qqnorm(data_reduced_good$INR_composite)
qqline(data_reduced_good$INR_composite, col = "red")

shapiro.test(data_reduced_good$INR_composite)

    Shapiro-Wilk normality test

data:  data_reduced_good$INR_composite
W = 0.94627, p-value = 0.0002873

Descriptive on Groupwise

data_reduced_good %>%
  group_by(Condition_reward, Condition_eco) %>%
  summarise(
    n = n(),
    shapiro_p = shapiro.test(IM_composite)$p.value
  )

`summarise()` has grouped output by 'Condition_reward'. You can override using
the `.groups` argument.

# A tibble: 9 × 4
# Groups:   Condition_reward [3]
  Condition_reward Condition_eco     n shapiro_p
  <fct>            <fct>         <int>     <dbl>
1 1                1                11   0.0362 
2 1                2                10   0.320  
3 1                3                24   0.0376 
4 2                1                16   0.188  
5 2                2                 8   0.0160 
6 2                3                12   0.00386
7 3                1                 6   0.0809 
8 3                2                 6   0.0475 
9 3                3                14   0.0135 

data_reduced_good %>%
  group_by(Condition_reward, Condition_eco) %>%
  summarise(
    n = n(),
    shapiro_p = shapiro.test(IDR_composite)$p.value
  )

`summarise()` has grouped output by 'Condition_reward'. You can override using
the `.groups` argument.

# A tibble: 9 × 4
# Groups:   Condition_reward [3]
  Condition_reward Condition_eco     n  shapiro_p
  <fct>            <fct>         <int>      <dbl>
1 1                1                11 0.00000283
2 1                2                10 0.0736    
3 1                3                24 0.000797  
4 2                1                16 0.0608    
5 2                2                 8 0.255     
6 2                3                12 0.00132   
7 3                1                 6 0.0000207 
8 3                2                 6 0.111     
9 3                3                14 0.00187   

data_reduced_good %>%
  group_by(Condition_reward, Condition_eco) %>%
  summarise(
    n = n(),
    shapiro_p = shapiro.test(INR_composite)$p.value
  )

`summarise()` has grouped output by 'Condition_reward'. You can override using
the `.groups` argument.

# A tibble: 9 × 4
# Groups:   Condition_reward [3]
  Condition_reward Condition_eco     n shapiro_p
  <fct>            <fct>         <int>     <dbl>
1 1                1                11    0.524 
2 1                2                10    0.231 
3 1                3                24    0.0138
4 2                1                16    0.833 
5 2                2                 8    0.786 
6 2                3                12    0.105 
7 3                1                 6    0.230 
8 3                2                 6    0.917 
9 3                3                14    0.110 

Data analysis

DVs

SEM

# 1️⃣ Prepare dummy variables----
# Reward dummies
dummy_reward <- model.matrix(~ Condition_reward, data = data_reduced_good)[, -1]
colnames(dummy_reward) <- paste0("reward_", colnames(dummy_reward))

# Eco dummies
dummy_eco <- model.matrix(~ Condition_eco, data = data_reduced_good)[, -1]
colnames(dummy_eco) <- paste0("eco_", colnames(dummy_eco))

# Bind dummies to dataset
data_prepared <- cbind(data_reduced_good, dummy_reward, dummy_eco)

# Create interaction terms manually (no ":")
data_prepared$rewardEco22 <- data_prepared$reward_Condition_reward2 * data_prepared$eco_Condition_eco2
data_prepared$rewardEco33 <- data_prepared$reward_Condition_reward3 * data_prepared$eco_Condition_eco3


# 2️⃣ Create latent x latent interaction (S x BV)----

data_int <- indProd(
  data = data_prepared,
  var1 = c("S1","S2","S3"),
  var2 = c("BV1","BV2","BV3"),
  match = FALSE,
  meanC = TRUE,
  residualC = FALSE
)

# Add back the dummy interactions
data_int$rewardEco22 <- data_prepared$rewardEco22
data_int$rewardEco33 <- data_prepared$rewardEco33


# 3️⃣ Create TR x condition latent x observed interactions----

# TR x reward dummies
TR_reward_int <- indProd(
  data = data_int,
  var1 = c("TR1","TR2","TR3"),
  var2 = c("reward_Condition_reward2","reward_Condition_reward3"),
  match = FALSE,
  meanC = TRUE,
  residualC = FALSE
)

# TR x eco dummies
TR_eco_int <- indProd(
  data = TR_reward_int,
  var1 = c("TR1","TR2","TR3"),
  var2 = c("eco_Condition_eco2","eco_Condition_eco3"),
  match = FALSE,
  meanC = TRUE,
  residualC = FALSE
)

# The final dataset for lavaan
final_data <- TR_eco_int


# 4️⃣ Define SEM model----
model2 <- '
  # Measurement model
  EEF =~ EEF1 + EEF2 + EEF3
  EEC =~ EEC1 + EEC2 + EEC3
  IM  =~ IM1 + IM2 + IM3
  S   =~ S1 + S2 + S3
  TR  =~ TR1 + TR2 + TR3
  BV  =~ BV1 + BV2 + BV3

  # Latent x latent interaction
  SxBV =~ S1.BV1 + S2.BV2 + S3.BV3

  # Structural model
  # S predicted by main effects + TR moderation
  S ~ a1*reward_Condition_reward2 + a2*reward_Condition_reward3
      + a3*eco_Condition_eco2 + a4*eco_Condition_eco3
      + a5*rewardEco22 + a6*rewardEco33
      + tr_r1*TR1.reward_Condition_reward2 + tr_r2*TR2.reward_Condition_reward2 + tr_r3*TR3.reward_Condition_reward2
      + tr_r4*TR1.reward_Condition_reward3 + tr_r5*TR2.reward_Condition_reward3 + tr_r6*TR3.reward_Condition_reward3
      + tr_e1*TR1.eco_Condition_eco2 + tr_e2*TR2.eco_Condition_eco2 + tr_e3*TR3.eco_Condition_eco2
      + tr_e4*TR1.eco_Condition_eco3 + tr_e5*TR2.eco_Condition_eco3 + tr_e6*TR3.eco_Condition_eco3

  # IM predicted by S + latent x latent interaction
  IM ~ b1*S + b2*SxBV

  # Outcomes
  EEF ~ c1*IM + c2*S
  EEC ~ d1*IM + d2*S
'


# 5️⃣ Fit the model----
fit2 <- sem(model2, data = final_data, estimator = "MLR")
summary(fit2, fit.measures = TRUE, rsquare=TRUE, standardized = TRUE)

lavaan 0.6-19 ended normally after 90 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        70

  Number of observations                           107

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               860.137     872.718
  Degrees of freedom                               539         539
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  0.986
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              2954.548    2954.951
  Degrees of freedom                               588         588
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.000

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.864       0.859
  Tucker-Lewis Index (TLI)                       0.852       0.846
                                                                  
  Robust Comparative Fit Index (CFI)                         0.861
  Robust Tucker-Lewis Index (TLI)                            0.848

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -3380.703   -3380.703
  Scaling correction factor                                  1.368
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -2950.634   -2950.634
  Scaling correction factor                                  1.030
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                6901.406    6901.406
  Bayesian (BIC)                              7088.504    7088.504
  Sample-size adjusted Bayesian (SABIC)       6867.336    6867.336

