PMB -> Batch 1 to 4

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    47   16
  2    43   35
  3    65    5

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

   
    FALSE TRUE
  1    73    0
  2    69    8
  3    47   14

table(data_combined$att_flag) #Attention check

FALSE  TRUE 
  209     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 
 211  121 

     vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
S1      1 121 5.00 1.46      5    5.14 1.48   1   7     6 -0.91     0.45 0.13
S2      2 121 4.80 1.53      5    4.94 1.48   1   7     6 -0.80    -0.02 0.14
S3      3 121 5.07 1.43      5    5.22 1.48   1   7     6 -0.99     0.90 0.13
IM1     4 121 5.12 1.56      5    5.32 1.48   1   7     6 -1.06     0.78 0.14
IM2     5 121 5.61 1.31      6    5.80 1.48   1   7     6 -1.61     3.44 0.12
IM3     6 121 5.58 1.32      6    5.76 1.48   1   7     6 -1.54     2.95 0.12
INR1    7 121 4.88 1.55      5    5.04 1.48   1   7     6 -0.86     0.20 0.14
INR2    8 121 4.42 1.82      5    4.49 1.48   1   7     6 -0.31    -0.98 0.17
INR3    9 121 4.27 1.80      5    4.33 1.48   1   7     6 -0.30    -0.98 0.16
IDR1   10 121 6.17 1.04      6    6.33 1.48   1   7     6 -1.89     5.47 0.09
IDR2   11 121 6.22 1.04      6    6.41 1.48   1   7     6 -2.32     7.40 0.09
IDR3   12 121 6.28 0.99      7    6.45 0.00   1   7     6 -1.99     5.97 0.09
EEF1   13 121 5.21 1.48      6    5.39 1.48   1   7     6 -1.02     0.70 0.13
EEF2   14 121 5.47 1.50      6    5.70 1.48   1   7     6 -1.28     1.49 0.14
EEF3   15 121 5.44 1.52      6    5.67 1.48   1   7     6 -1.20     1.19 0.14
EEC1   16 121 4.25 1.57      4    4.33 1.48   1   7     6 -0.40    -0.42 0.14
EEC2   17 121 4.26 1.67      5    4.31 1.48   1   7     6 -0.23    -0.87 0.15
EEC3   18 121 4.25 1.69      4    4.30 1.48   1   7     6 -0.27    -0.74 0.15
TR1    19 121 3.35 1.62      3    3.31 1.48   1   7     6  0.12    -0.90 0.15
TR2    20 121 3.42 1.65      3    3.40 2.97   1   7     6  0.00    -1.01 0.15
TR3    21 121 2.97 1.60      3    2.91 1.48   1   7     6  0.29    -1.05 0.15
BV1    22 121 6.79 1.90      7    6.98 1.48   2   9     7 -0.69    -0.42 0.17
BV2    23 121 7.16 1.83      7    7.39 2.97   3   9     6 -0.72    -0.50 0.17
BV3    24 121 7.31 1.79      8    7.58 1.48   3   9     6 -0.88    -0.21 0.16

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 
0.90 0.90 0.93 0.96 0.95 0.95 0.92 0.92 0.92 0.93 0.93 0.93 0.93 0.91 0.93 0.96 
EEC2 EEC3  TR1  TR2  TR3  BV1  BV2  BV3 
0.91 0.89 0.94 0.76 0.82 0.97 0.90 0.92 

Non-normality test across all scales

$S1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89058, p-value = 6.039e-08


$S2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89416, p-value = 9.059e-08


$S3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.88207, p-value = 2.377e-08


$IM1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.86473, p-value = 4.017e-09


$IM2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.79551, p-value = 1.086e-11


$IM3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.80991, p-value = 3.282e-11


$INR1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89173, p-value = 6.872e-08


$INR2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92716, p-value = 5.93e-06


$INR3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92934, p-value = 8.08e-06


$IDR1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.74475, p-value = 3.217e-13


$IDR2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.68878, p-value = 1.127e-14


$IDR3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.71528, p-value = 5.196e-14


$EEF1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.8749, p-value = 1.119e-08


$EEF2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.83381, p-value = 2.345e-10


$EEF3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.84418, p-value = 5.837e-10


$EEC1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92946, p-value = 8.224e-06


$EEC2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.93973, p-value = 3.818e-05


$EEC3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.94119, p-value = 4.795e-05