Root Mean Square Error of Approximation:

  RMSEA                                          0.075       0.076
  90 Percent confidence interval - lower         0.065       0.067
  90 Percent confidence interval - upper         0.084       0.085
  P-value H_0: RMSEA <= 0.050                    0.000       0.000
  P-value H_0: RMSEA >= 0.080                    0.172       0.246
                                                                  
  Robust RMSEA                                               0.076
  90 Percent confidence interval - lower                     0.066
  90 Percent confidence interval - upper                     0.085
  P-value H_0: Robust RMSEA <= 0.050                         0.000
  P-value H_0: Robust RMSEA >= 0.080                         0.213

Standardized Root Mean Square Residual:

  SRMR                                           0.153       0.153

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF =~                                                                
    EEF1              1.000                               1.406    0.951
    EEF2              0.987    0.040   24.441    0.000    1.388    0.953
    EEF3              0.923    0.057   16.124    0.000    1.297    0.892
  EEC =~                                                                
    EEC1              1.000                               1.369    0.879
    EEC2              1.118    0.070   16.074    0.000    1.529    0.933
    EEC3              1.160    0.071   16.362    0.000    1.588    0.960
  IM =~                                                                 
    IM1               1.000                               1.264    0.845
    IM2               0.861    0.092    9.405    0.000    1.088    0.892
    IM3               0.906    0.074   12.322    0.000    1.145    0.922
  S =~                                                                  
    S1                1.000                               1.248    0.877
    S2                1.006    0.089   11.285    0.000    1.255    0.831
    S3                0.954    0.097    9.868    0.000    1.190    0.851
  TR =~                                                                 
    TR1               1.000                               1.210    0.756
    TR2               1.239    0.139    8.944    0.000    1.500    0.934
    TR3               1.194    0.119   10.077    0.000    1.446    0.917
  BV =~                                                                 
    BV1               1.000                               1.519    0.805
    BV2               1.137    0.109   10.445    0.000    1.727    0.967
    BV3               1.066    0.112    9.533    0.000    1.620    0.929
  SxBV =~                                                               
    S1.BV1            1.000                               2.788    0.839
    S2.BV2            1.035    0.137    7.583    0.000    2.887    0.906
    S3.BV3            1.142    0.148    7.741    0.000    3.184    0.916

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  S ~                                                                   
    rw_C_2    (a1)   -0.345    0.418   -0.824    0.410   -0.276   -0.130
    rw_C_3    (a2)    0.327    0.436    0.750    0.453    0.262    0.112
    ec_C_2    (a3)   -0.381    0.501   -0.760    0.447   -0.305   -0.127
    ec_C_3    (a4)   -0.104    0.400   -0.260    0.795   -0.083   -0.041
    rwrE22    (a5)    0.020    0.737    0.027    0.978    0.016    0.004
    rwrE33    (a6)   -0.046    0.603   -0.076    0.940   -0.037   -0.012
    TR1._C (tr_r1)    0.105    0.396    0.265    0.791    0.084    0.062
    TR2._C (tr_r2)   -0.095    0.336   -0.282    0.778   -0.076   -0.060
    TR3._C (tr_r3)   -0.073    0.432   -0.169    0.866   -0.058   -0.044
    TR1._C (tr_r4)    0.191    0.256    0.749    0.454    0.153    0.108
    TR2._C (tr_r5)   -0.063    0.329   -0.192    0.848   -0.051   -0.036
    TR3._C (tr_r6)   -0.070    0.359   -0.196    0.844   -0.056   -0.038
    TR1._C (tr_e1)    0.046    0.343    0.135    0.892    0.037    0.025
    TR2._C (tr_e2)    0.077    0.421    0.182    0.855    0.062    0.044
    TR3._C (tr_e3)   -0.332    0.451   -0.735    0.462   -0.266   -0.183
    TR1._C (tr_e4)    0.283    0.386    0.734    0.463    0.227    0.180
    TR2._C (tr_e5)   -0.481    0.377   -1.275    0.202   -0.385   -0.307
    TR3._C (tr_e6)    0.109    0.500    0.217    0.828    0.087    0.068
  IM ~                                                                  
    S         (b1)    0.576    0.105    5.473    0.000    0.569    0.569
    SxBV      (b2)   -0.179    0.035   -5.139    0.000   -0.395   -0.395
  EEF ~                                                                 
    IM        (c1)    0.664    0.145    4.596    0.000    0.597    0.597
    S         (c2)    0.144    0.159    0.907    0.364    0.128    0.128
  EEC ~                                                                 
    IM        (d1)    0.462    0.102    4.520    0.000    0.427    0.427
    S         (d2)    0.370    0.127    2.906    0.004    0.338    0.338

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  TR ~~                                                                 
    BV                0.430    0.242    1.780    0.075    0.234    0.234
    SxBV             -0.750    0.488   -1.535    0.125   -0.222   -0.222
  BV ~~                                                                 
    SxBV             -1.578    1.041   -1.516    0.130   -0.372   -0.372
 .EEF ~~                                                                
   .EEC               0.553    0.137    4.035    0.000    0.532    0.532

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEF1              0.208    0.064    3.254    0.001    0.208    0.095
   .EEF2              0.195    0.056    3.489    0.000    0.195    0.092
   .EEF3              0.432    0.108    3.985    0.000    0.432    0.204
   .EEC1              0.549    0.120    4.573    0.000    0.549    0.227
   .EEC2              0.351    0.088    3.967    0.000    0.351    0.130
   .EEC3              0.217    0.086    2.528    0.011    0.217    0.079
   .IM1               0.640    0.164    3.891    0.000    0.640    0.286
   .IM2               0.305    0.108    2.809    0.005    0.305    0.205
   .IM3               0.230    0.067    3.434    0.001    0.230    0.149
   .S1                0.468    0.103    4.553    0.000    0.468    0.231
   .S2                0.707    0.184    3.854    0.000    0.707    0.310
   .S3                0.541    0.146    3.701    0.000    0.541    0.276
   .TR1               1.100    0.258    4.265    0.000    1.100    0.429
   .TR2               0.329    0.142    2.324    0.020    0.329    0.128
   .TR3               0.395    0.123    3.210    0.001    0.395    0.159
   .BV1               1.253    0.261    4.797    0.000    1.253    0.352
   .BV2               0.205    0.100    2.049    0.040    0.205    0.064
   .BV3               0.413    0.137    3.021    0.003    0.413    0.136
   .S1.BV1            3.259    0.674    4.838    0.000    3.259    0.295
   .S2.BV2            1.828    0.580    3.152    0.002    1.828    0.180
   .S3.BV3            1.958    0.652    3.000    0.003    1.958    0.162
   .EEF               1.068    0.184    5.799    0.000    0.540    0.540
   .EEC               1.011    0.161    6.295    0.000    0.540    0.540
   .IM                0.832    0.203    4.098    0.000    0.521    0.521
   .S                 1.455    0.309    4.714    0.000    0.934    0.934
    TR                1.465    0.340    4.306    0.000    1.000    1.000
    BV                2.307    0.482    4.783    0.000    1.000    1.000
    SxBV              7.775    3.778    2.058    0.040    1.000    1.000