$TR1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.92651, p-value = 5.41e-06


$TR2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.9194, p-value = 2.04e-06


$TR3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89188, p-value = 6.991e-08


$BV1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89855, p-value = 1.506e-07


$BV2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.86408, p-value = 3.771e-09


$BV3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.84299, p-value = 5.248e-10

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 = 0.8786, p-value = 1.646e-08

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 = 0.9685, p-value = 0.006193

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                14   0.00993
2 1                2                10   0.543  
3 1                3                24   0.0206 
4 2                1                16   0.0987 
5 2                2                19   0.0398 
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                14     0.820
2 1                2                10     0.978
3 1                3                24     0.604
4 2                1                16     0.238
5 2                2                19     0.890
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 = 0.86251, p-value = 3.233e-09

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 = 0.75524, p-value = 6.383e-13

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 = 0.95159, p-value = 0.0002658

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                14  0.0273  
2 1                2                10  0.320   
3 1                3                24  0.0376  
4 2                1                16  0.188   
5 2                2                19  0.000232
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                14 0.00000917
2 1                2                10 0.0736    
3 1                3                24 0.000797  
4 2                1                16 0.0608    
5 2                2                19 0.0112    
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                14    0.609 
2 1                2                10    0.231 
3 1                3                24    0.0138
4 2                1                16    0.833 
5 2                2                19    0.996 
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 94 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        70

  Number of observations                           121

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               867.358     874.586
  Degrees of freedom                               539         539
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  0.992
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              3314.386    3288.105
  Degrees of freedom                               588         588
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.008

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.880       0.876
  Tucker-Lewis Index (TLI)                       0.869       0.864
                                                                  
  Robust Comparative Fit Index (CFI)                         0.878
  Robust Tucker-Lewis Index (TLI)                            0.867

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -3811.224   -3811.224
  Scaling correction factor                                  1.375
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -3377.545   -3377.545
  Scaling correction factor                                  1.036
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                7762.448    7762.448
  Bayesian (BIC)                              7958.154    7958.154
  Sample-size adjusted Bayesian (SABIC)       7736.838    7736.838

Root Mean Square Error of Approximation:

  RMSEA                                          0.071       0.072
  90 Percent confidence interval - lower         0.062       0.063
  90 Percent confidence interval - upper         0.080       0.080
  P-value H_0: RMSEA <= 0.050                    0.000       0.000
  P-value H_0: RMSEA >= 0.080                    0.042       0.057
                                                                  
  Robust RMSEA                                               0.071
  90 Percent confidence interval - lower                     0.063
  90 Percent confidence interval - upper                     0.080
  P-value H_0: Robust RMSEA <= 0.050                         0.000
  P-value H_0: Robust RMSEA >= 0.080                         0.049

Standardized Root Mean Square Residual:

  SRMR                                           0.148       0.148

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                               1.327    0.926
    EEF2              1.041    0.073   14.183    0.000    1.382    0.955
    EEF3              0.996    0.084   11.906    0.000    1.321    0.901
  EEC =~                                                                
    EEC1              1.000                               1.322    0.864
    EEC2              1.143    0.067   16.973    0.000    1.511    0.932
    EEC3              1.187    0.069   17.227    0.000    1.569    0.956
  IM =~                                                                 
    IM1               1.000                               1.248    0.843
    IM2               0.889    0.079   11.225    0.000    1.110    0.897
    IM3               0.926    0.064   14.441    0.000    1.155    0.932
  S =~                                                                  
    S1                1.000                               1.285    0.883
    S2                1.000    0.072   13.882    0.000    1.284    0.842
    S3                0.958    0.080   11.992    0.000    1.230    0.862
  TR =~                                                                 
    TR1               1.000                               1.261    0.781
    TR2               1.228    0.115   10.675    0.000    1.549    0.942
    TR3               1.168    0.097   12.023    0.000    1.474    0.924
  BV =~                                                                 
    BV1               1.000                               1.557    0.824
    BV2               1.141    0.092   12.450    0.000    1.777    0.975
    BV3               1.072    0.094   11.431    0.000    1.669    0.935
  SxBV =~                                                               
    S1.BV1            1.000                               2.944    0.863
    S2.BV2            1.043    0.107    9.754    0.000    3.070    0.915
    S3.BV3            1.159    0.113   10.219    0.000    3.413    0.936