R-Square:
                   Estimate
    EEF1              0.905
    EEF2              0.908
    EEF3              0.796
    EEC1              0.773
    EEC2              0.870
    EEC3              0.921
    IM1               0.714
    IM2               0.795
    IM3               0.851
    S1                0.769
    S2                0.690
    S3                0.724
    TR1               0.571
    TR2               0.872
    TR3               0.841
    BV1               0.648
    BV2               0.936
    BV3               0.864
    S1.BV1            0.705
    S2.BV2            0.820
    S3.BV3            0.838
    EEF               0.460
    EEC               0.460
    IM                0.479
    S                 0.066

lavaanPlot(model = fit2, node_options = list(shape = "box", fontname = "Helvetica"), edge_options = list(color = "grey"),
           coefs = T, stand=T)

#Construct Reliability:
semTools::compRelSEM(fit2, tau.eq=T, obs.var=T) #Cronbach Alpha

  EEF   EEC    IM     S    TR    BV  SxBV 
0.954 0.947 0.917 0.888 0.900 0.925 0.916 

semTools::compRelSEM(fit2, tau.eq=F, obs.var=T) #Omega

  EEF   EEC    IM     S    TR    BV  SxBV 
0.897 0.900 0.817 0.888 0.906 0.928 0.918 

AVE(fit2, obs.var = TRUE, omit.imps = c("no.conv", "no.se"),
    omit.factors = character(0), dropSingle = TRUE, return.df = TRUE)

  EEF   EEC    IM     S    TR    BV  SxBV 
0.823 0.817 0.704 0.726 0.761 0.809 0.788 

#Standardized residuals
lavResiduals(fit2, type = "cor.bentler", custom.rmr = NULL,
             se = FALSE, zstat = TRUE, summary = TRUE, h1.acov = "unstructured",
             add.type = TRUE, add.labels = TRUE, add.class = TRUE,
             drop.list.single.group = TRUE,
             maximum.number = length(res.vech), output = "list")

$type
[1] "cor.bentler"

$cov
                               EEF1   EEF2   EEF3   EEC1   EEC2   EEC3    IM1
EEF1                          0.056                                          
EEF2                          0.059  0.056                                   
EEF3                          0.045  0.056  0.050                            
EEC1                          0.165  0.121  0.139  0.043                     
EEC2                          0.041  0.007  0.028  0.032  0.048              
EEC3                          0.049  0.034  0.052  0.042  0.056  0.051       
IM1                           0.120  0.097  0.129  0.267  0.195  0.186  0.087
IM2                           0.072  0.063  0.139  0.086  0.052  0.052  0.064
IM3                           0.043  0.029  0.089  0.070  0.017  0.033  0.091
S1                            0.105  0.127  0.114  0.092  0.074  0.052  0.156
S2                           -0.021 -0.005 -0.014  0.018  0.047 -0.013  0.186
S3                            0.057  0.087  0.100  0.073  0.070  0.032  0.171
TR1                           0.363  0.373  0.384  0.483  0.469  0.517  0.431
TR2                           0.245  0.191  0.262  0.358  0.351  0.338  0.312
TR3                           0.255  0.244  0.231  0.374  0.403  0.426  0.331
BV1                           0.570  0.537  0.565  0.544  0.453  0.453  0.568
BV2                           0.543  0.530  0.559  0.528  0.454  0.452  0.487
BV3                           0.527  0.501  0.526  0.485  0.432  0.412  0.549
S1.BV1                       -0.145 -0.177 -0.194 -0.110 -0.043 -0.063 -0.106
S2.BV2                       -0.125 -0.151 -0.153 -0.144 -0.063 -0.072 -0.111
S3.BV3                       -0.135 -0.193 -0.242 -0.144 -0.069 -0.103 -0.117
reward_Condition_reward2      0.020  0.014  0.073  0.058  0.065  0.098  0.033
reward_Condition_reward3     -0.033 -0.012 -0.034 -0.075 -0.049 -0.080 -0.058
eco_Condition_eco2            0.173  0.131  0.101  0.085  0.100  0.084  0.077
eco_Condition_eco3           -0.109 -0.091 -0.073  0.038  0.027  0.054 -0.037
rewardEco22                   0.055  0.047 -0.018  0.104  0.105  0.084  0.037
rewardEco33                  -0.104 -0.087 -0.073 -0.035 -0.036 -0.056 -0.064
TR1.reward_Condition_reward2  0.085  0.020  0.014  0.100  0.027  0.011 -0.064
TR2.reward_Condition_reward2  0.000 -0.013 -0.008  0.089  0.039  0.002  0.018
TR3.reward_Condition_reward2  0.066  0.049  0.094  0.110  0.039  0.013  0.022
TR1.reward_Condition_reward3 -0.052 -0.049 -0.051 -0.101 -0.073 -0.097  0.053
TR2.reward_Condition_reward3 -0.054 -0.011  0.000 -0.119 -0.129 -0.147 -0.098
TR3.reward_Condition_reward3 -0.046 -0.036 -0.020 -0.167 -0.122 -0.153  0.009
TR1.eco_Condition_eco2       -0.239 -0.180 -0.198 -0.159 -0.135 -0.117 -0.155
TR2.eco_Condition_eco2       -0.139 -0.089 -0.113 -0.149 -0.066 -0.057 -0.141
TR3.eco_Condition_eco2       -0.139 -0.080 -0.087 -0.148 -0.075 -0.063 -0.121
TR1.eco_Condition_eco3        0.205  0.172  0.245  0.083  0.086  0.081  0.117
TR2.eco_Condition_eco3        0.198  0.137  0.197  0.128  0.091  0.055  0.081
TR3.eco_Condition_eco3        0.172  0.079  0.113  0.099  0.079  0.045  0.054
                                IM2    IM3     S1     S2     S3    TR1    TR2
EEF1                                                                         
EEF2                                                                         
EEF3                                                                         
EEC1                                                                         
EEC2                                                                         
EEC3                                                                         
IM1                                                                          
IM2                           0.096                                          
IM3                           0.116  0.102                                   
S1                            0.067  0.080  0.000                            
S2                            0.058  0.079  0.001  0.000                     
S3                            0.073  0.093 -0.001  0.002  0.000              
TR1                           0.399  0.393  0.411  0.467  0.372  0.000       
TR2                           0.223  0.257  0.367  0.447  0.356 -0.005  0.000
TR3                           0.281  0.303  0.426  0.441  0.366 -0.003  0.002
BV1                           0.528  0.550  0.361  0.292  0.369  0.289  0.113
BV2                           0.531  0.515  0.323  0.242  0.337  0.221 -0.047
BV3                           0.560  0.556  0.358  0.317  0.318  0.213 -0.046
S1.BV1                       -0.205 -0.166 -0.249 -0.226 -0.227 -0.084 -0.021
S2.BV2                       -0.110 -0.093 -0.279 -0.228 -0.247 -0.019 -0.004
S3.BV3                       -0.104 -0.114 -0.320 -0.233 -0.382 -0.026 -0.005
reward_Condition_reward2      0.064  0.036  0.011 -0.023 -0.008  0.040 -0.063
reward_Condition_reward3     -0.042 -0.004 -0.019 -0.028  0.068  0.010  0.042
eco_Condition_eco2            0.055  0.079  0.073 -0.035 -0.083 -0.119 -0.015
eco_Condition_eco3           -0.095 -0.040 -0.027  0.028 -0.003  0.096  0.058
rewardEco22                  -0.044 -0.055  0.074 -0.032 -0.061 -0.063 -0.030
rewardEco33                  -0.135 -0.097 -0.036  0.000  0.078  0.070  0.071
TR1.reward_Condition_reward2  0.008  0.021 -0.033  0.046 -0.013 -0.057 -0.022
TR2.reward_Condition_reward2 -0.076 -0.045 -0.061  0.063  0.027 -0.021  0.097
TR3.reward_Condition_reward2 -0.055 -0.010 -0.066  0.070  0.024 -0.030  0.080
TR1.reward_Condition_reward3  0.047  0.079  0.034 -0.010 -0.034  0.045  0.081
TR2.reward_Condition_reward3  0.031  0.005  0.062 -0.039 -0.017  0.080  0.063
TR3.reward_Condition_reward3  0.162  0.087  0.051 -0.028 -0.035  0.079  0.045
TR1.eco_Condition_eco2       -0.232 -0.213 -0.014  0.094  0.002  0.047  0.154
TR2.eco_Condition_eco2       -0.147 -0.145 -0.029  0.075  0.014  0.146  0.111
TR3.eco_Condition_eco2       -0.132 -0.147 -0.037  0.055  0.041  0.138  0.099
TR1.eco_Condition_eco3        0.178  0.124  0.019 -0.051 -0.013 -0.033 -0.117
TR2.eco_Condition_eco3        0.179  0.135  0.006 -0.055  0.001 -0.117 -0.088
TR3.eco_Condition_eco3        0.178  0.130  0.028 -0.076 -0.010 -0.118 -0.080
                                TR3    BV1    BV2    BV3 S1.BV1 S2.BV2 S3.BV3
EEF1                                                                         
EEF2                                                                         
EEF3                                                                         
EEC1                                                                         
EEC2                                                                         
EEC3                                                                         
IM1                                                                          
IM2                                                                          
IM3                                                                          
S1                                                                           
S2                                                                           
S3                                                                           
TR1                                                                          
TR2                                                                          
TR3                           0.000                                          
BV1                           0.117  0.000                                   
BV2                          -0.045  0.001  0.000                            
BV3                          -0.041 -0.007  0.001  0.000                     
S1.BV1                        0.044 -0.076 -0.046 -0.085  0.000              
S2.BV2                        0.017  0.065  0.068 -0.003 -0.010  0.000       
S3.BV3                        0.044  0.005  0.039  0.043 -0.003  0.011  0.000
reward_Condition_reward2     -0.008  0.001  0.018  0.006 -0.064 -0.129 -0.143
reward_Condition_reward3     -0.042 -0.042 -0.074 -0.059  0.066  0.060 -0.029
eco_Condition_eco2           -0.087  0.072  0.105  0.155 -0.103 -0.141 -0.083
eco_Condition_eco3            0.058  0.004  0.014 -0.040  0.102  0.176  0.112
rewardEco22                  -0.083 -0.069  0.122  0.102 -0.071 -0.132 -0.099
rewardEco33                  -0.026 -0.127 -0.051 -0.099  0.044  0.042 -0.006
TR1.reward_Condition_reward2 -0.031 -0.022 -0.033 -0.001  0.023  0.068  0.076
TR2.reward_Condition_reward2  0.078 -0.012 -0.120 -0.095 -0.014 -0.006 -0.021
TR3.reward_Condition_reward2  0.019  0.030 -0.062 -0.035 -0.068 -0.044 -0.057
TR1.reward_Condition_reward3  0.077  0.043  0.049 -0.011 -0.012 -0.005  0.095
TR2.reward_Condition_reward3  0.044 -0.048  0.015 -0.050  0.016  0.027  0.122
TR3.reward_Condition_reward3  0.010  0.013  0.083  0.055 -0.044  0.003  0.109
TR1.eco_Condition_eco2        0.142 -0.169 -0.267 -0.232  0.109  0.155  0.097
TR2.eco_Condition_eco2        0.096 -0.076 -0.130 -0.089  0.057  0.110  0.077
TR3.eco_Condition_eco2        0.076 -0.069 -0.099 -0.088  0.061  0.116  0.051
TR1.eco_Condition_eco3       -0.119  0.138  0.174  0.168 -0.182 -0.178 -0.126
TR2.eco_Condition_eco3       -0.081  0.040  0.176  0.167 -0.135 -0.141 -0.040
TR3.eco_Condition_eco3       -0.053  0.047  0.144  0.165 -0.074 -0.108  0.014
                             rw_C_2 rw_C_3 ec_C_2 ec_C_3 rwrE22 rwrE33
EEF1                                                                  
EEF2                                                                  
EEF3                                                                  
EEC1                                                                  
EEC2                                                                  
EEC3                                                                  
IM1                                                                   
IM2                                                                   
IM3                                                                   
S1                                                                    
S2                                                                    
S3                                                                    
TR1                                                                   
TR2                                                                   
TR3                                                                   
BV1                                                                   
BV2                                                                   
BV3                                                                   
S1.BV1                                                                
S2.BV2                                                                
S3.BV3                                                                
reward_Condition_reward2      0.000                                   
reward_Condition_reward3      0.000  0.000                            
eco_Condition_eco2            0.000  0.000  0.000                     
eco_Condition_eco3            0.000  0.000  0.000  0.000              
rewardEco22                   0.000  0.000  0.000  0.000  0.000       
rewardEco33                   0.000  0.000  0.000  0.000  0.000  0.000
TR1.reward_Condition_reward2  0.000  0.000  0.000  0.000  0.000  0.000
TR2.reward_Condition_reward2  0.000  0.000  0.000  0.000  0.000  0.000
TR3.reward_Condition_reward2  0.000  0.000  0.000  0.000  0.000  0.000
TR1.reward_Condition_reward3  0.000  0.000  0.000  0.000  0.000  0.000
TR2.reward_Condition_reward3  0.000  0.000  0.000  0.000  0.000  0.000
TR3.reward_Condition_reward3  0.000  0.000  0.000  0.000  0.000  0.000
TR1.eco_Condition_eco2        0.000  0.000  0.000  0.000  0.000  0.000
TR2.eco_Condition_eco2        0.000  0.000  0.000  0.000  0.000  0.000
TR3.eco_Condition_eco2        0.000  0.000  0.000  0.000  0.000  0.000
TR1.eco_Condition_eco3        0.000  0.000  0.000  0.000  0.000  0.000
TR2.eco_Condition_eco3        0.000  0.000  0.000  0.000  0.000  0.000
TR3.eco_Condition_eco3        0.000  0.000  0.000  0.000  0.000  0.000
                             TR1.r_C_2 TR2.r_C_2 TR3.r_C_2 TR1.r_C_3 TR2.r_C_3
EEF1                                                                          
EEF2                                                                          
EEF3                                                                          
EEC1                                                                          
EEC2                                                                          
EEC3                                                                          
IM1                                                                           
IM2                                                                           
IM3                                                                           
S1                                                                            
S2                                                                            
S3                                                                            
TR1                                                                           
TR2                                                                           
TR3                                                                           
BV1                                                                           
BV2                                                                           
BV3                                                                           
S1.BV1                                                                        
S2.BV2                                                                        
S3.BV3                                                                        
reward_Condition_reward2                                                      
reward_Condition_reward3                                                      
eco_Condition_eco2                                                            
eco_Condition_eco3                                                            
rewardEco22                                                                   
rewardEco33                                                                   
TR1.reward_Condition_reward2     0.000                                        
TR2.reward_Condition_reward2     0.000     0.000                              
TR3.reward_Condition_reward2     0.000     0.000     0.000                    
TR1.reward_Condition_reward3     0.000     0.000     0.000     0.000          
TR2.reward_Condition_reward3     0.000     0.000     0.000     0.000     0.000
TR3.reward_Condition_reward3     0.000     0.000     0.000     0.000     0.000
TR1.eco_Condition_eco2           0.000     0.000     0.000     0.000     0.000
TR2.eco_Condition_eco2           0.000     0.000     0.000     0.000     0.000
TR3.eco_Condition_eco2           0.000     0.000     0.000     0.000     0.000
TR1.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR2.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR3.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
                             TR3.r_C_3 TR1.c_C_2 TR2.c_C_2 TR3.c_C_2 TR1.c_C_3
EEF1                                                                          
EEF2                                                                          
EEF3                                                                          
EEC1                                                                          
EEC2                                                                          
EEC3                                                                          
IM1                                                                           
IM2                                                                           
IM3                                                                           
S1                                                                            
S2                                                                            
S3                                                                            
TR1                                                                           
TR2                                                                           
TR3                                                                           
BV1                                                                           
BV2                                                                           
BV3                                                                           
S1.BV1                                                                        
S2.BV2                                                                        
S3.BV3                                                                        
reward_Condition_reward2                                                      
reward_Condition_reward3                                                      
eco_Condition_eco2                                                            
eco_Condition_eco3                                                            
rewardEco22                                                                   
rewardEco33                                                                   
TR1.reward_Condition_reward2                                                  
TR2.reward_Condition_reward2                                                  
TR3.reward_Condition_reward2                                                  
TR1.reward_Condition_reward3                                                  
TR2.reward_Condition_reward3                                                  
TR3.reward_Condition_reward3     0.000                                        
TR1.eco_Condition_eco2           0.000     0.000                              
TR2.eco_Condition_eco2           0.000     0.000     0.000                    
TR3.eco_Condition_eco2           0.000     0.000     0.000     0.000          
TR1.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR2.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR3.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
                             TR2.c_C_3 TR3.c_C_3
EEF1                                            
EEF2                                            
EEF3                                            
EEC1                                            
EEC2                                            
EEC3                                            
IM1                                             
IM2                                             
IM3                                             
S1                                              
S2                                              
S3                                              
TR1                                             
TR2                                             
TR3                                             
BV1                                             
BV2                                             
BV3                                             
S1.BV1                                          
S2.BV2                                          
S3.BV3                                          
reward_Condition_reward2                        
reward_Condition_reward3                        
eco_Condition_eco2                              
eco_Condition_eco3                              
rewardEco22                                     
rewardEco33                                     
TR1.reward_Condition_reward2                    
TR2.reward_Condition_reward2                    
TR3.reward_Condition_reward2                    
TR1.reward_Condition_reward3                    
TR2.reward_Condition_reward3                    
TR3.reward_Condition_reward3                    
TR1.eco_Condition_eco2                          
TR2.eco_Condition_eco2                          
TR3.eco_Condition_eco2                          
TR1.eco_Condition_eco3                          
TR2.eco_Condition_eco3           0.000          
TR3.eco_Condition_eco3           0.000     0.000