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  S ~                                                                   
    rw_C_2    (a1)   -0.325    0.392   -0.829    0.407   -0.253   -0.123
    rw_C_3    (a2)    0.316    0.426    0.741    0.459    0.246    0.101
    ec_C_2    (a3)   -0.388    0.482   -0.805    0.421   -0.302   -0.137
    ec_C_3    (a4)   -0.074    0.375   -0.199    0.843   -0.058   -0.029
    rwrE22    (a5)    0.064    0.647    0.099    0.921    0.050    0.018
    rwrE33    (a6)   -0.008    0.579   -0.013    0.989   -0.006   -0.002
    TR1._C (tr_r1)   -0.100    0.360   -0.277    0.782   -0.078   -0.061
    TR2._C (tr_r2)    0.012    0.304    0.039    0.969    0.009    0.008
    TR3._C (tr_r3)    0.032    0.382    0.083    0.934    0.025    0.019
    TR1._C (tr_r4)    0.152    0.241    0.632    0.528    0.118    0.080
    TR2._C (tr_r5)   -0.048    0.311   -0.154    0.878   -0.037   -0.026
    TR3._C (tr_r6)   -0.017    0.351   -0.049    0.961   -0.013   -0.009
    TR1._C (tr_e1)   -0.186    0.288   -0.648    0.517   -0.145   -0.109
    TR2._C (tr_e2)    0.282    0.363    0.777    0.437    0.220    0.175
    TR3._C (tr_e3)   -0.316    0.385   -0.820    0.412   -0.246   -0.186
    TR1._C (tr_e4)    0.122    0.344    0.353    0.724    0.095    0.074
    TR2._C (tr_e5)   -0.452    0.322   -1.402    0.161   -0.352   -0.279
    TR3._C (tr_e6)    0.291    0.456    0.639    0.523    0.227    0.176
  IM ~                                                                  
    S         (b1)    0.547    0.092    5.929    0.000    0.563    0.563
    SxBV      (b2)   -0.171    0.031   -5.459    0.000   -0.403   -0.403
  EEF ~                                                                 
    IM        (c1)    0.689    0.135    5.091    0.000    0.647    0.647
    S         (c2)    0.075    0.135    0.556    0.578    0.072    0.072
  EEC ~                                                                 
    IM        (d1)    0.452    0.092    4.936    0.000    0.427    0.427
    S         (d2)    0.344    0.111    3.101    0.002    0.334    0.334

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  TR ~~                                                                 
    BV                0.411    0.229    1.791    0.073    0.209    0.209
    SxBV             -0.825    0.488   -1.691    0.091   -0.222   -0.222
  BV ~~                                                                 
    SxBV             -1.550    0.992   -1.561    0.118   -0.338   -0.338
 .EEF ~~                                                                
   .EEC               0.485    0.125    3.889    0.000    0.517    0.517

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEF1              0.291    0.103    2.820    0.005    0.291    0.142
   .EEF2              0.184    0.051    3.587    0.000    0.184    0.088
   .EEF3              0.405    0.101    4.031    0.000    0.405    0.188
   .EEC1              0.593    0.112    5.305    0.000    0.593    0.253
   .EEC2              0.347    0.084    4.129    0.000    0.347    0.132
   .EEC3              0.231    0.079    2.935    0.003    0.231    0.086
   .IM1               0.633    0.147    4.319    0.000    0.633    0.289
   .IM2               0.298    0.095    3.128    0.002    0.298    0.195
   .IM3               0.202    0.058    3.464    0.001    0.202    0.132
   .S1                0.466    0.094    4.932    0.000    0.466    0.220
   .S2                0.675    0.162    4.162    0.000    0.675    0.290
   .S3                0.522    0.128    4.089    0.000    0.522    0.257
   .TR1               1.015    0.232    4.382    0.000    1.015    0.390
   .TR2               0.307    0.129    2.391    0.017    0.307    0.114
   .TR3               0.373    0.110    3.405    0.001    0.373    0.147
   .BV1               1.149    0.233    4.928    0.000    1.149    0.322
   .BV2               0.166    0.091    1.827    0.068    0.166    0.050
   .BV3               0.404    0.124    3.264    0.001    0.404    0.127
   .S1.BV1            2.972    0.596    4.987    0.000    2.972    0.255
   .S2.BV2            1.821    0.520    3.501    0.000    1.821    0.162
   .S3.BV3            1.641    0.555    2.955    0.003    1.641    0.123
   .EEF               0.920    0.195    4.727    0.000    0.523    0.523
   .EEC               0.954    0.153    6.229    0.000    0.546    0.546
   .IM                0.810    0.185    4.388    0.000    0.520    0.520
   .S                 1.510    0.290    5.209    0.000    0.915    0.915
    TR                1.591    0.312    5.096    0.000    1.000    1.000
    BV                2.424    0.447    5.429    0.000    1.000    1.000
    SxBV              8.668    3.570    2.428    0.015    1.000    1.000

R-Square:
                   Estimate
    EEF1              0.858
    EEF2              0.912
    EEF3              0.812
    EEC1              0.747
    EEC2              0.868
    EEC3              0.914
    IM1               0.711
    IM2               0.805
    IM3               0.868
    S1                0.780
    S2                0.710
    S3                0.743
    TR1               0.610
    TR2               0.886
    TR3               0.853
    BV1               0.678
    BV2               0.950
    BV3               0.873
    S1.BV1            0.745
    S2.BV2            0.838
    S3.BV3            0.877
    EEF               0.477
    EEC               0.454
    IM                0.480
    S                 0.085

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 
0.951 0.942 0.922 0.897 0.912 0.934 0.930 

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

  EEF   EEC    IM     S    TR    BV  SxBV 
0.888 0.892 0.812 0.896 0.916 0.937 0.933 

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 
0.809 0.804 0.704 0.743 0.784 0.830 0.822 

#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                          0.059                                          
EEF2                          0.065  0.062                                   
EEF3                          0.048  0.059  0.056                            
EEC1                          0.182  0.137  0.149  0.045                     
EEC2                          0.056  0.017  0.036  0.033  0.052              
EEC3                          0.058  0.037  0.059  0.046  0.060  0.055       
IM1                           0.120  0.110  0.146  0.271  0.208  0.198  0.094
IM2                           0.047  0.078  0.140  0.087  0.052  0.053  0.077
IM3                           0.033  0.051  0.105  0.088  0.036  0.048  0.099
S1                            0.076  0.134  0.114  0.073  0.076  0.047  0.153
S2                           -0.023  0.023  0.013  0.035  0.047 -0.010  0.180
S3                            0.054  0.116  0.115  0.080  0.082  0.037  0.161
TR1                           0.352  0.367  0.366  0.464  0.437  0.450  0.415
TR2                           0.255  0.208  0.264  0.365  0.343  0.301  0.311
TR3                           0.260  0.245  0.234  0.367  0.388  0.382  0.328
BV1                           0.566  0.551  0.589  0.544  0.460  0.483  0.591
BV2                           0.534  0.543  0.581  0.526  0.450  0.472  0.520
BV3                           0.519  0.522  0.554  0.485  0.426  0.425  0.572
S1.BV1                       -0.089 -0.183 -0.190 -0.095 -0.040 -0.050 -0.100
S2.BV2                       -0.066 -0.159 -0.153 -0.141 -0.058 -0.061 -0.100
S3.BV3                       -0.085 -0.207 -0.239 -0.152 -0.076 -0.098 -0.116
reward_Condition_reward2      0.048  0.022  0.081  0.029  0.059  0.089  0.005
reward_Condition_reward3     -0.040 -0.013 -0.039 -0.053 -0.039 -0.060 -0.043
eco_Condition_eco2            0.187  0.123  0.109  0.044  0.086  0.071  0.036
eco_Condition_eco3           -0.122 -0.091 -0.081  0.058  0.032  0.068 -0.019
rewardEco22                   0.100  0.055  0.031  0.025  0.069  0.048 -0.016
rewardEco33                  -0.106 -0.083 -0.073 -0.021 -0.030 -0.043 -0.053
TR1.reward_Condition_reward2  0.088  0.050  0.037  0.123  0.036  0.004 -0.035
TR2.reward_Condition_reward2  0.024  0.033  0.029  0.102  0.059  0.003  0.046
TR3.reward_Condition_reward2  0.085  0.081  0.122  0.124  0.047  0.004  0.055
TR1.reward_Condition_reward3 -0.048 -0.054 -0.052 -0.093 -0.063 -0.068  0.046
TR2.reward_Condition_reward3 -0.063 -0.030 -0.015 -0.122 -0.125 -0.127 -0.099
TR3.reward_Condition_reward3 -0.054 -0.048 -0.034 -0.166 -0.121 -0.135 -0.005
TR1.eco_Condition_eco2       -0.178 -0.105 -0.126 -0.094 -0.100 -0.112 -0.106