$cov.z
                               EEF1   EEF2   EEF3   EEC1   EEC2   EEC3    IM1
EEF1                          0.295                                          
EEF2                          0.336  0.330                                   
EEF3                          0.269  0.342  0.312                            
EEC1                          1.118  0.823  1.000  0.213                     
EEC2                          0.271  0.050  0.199  0.175  0.274              
EEC3                          0.321  0.224  0.365  0.226  0.313  0.270       
IM1                           0.809  0.681  0.980  1.976  1.328  1.276  0.507
IM2                           0.444  0.404  0.935  0.529  0.317  0.327  0.363
IM3                           0.275  0.187  0.596  0.425  0.103  0.212  0.524
S1                            0.576  0.677  0.658  0.558  0.463  0.315  0.967
S2                           -0.123 -0.028 -0.082  0.112  0.306 -0.081  1.136
S3                            0.320  0.488  0.616  0.454  0.444  0.193  1.053
TR1                           3.867  3.876  4.263  4.868  4.451  4.997  4.417
TR2                           2.410  1.868  2.801  3.588  3.417  3.312  3.380
TR3                           2.603  2.554  2.622  3.835  3.941  4.113  3.380
BV1                           7.334  7.468  7.788  6.989  5.736  5.433  6.614
BV2                           7.966  7.998  8.544  7.376  6.384  6.193  5.991
BV3                           8.001  7.358  7.825  6.367  5.708  5.620  6.867
S1.BV1                       -0.809 -0.955 -1.077 -0.695 -0.266 -0.392 -0.572
S2.BV2                       -0.641 -0.774 -0.802 -0.864 -0.386 -0.429 -0.585
S3.BV3                       -0.641 -0.905 -1.205 -0.831 -0.414 -0.608 -0.596
reward_Condition_reward2      0.282  0.186  1.080  0.896  0.964  1.365  0.569
reward_Condition_reward3     -0.498 -0.180 -0.504 -1.217 -0.704 -1.116 -0.994
eco_Condition_eco2            2.357  1.557  1.430  1.057  1.238  1.037  1.348
eco_Condition_eco3           -1.568 -1.310 -1.073  0.570  0.362  0.681 -0.659
rewardEco22                   0.761  0.522 -0.299  1.014  1.208  0.975  0.734
rewardEco33                  -1.598 -1.406 -1.199 -0.563 -0.514 -0.733 -1.076
TR1.reward_Condition_reward2  1.126  0.249  0.258  1.636  0.381  0.137 -1.168
TR2.reward_Condition_reward2  0.002 -0.173 -0.141  1.366  0.526  0.021  0.327
TR3.reward_Condition_reward2  0.900  0.661  1.533  1.625  0.542  0.172  0.393
TR1.reward_Condition_reward3 -0.846 -0.763 -0.897 -1.746 -1.082 -1.379  1.023
TR2.reward_Condition_reward3 -0.689 -0.136  0.004 -1.750 -1.648 -1.839 -1.614
TR3.reward_Condition_reward3 -0.610 -0.464 -0.276 -2.386 -1.555 -1.824  0.143
TR1.eco_Condition_eco2       -3.145 -2.112 -2.936 -2.672 -1.740 -1.462 -2.980
TR2.eco_Condition_eco2       -1.795 -1.009 -1.522 -2.294 -0.856 -0.709 -3.034
TR3.eco_Condition_eco2       -1.930 -0.992 -1.190 -2.496 -1.092 -0.919 -2.638
TR1.eco_Condition_eco3        2.931  2.417  4.133  1.343  1.169  1.026  2.147
TR2.eco_Condition_eco3        2.693  1.790  3.052  1.976  1.143  0.647  1.444
TR3.eco_Condition_eco3        2.442  1.088  1.660  1.539  1.053  0.528  0.952
                                IM2    IM3     S1     S2     S3    TR1    TR2
EEF1                                                                         
EEF2                                                                         
EEF3                                                                         
EEC1                                                                         
EEC2                                                                         
EEC3                                                                         
IM1                                                                          
IM2                           0.439                                          
IM3                           0.566  0.499                                   
S1                            0.370  0.445  0.000                            
S2                            0.314  0.430  0.003  0.000                     
S3                            0.400  0.522 -0.006  0.009  0.000              
TR1                           4.402  4.467  3.887  4.805  3.288  0.000       
TR2                           2.477  2.896  3.439  4.600  3.340 -0.033  0.000
TR3                           2.775  3.011  4.337  4.761  3.708 -0.021  0.014
BV1                           5.627  5.715  3.043  2.761  3.112  2.228  0.718
BV2                           6.192  5.481  2.656  2.203  2.588  1.507 -0.257
BV3                           6.437  6.255  2.800  2.693  2.341  1.507 -0.265
S1.BV1                       -1.067 -0.881 -1.153 -1.288 -1.073 -0.798 -0.143
S2.BV2                       -0.595 -0.497 -1.438 -1.275 -1.196 -0.165 -0.023
S3.BV3                       -0.552 -0.591 -1.512 -1.284 -1.634 -0.209 -0.032
reward_Condition_reward2      0.959  0.504  0.121 -0.245 -0.091  0.421 -0.715
reward_Condition_reward3     -0.588 -0.058 -0.266 -0.383  0.719  0.118  0.474
eco_Condition_eco2            0.731  1.139  0.778 -0.384 -0.886 -1.291 -0.181
eco_Condition_eco3           -1.402 -0.604 -0.291  0.312 -0.037  1.048  0.633
rewardEco22                  -0.607 -0.706  0.735 -0.307 -0.578 -0.553 -0.364
rewardEco33                  -1.765 -1.328 -0.473  0.000  0.805  0.745  0.727
TR1.reward_Condition_reward2  0.118  0.292 -0.281  0.367 -0.110 -0.388 -0.171
TR2.reward_Condition_reward2 -1.335 -0.706 -0.582  0.552  0.250 -0.160  0.739
TR3.reward_Condition_reward2 -0.907 -0.138 -0.639  0.596  0.215 -0.230  0.682
TR1.reward_Condition_reward3  0.730  1.247  0.363 -0.104 -0.324  0.397  0.776
TR2.reward_Condition_reward3  0.465  0.080  0.601 -0.372 -0.139  0.792  0.544
TR3.reward_Condition_reward3  2.203  1.296  0.490 -0.275 -0.302  0.786  0.429
TR1.eco_Condition_eco2       -2.909 -2.743 -0.126  0.784  0.020  0.345  1.376
TR2.eco_Condition_eco2       -2.220 -2.358 -0.305  0.698  0.134  1.168  0.953
TR3.eco_Condition_eco2       -1.859 -2.272 -0.392  0.492  0.378  1.053  0.879
TR1.eco_Condition_eco3        2.517  1.871  0.153 -0.428 -0.107 -0.242 -0.924
TR2.eco_Condition_eco3        2.919  2.114  0.045 -0.460  0.006 -0.944 -0.662
TR3.eco_Condition_eco3        2.478  1.776  0.238 -0.643 -0.081 -0.955 -0.661
                                TR3    BV1    BV2    BV3 S1.BV1 S2.BV2 S3.BV3
EEF1                                                                         
EEF2                                                                         
EEF3                                                                         
EEC1                                                                         
EEC2                                                                         
EEC3                                                                         
IM1                                                                          
IM2                                                                          
IM3                                                                          
S1                                                                           
S2                                                                           
S3                                                                           
TR1                                                                          
TR2                                                                          
TR3                           0.000                                          
BV1                           0.733  0.000                                   
BV2                          -0.242  0.004  0.000                            
BV3                          -0.232 -0.024  0.002  0.000                     
S1.BV1                        0.275 -0.262 -0.137 -0.265  0.000              
S2.BV2                        0.103  0.206  0.189 -0.008 -0.044  0.000       
S3.BV3                        0.247  0.016  0.108  0.127 -0.011  0.041  0.000
reward_Condition_reward2     -0.090  0.007  0.214  0.074 -0.669 -1.358 -1.528
reward_Condition_reward3     -0.471 -0.466 -0.835 -0.694  0.901  0.796 -0.447
eco_Condition_eco2           -1.006  0.845  1.224  1.856 -1.620 -1.895 -1.274
eco_Condition_eco3            0.637  0.045  0.163 -0.469  1.112  1.917  1.210
rewardEco22                  -0.850 -0.702  1.588  1.358 -2.325 -2.021 -2.991
rewardEco33                  -0.251 -1.281 -0.591 -1.107  0.562  0.599 -0.119
TR1.reward_Condition_reward2 -0.238 -0.210 -0.377 -0.010  0.187  0.557  0.573
TR2.reward_Condition_reward2  0.639 -0.116 -1.448 -1.065 -0.122 -0.054 -0.172
TR3.reward_Condition_reward2  0.144  0.299 -0.713 -0.376 -0.648 -0.423 -0.530
TR1.reward_Condition_reward3  0.734  0.492  0.569 -0.131 -0.143 -0.066  1.183
TR2.reward_Condition_reward3  0.419 -0.490  0.167 -0.604  0.189  0.304  1.609
TR3.reward_Condition_reward3  0.087  0.135  0.940  0.618 -0.537  0.032  1.512
TR1.eco_Condition_eco2        1.110 -1.727 -2.861 -2.569  1.405  1.715  1.110
TR2.eco_Condition_eco2        0.793 -0.806 -1.508 -1.097  0.811  1.289  0.977
TR3.eco_Condition_eco2        0.547 -0.692 -1.088 -1.006  0.896  1.474  0.698
TR1.eco_Condition_eco3       -0.936  1.391  1.862  1.737 -1.540 -1.508 -0.972
TR2.eco_Condition_eco3       -0.656  0.397  1.947  1.792 -1.137 -1.201 -0.323
TR3.eco_Condition_eco3       -0.395  0.468  1.583  1.723 -0.718 -1.054  0.135
                             rw_C_2 rw_C_3 ec_C_2 ec_C_3 rwrE22 rwrE33
EEF1                                                                  
EEF2                                                                  
EEF3                                                                  
EEC1                                                                  
EEC2                                                                  
EEC3                                                                  
IM1                                                                   
IM2                                                                   
IM3                                                                   
S1                                                                    
S2                                                                    