TR2.eco_Condition_eco2       -0.086 -0.019 -0.048 -0.089 -0.024 -0.046 -0.077
TR3.eco_Condition_eco2       -0.081 -0.018 -0.016 -0.089 -0.045 -0.064 -0.057
TR1.eco_Condition_eco3        0.187  0.139  0.205  0.080  0.087  0.111  0.102
TR2.eco_Condition_eco3        0.158  0.088  0.147  0.095  0.070  0.062  0.056
TR3.eco_Condition_eco3        0.138  0.046  0.071  0.078  0.061  0.054  0.030
                                IM2    IM3     S1     S2     S3    TR1    TR2
EEF1                                                                         
EEF2                                                                         
EEF3                                                                         
EEC1                                                                         
EEC2                                                                         
EEC3                                                                         
IM1                                                                          
IM2                           0.105                                          
IM3                           0.120  0.112                                   
S1                            0.091  0.094  0.000                            
S2                            0.069  0.094  0.001  0.000                     
S3                            0.086  0.110 -0.001  0.002  0.000              
TR1                           0.380  0.381  0.359  0.414  0.333  0.000       
TR2                           0.212  0.260  0.314  0.409  0.328 -0.004  0.000
TR3                           0.264  0.299  0.356  0.388  0.321 -0.002  0.002
BV1                           0.547  0.563  0.352  0.292  0.358  0.258  0.101
BV2                           0.558  0.531  0.321  0.252  0.329  0.193 -0.043
BV3                           0.588  0.567  0.350  0.308  0.315  0.199 -0.035
S1.BV1                       -0.205 -0.179 -0.270 -0.251 -0.252 -0.072 -0.018
S2.BV2                       -0.121 -0.118 -0.298 -0.266 -0.281 -0.001  0.001
S3.BV3                       -0.124 -0.143 -0.338 -0.271 -0.394 -0.027 -0.010
reward_Condition_reward2      0.045  0.042 -0.003 -0.021  0.010 -0.014 -0.101
reward_Condition_reward3     -0.027 -0.001 -0.013 -0.024  0.049  0.012  0.037
eco_Condition_eco2            0.032  0.077  0.044 -0.030 -0.043 -0.148 -0.064
eco_Condition_eco3           -0.067 -0.034 -0.016  0.028 -0.022  0.090  0.050
rewardEco22                  -0.051 -0.020  0.024 -0.025 -0.003 -0.107 -0.083
rewardEco33                  -0.116 -0.088 -0.031  0.001  0.062  0.066  0.064
TR1.reward_Condition_reward2  0.044  0.062 -0.038  0.042 -0.006 -0.015  0.049
TR2.reward_Condition_reward2 -0.006  0.019 -0.056  0.051  0.017  0.048  0.127
TR3.reward_Condition_reward2  0.004  0.045 -0.067  0.069  0.017  0.036  0.123
TR1.reward_Condition_reward3  0.033  0.063  0.030 -0.006 -0.037  0.033  0.046
TR2.reward_Condition_reward3  0.021 -0.010  0.062 -0.035 -0.022  0.046  0.032
TR3.reward_Condition_reward3  0.135  0.064  0.051 -0.025 -0.036  0.049  0.018
TR1.eco_Condition_eco2       -0.144 -0.121 -0.025  0.076  0.010  0.073  0.204
TR2.eco_Condition_eco2       -0.053 -0.052 -0.030  0.058  0.007  0.195  0.144
TR3.eco_Condition_eco2       -0.050 -0.057 -0.046  0.054  0.033  0.183  0.146
TR1.eco_Condition_eco3        0.143  0.096  0.019 -0.037 -0.021 -0.041 -0.146
TR2.eco_Condition_eco3        0.143  0.096  0.016 -0.047 -0.009 -0.148 -0.116
TR3.eco_Condition_eco3        0.141  0.091  0.035 -0.066 -0.018 -0.142 -0.106
                                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                           0.107  0.000                                   
BV2                          -0.042  0.001  0.000                            
BV3                          -0.032 -0.006  0.000  0.000                     