S3                                                                    
TR1                                                                   
TR2                                                                   
TR3                                                                   
BV1                                                                   
BV2                                                                   
BV3                                                                   
S1.BV1                                                                
S2.BV2                                                                
S3.BV3                                                                
reward_Condition_reward2      0.000                                   
reward_Condition_reward3      0.000  0.000                            
eco_Condition_eco2            0.000  0.000  0.000                     
eco_Condition_eco3            0.000  0.000  0.000  0.000              
rewardEco22                   0.000  0.000  0.000  0.000  0.000       
rewardEco33                   0.000  0.000  0.000  0.000  0.000  0.000
TR1.reward_Condition_reward2  0.000  0.000  0.000  0.000  0.000  0.000
TR2.reward_Condition_reward2  0.000  0.000  0.000  0.000  0.000  0.000
TR3.reward_Condition_reward2  0.000  0.000  0.000  0.000  0.000  0.000
TR1.reward_Condition_reward3  0.000  0.000  0.000  0.000  0.000  0.000
TR2.reward_Condition_reward3  0.000  0.000  0.000  0.000  0.000  0.000
TR3.reward_Condition_reward3  0.000  0.000  0.000  0.000  0.000  0.000
TR1.eco_Condition_eco2        0.000  0.000  0.000  0.000  0.000  0.000
TR2.eco_Condition_eco2        0.000  0.000  0.000  0.000  0.000  0.000
TR3.eco_Condition_eco2        0.000  0.000  0.000  0.000  0.000  0.000
TR1.eco_Condition_eco3        0.000  0.000  0.000  0.000  0.000  0.000
TR2.eco_Condition_eco3        0.000  0.000  0.000  0.000  0.000  0.000
TR3.eco_Condition_eco3        0.000  0.000  0.000  0.000  0.000  0.000
                             TR1.r_C_2 TR2.r_C_2 TR3.r_C_2 TR1.r_C_3 TR2.r_C_3
EEF1                                                                          
EEF2                                                                          
EEF3                                                                          
EEC1                                                                          
EEC2                                                                          
EEC3                                                                          
IM1                                                                           
IM2                                                                           
IM3                                                                           
S1                                                                            
S2                                                                            
S3                                                                            
TR1                                                                           
TR2                                                                           
TR3                                                                           
BV1                                                                           
BV2                                                                           
BV3                                                                           
S1.BV1                                                                        
S2.BV2                                                                        
S3.BV3                                                                        
reward_Condition_reward2                                                      
reward_Condition_reward3                                                      
eco_Condition_eco2                                                            
eco_Condition_eco3                                                            
rewardEco22                                                                   
rewardEco33                                                                   
TR1.reward_Condition_reward2     0.000                                        
TR2.reward_Condition_reward2     0.000     0.000                              
TR3.reward_Condition_reward2     0.000     0.000     0.000                    
TR1.reward_Condition_reward3     0.000     0.000     0.000     0.000          
TR2.reward_Condition_reward3     0.000     0.000     0.000     0.000     0.000
TR3.reward_Condition_reward3     0.000     0.000     0.000     0.000     0.000
TR1.eco_Condition_eco2           0.000     0.000     0.000     0.000     0.000
TR2.eco_Condition_eco2           0.000     0.000     0.000     0.000     0.000
TR3.eco_Condition_eco2           0.000     0.000     0.000     0.000     0.000
TR1.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR2.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR3.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
                             TR3.r_C_3 TR1.c_C_2 TR2.c_C_2 TR3.c_C_2 TR1.c_C_3
EEF1                                                                          
EEF2                                                                          
EEF3                                                                          
EEC1                                                                          
EEC2                                                                          
EEC3                                                                          
IM1                                                                           
IM2                                                                           
IM3                                                                           
S1                                                                            
S2                                                                            
S3                                                                            
TR1                                                                           
TR2                                                                           
TR3                                                                           
BV1                                                                           
BV2                                                                           
BV3                                                                           
S1.BV1                                                                        
S2.BV2                                                                        
S3.BV3                                                                        
reward_Condition_reward2                                                      
reward_Condition_reward3                                                      
eco_Condition_eco2                                                            
eco_Condition_eco3                                                            
rewardEco22                                                                   
rewardEco33                                                                   
TR1.reward_Condition_reward2                                                  
TR2.reward_Condition_reward2                                                  
TR3.reward_Condition_reward2                                                  
TR1.reward_Condition_reward3                                                  
TR2.reward_Condition_reward3                                                  
TR3.reward_Condition_reward3     0.000                                        
TR1.eco_Condition_eco2           0.000     0.000                              
TR2.eco_Condition_eco2           0.000     0.000     0.000                    
TR3.eco_Condition_eco2           0.000     0.000     0.000     0.000          
TR1.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR2.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
TR3.eco_Condition_eco3           0.000     0.000     0.000     0.000     0.000
                             TR2.c_C_3 TR3.c_C_3
EEF1                                            
EEF2                                            
EEF3                                            
EEC1                                            
EEC2                                            
EEC3                                            
IM1                                             
IM2                                             
IM3                                             
S1                                              
S2                                              
S3                                              
TR1                                             
TR2                                             
TR3                                             
BV1                                             
BV2                                             
BV3                                             
S1.BV1                                          
S2.BV2                                          
S3.BV3                                          
reward_Condition_reward2                        
reward_Condition_reward3                        
eco_Condition_eco2                              
eco_Condition_eco3                              
rewardEco22                                     
rewardEco33                                     
TR1.reward_Condition_reward2                    
TR2.reward_Condition_reward2                    
TR3.reward_Condition_reward2                    
TR1.reward_Condition_reward3                    
TR2.reward_Condition_reward3                    
TR3.reward_Condition_reward3                    
TR1.eco_Condition_eco2                          
TR2.eco_Condition_eco2                          
TR3.eco_Condition_eco2                          
TR1.eco_Condition_eco3                          
TR2.eco_Condition_eco3           0.000          
TR3.eco_Condition_eco3           0.000     0.000

$summary
                          cov
srmr                    0.153
srmr.se                 0.033
srmr.exactfit.z         1.369
srmr.exactfit.pvalue    0.086
usrmr                   0.105
usrmr.se                0.030
usrmr.ci.lower          0.055
usrmr.ci.upper          0.156
usrmr.closefit.h0.value 0.050
usrmr.closefit.z        1.817
usrmr.closefit.pvalue   0.035

Group comparison test_non-normal data

# Art for EEF_composite
art_model_EEF <- art(EEF_composite ~ Condition_reward * Condition_eco, data = data_reduced_good)
summary(art_model_EEF)

Warning in summary.art(art_model_EEF): F values of ANOVAs on aligned responses
not of interest are not all ~0. ART may not be appropriate.

Aligned Rank Transform of Factorial Model

Call:
art(formula = EEF_composite ~ Condition_reward * Condition_eco, 
    data = data_reduced_good)

Column sums of aligned responses (should all be ~0):
              Condition_reward                  Condition_eco 
                             0                              0 
Condition_reward:Condition_eco 
                             0 

F values of ANOVAs on aligned responses not of interest (should all be ~0):
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
0.000000 0.000000 0.000000 0.008160 0.005575 0.041528 

# Art for for EEC_composite
art_model_EEC <- art(EEC_composite ~ Condition_reward * Condition_eco, data = data_reduced_good)
summary(art_model_EEC)

Warning in summary.art(art_model_EEC): F values of ANOVAs on aligned responses
not of interest are not all ~0. ART may not be appropriate.