S1.BV1                        0.038 -0.058 -0.034 -0.069  0.000              
S2.BV2                        0.024  0.057  0.062  0.007 -0.006  0.000       
S3.BV3                        0.036 -0.003  0.027  0.026 -0.003  0.007  0.000
reward_Condition_reward2     -0.037 -0.008 -0.013 -0.026 -0.049 -0.100 -0.101
reward_Condition_reward3     -0.040 -0.026 -0.045 -0.036  0.061  0.047 -0.026
eco_Condition_eco2           -0.101  0.044  0.045  0.082 -0.073 -0.098 -0.046
eco_Condition_eco3            0.049  0.024  0.047 -0.007  0.091  0.142  0.091
rewardEco22                  -0.091 -0.071  0.013  0.000 -0.038 -0.061 -0.034
rewardEco33                  -0.025 -0.109 -0.031 -0.078  0.039  0.034 -0.005
TR1.reward_Condition_reward2  0.037 -0.021 -0.027  0.003 -0.014  0.004  0.019
TR2.reward_Condition_reward2  0.122  0.006 -0.072 -0.048 -0.048 -0.050 -0.048
TR3.reward_Condition_reward2  0.060  0.040 -0.025 -0.003 -0.095 -0.086 -0.080
TR1.reward_Condition_reward3  0.047  0.057  0.059 -0.003  0.004  0.009  0.098
TR2.reward_Condition_reward3  0.018 -0.033  0.019 -0.043  0.029  0.038  0.123
TR3.reward_Condition_reward3 -0.003  0.021  0.079  0.051 -0.021  0.017  0.111
TR1.eco_Condition_eco2        0.188 -0.150 -0.222 -0.185  0.043  0.061  0.027
TR2.eco_Condition_eco2        0.143 -0.047 -0.074 -0.038  0.001  0.030  0.020
TR3.eco_Condition_eco2        0.112 -0.047 -0.055 -0.045 -0.002  0.030 -0.003
TR1.eco_Condition_eco3       -0.142  0.154  0.181  0.161 -0.134 -0.129 -0.083
TR2.eco_Condition_eco3       -0.107  0.053  0.163  0.147 -0.093 -0.093 -0.007
TR3.eco_Condition_eco3       -0.067  0.060  0.137  0.148 -0.035 -0.071  0.037
                             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                          0.330                                          
EEF2                          0.408  0.406                                   
EEF3                          0.307  0.399  0.383                            
EEC1                          1.395  1.026  1.166  0.246                     
EEC2                          0.407  0.127  0.285  0.198  0.321              
EEC3                          0.421  0.271  0.462  0.272  0.366  0.323       
IM1                           0.871  0.853  1.186  2.333  1.639  1.573  0.572
IM2                           0.332  0.564  1.029  0.627  0.378  0.397  0.493
IM3                           0.235  0.366  0.762  0.632  0.263  0.358  0.633
S1                            0.444  0.734  0.679  0.475  0.494  0.300  0.979
S2                           -0.140  0.135  0.083  0.239  0.323 -0.066  1.144
S3                            0.329  0.676  0.740  0.553  0.551  0.237  1.037
TR1                           3.928  4.137  4.310  4.939  4.369  4.512  4.529
TR2                           2.675  2.243  3.044  3.915  3.559  3.128  3.533
TR3                           2.833  2.819  2.902  4.008  4.025  3.877  3.583
BV1                           7.053  8.076  8.211  7.101  6.017  6.176  7.123
BV2                           7.039  8.233  8.280  7.321  6.274  6.686  6.258
BV3                           7.029  7.804  7.717  6.338  5.579  5.877  6.973
S1.BV1                       -0.465 -0.889 -0.943 -0.557 -0.230 -0.288 -0.483
S2.BV2                       -0.323 -0.726 -0.713 -0.787 -0.325 -0.338 -0.469
S3.BV3                       -0.385 -0.883 -1.066 -0.815 -0.417 -0.531 -0.525
reward_Condition_reward2      0.675  0.307  1.233  0.463  0.938  1.328  0.085
reward_Condition_reward3     -0.601 -0.211 -0.612 -0.871 -0.582 -0.883 -0.764
eco_Condition_eco2            2.509  1.565  1.548  0.606  1.181  0.944  0.640
eco_Condition_eco3           -1.814 -1.411 -1.287  0.897  0.459  0.928 -0.344
rewardEco22                   1.358  0.732  0.455  0.332  1.022  0.680 -0.282