Aligned Rank Transform of Factorial Model

Call:
art(formula = EEC_composite ~ Condition_reward * Condition_eco, 
    data = data_reduced_good)

Column sums of aligned responses (should all be ~0):
              Condition_reward                  Condition_eco 
                             0                              0 
Condition_reward:Condition_eco 
                             0 

F values of ANOVAs on aligned responses not of interest (should all be ~0):
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.00000 0.00000 0.00000 0.01775 0.03853 0.05514 

Regression between PEB and EEF

data_reduced_good$PEB <- factor(data_reduced_good$PEB)

model_PEB_EEF <- multinom(PEB ~ EEF_composite, data = data_reduced_good)

# weights:  9 (4 variable)
initial  value 117.551515 
iter  10 value 58.569983
final  value 58.569977 
converged

z <- summary(model_PEB_EEF)$coefficients / summary(model_PEB_EEF)$standard.errors
p <- (1 - pnorm(abs(z))) * 2
p

  (Intercept) EEF_composite
2 0.108664870  6.848838e-02
3 0.002195332  1.432207e-05

summary(model_PEB_EEF)

Call:
multinom(formula = PEB ~ EEF_composite, data = data_reduced_good)

Coefficients:
  (Intercept) EEF_composite
2   -1.842196     0.4846964
3   -4.124300     1.2680242

Std. Errors:
  (Intercept) EEF_composite
2    1.148341     0.2660565
3    1.346732     0.2922479

Residual Deviance: 117.14 
AIC: 125.14 

Regression between PEB and EEC

data_reduced_good$PEB <- factor(data_reduced_good$PEB)

model_PEB_EEC <- multinom(PEB ~ EEC_composite, data = data_reduced_good)

# weights:  9 (4 variable)
initial  value 117.551515 
iter  10 value 64.439607
iter  10 value 64.439607
final  value 64.439607 
converged

z <- summary(model_PEB_EEC)$coefficients / summary(model_PEB_EEC)$standard.errors
p <- (1 - pnorm(abs(z))) * 2
p

  (Intercept) EEC_composite
2  0.18719657    0.12251717
3  0.06949578    0.00016131

summary(model_PEB_EEC)

Call:
multinom(formula = PEB ~ EEC_composite, data = data_reduced_good)

Coefficients:
  (Intercept) EEC_composite
2   -1.255863     0.4341614
3   -1.535411     0.9474827

Std. Errors:
  (Intercept) EEC_composite
2   0.9521920     0.2811391
3   0.8458709     0.2511232

Residual Deviance: 128.8792 
AIC: 136.8792 

Motivation variables

Group comparison test_non-normal data

# Run two-way ANOVA for IM_composite
art_model_IM <- art(IM_composite ~ Condition_reward * Condition_eco, data = data_reduced_good)
summary(art_model_IM)

Warning in summary.art(art_model_IM): F values of ANOVAs on aligned responses
not of interest are not all ~0. ART may not be appropriate.

Aligned Rank Transform of Factorial Model

Call:
art(formula = IM_composite ~ Condition_reward * Condition_eco, 
    data = data_reduced_good)

Column sums of aligned responses (should all be ~0):
              Condition_reward                  Condition_eco 
                             0                              0 
Condition_reward:Condition_eco 
                             0 

F values of ANOVAs on aligned responses not of interest (should all be ~0):
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
0.000000 0.000000 0.000000 0.013588 0.002768 0.077837 

# Run two-way ANOVA for IDR_composite
art_model_IDR <- art(IDR_composite ~ Condition_reward * Condition_eco, data = data_reduced_good)
summary(art_model_IDR)

Warning in summary.art(art_model_IDR): F values of ANOVAs on aligned responses
not of interest are not all ~0. ART may not be appropriate.

Aligned Rank Transform of Factorial Model

Call:
art(formula = IDR_composite ~ Condition_reward * Condition_eco, 
    data = data_reduced_good)

Column sums of aligned responses (should all be ~0):
              Condition_reward                  Condition_eco 
                             0                              0 
Condition_reward:Condition_eco 
                             0 

F values of ANOVAs on aligned responses not of interest (should all be ~0):
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.00000 0.00000 0.00000 0.01833 0.04088 0.05546 

# Run two-way ANOVA for INR_composite
art_model_IM <- art(IM_composite ~ Condition_reward * Condition_eco, data = data_reduced_good)
summary(art_model_IM)

Warning in summary.art(art_model_IM): F values of ANOVAs on aligned responses
not of interest are not all ~0. ART may not be appropriate.

Aligned Rank Transform of Factorial Model

Call:
art(formula = IM_composite ~ Condition_reward * Condition_eco, 
    data = data_reduced_good)

Column sums of aligned responses (should all be ~0):
              Condition_reward                  Condition_eco 
                             0                              0 
Condition_reward:Condition_eco 
                             0 

F values of ANOVAs on aligned responses not of interest (should all be ~0):
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
0.000000 0.000000 0.000000 0.013588 0.002768 0.077837 

Regression between PEB and IM

data_reduced_good$PEB <- factor(data_reduced_good$PEB)

model_PEB_IM <- multinom(PEB ~ IM_composite, data = data_reduced_good)

# weights:  9 (4 variable)
initial  value 117.551515 
iter  10 value 57.968768
final  value 57.968031 
converged

z <- summary(model_PEB_IM)$coefficients / summary(model_PEB_IM)$standard.errors
p <- (1 - pnorm(abs(z))) * 2
p

  (Intercept) IM_composite
2 0.026195878  1.49928e-02
3 0.001731996  5.28967e-05

summary(model_PEB_IM)

Call:
multinom(formula = PEB ~ IM_composite, data = data_reduced_good)

Coefficients:
  (Intercept) IM_composite
2   -4.218293    0.9671431
3   -5.983518    1.6178277

Std. Errors:
  (Intercept) IM_composite
2    1.897315    0.3975836
3    1.910013    0.4002102

Residual Deviance: 115.9361 
AIC: 123.9361 

data_reduced_good$PEB <- factor(data_reduced_good$PEB)

model_PEB_IDR <- multinom(PEB ~ IDR_composite, data = data_reduced_good)

# weights:  9 (4 variable)
initial  value 117.551515 
iter  10 value 63.632361
final  value 63.495330 
converged

z <- summary(model_PEB_IDR)$coefficients / summary(model_PEB_IDR)$standard.errors
p <- (1 - pnorm(abs(z))) * 2
p

  (Intercept) IDR_composite
2 0.088464695  0.0720808278
3 0.002158701  0.0001615415

summary(model_PEB_IDR)

Call:
multinom(formula = PEB ~ IDR_composite, data = data_reduced_good)

Coefficients:
  (Intercept) IDR_composite
2   -4.278067     0.7818104
3   -7.464752     1.5824088

Std. Errors:
  (Intercept) IDR_composite
2    2.511262     0.4346755
3    2.433511     0.4194455

Residual Deviance: 126.9907 
AIC: 134.9907 

data_reduced_good$PEB <- factor(data_reduced_good$PEB)

model_PEB_INR <- multinom(PEB ~ INR_composite, data = data_reduced_good)

# weights:  9 (4 variable)
initial  value 117.551515 
iter  10 value 56.512525
final  value 56.512506 
converged

z <- summary(model_PEB_INR)$coefficients / summary(model_PEB_INR)$standard.errors
p <- (1 - pnorm(abs(z))) * 2
p

  (Intercept) INR_composite
2 0.018620868  1.049672e-02
3 0.001951817  1.643024e-05

summary(model_PEB_INR)

Call:
multinom(formula = PEB ~ INR_composite, data = data_reduced_good)

Coefficients:
  (Intercept) INR_composite
2   -2.496438     0.8730919
3   -3.142011     1.4259177

Std. Errors:
  (Intercept) INR_composite
2    1.060944     0.3411819
3    1.014381     0.3309480

Residual Deviance: 113.025 
AIC: 121.025