rewardEco33                  -1.555 -1.346 -1.212 -0.358 -0.445 -0.606 -0.883
TR1.reward_Condition_reward2  1.364  0.732  0.701  2.013  0.523  0.060 -0.684
TR2.reward_Condition_reward2  0.360  0.490  0.525  1.601  0.841  0.046  0.898
TR3.reward_Condition_reward2  1.257  1.253  2.240  1.885  0.684  0.058  1.059
TR1.reward_Condition_reward3 -0.767 -0.857 -0.948 -1.559 -0.952 -1.021  0.926
TR2.reward_Condition_reward3 -0.801 -0.380 -0.204 -1.827 -1.682 -1.700 -1.711
TR3.reward_Condition_reward3 -0.743 -0.667 -0.522 -2.531 -1.653 -1.774 -0.080
TR1.eco_Condition_eco2       -2.504 -1.396 -1.999 -1.507 -1.444 -1.544 -2.158
TR2.eco_Condition_eco2       -1.211 -0.254 -0.726 -1.441 -0.362 -0.652 -1.660
TR3.eco_Condition_eco2       -1.181 -0.252 -0.241 -1.506 -0.727 -0.967 -1.234
TR1.eco_Condition_eco3        2.817  2.120  3.674  1.313  1.297  1.586  1.967
TR2.eco_Condition_eco3        2.225  1.268  2.444  1.495  0.975  0.834  1.082
TR3.eco_Condition_eco3        2.027  0.704  1.167  1.245  0.885  0.702  0.582
                                IM2    IM3     S1     S2     S3    TR1    TR2
EEF1                                                                         
EEF2                                                                         
EEF3                                                                         
EEC1                                                                         
EEC2                                                                         
EEC3                                                                         
IM1                                                                          
IM2                           0.559                                          
IM3                           0.683  0.641                                   
S1                            0.513  0.520  0.000                            
S2                            0.382  0.512  0.008  0.000                     
S3                            0.492  0.620 -0.004  0.012  0.000              
TR1                           4.509  4.644  3.547  4.428  3.100  0.000       
TR2                           2.463  3.158  3.125  4.450  3.229 -0.027  0.000
TR3                           2.878  3.305  3.732  4.318  3.357 -0.013  0.011
BV1                           6.524  6.562  3.135  2.852  3.135  2.048  0.665
BV2                           7.005  6.173  2.802  2.326  2.649  1.387 -0.254
BV3                           7.284  6.938  2.886  2.710  2.437  1.482 -0.216
S1.BV1                       -0.945 -0.833 -1.343 -1.476 -1.254 -0.570 -0.109
S2.BV2                       -0.551 -0.535 -1.620 -1.531 -1.425 -0.005  0.008
S3.BV3                       -0.558 -0.636 -1.698 -1.537 -1.798 -0.192 -0.055
reward_Condition_reward2      0.700  0.661 -0.041 -0.287  0.136 -0.161 -1.212
reward_Condition_reward3     -0.397 -0.017 -0.211 -0.383  0.597  0.148  0.445
eco_Condition_eco2            0.449  1.193  0.549 -0.386 -0.514 -1.762 -0.798
eco_Condition_eco3           -1.068 -0.562 -0.205  0.370 -0.283  1.049  0.575
rewardEco22                  -0.794 -0.325  0.343 -0.345 -0.038 -1.176 -1.066
rewardEco33                  -1.558 -1.246 -0.446  0.009  0.724  0.755  0.680
TR1.reward_Condition_reward2  0.727  1.040 -0.396  0.405 -0.064 -0.120  0.435
TR2.reward_Condition_reward2 -0.115  0.355 -0.625  0.518  0.192  0.421  1.071
TR3.reward_Condition_reward2  0.083  0.792 -0.743  0.683  0.180  0.319  1.168
TR1.reward_Condition_reward3  0.538  1.094  0.364 -0.065 -0.397  0.326  0.476
TR2.reward_Condition_reward3  0.324 -0.194  0.674 -0.370 -0.203  0.491  0.298
TR3.reward_Condition_reward3  1.988  1.067  0.555 -0.274 -0.355  0.535  0.184
TR1.eco_Condition_eco2       -2.102 -1.868 -0.265  0.764  0.102  0.639  2.029
TR2.eco_Condition_eco2       -0.858 -0.931 -0.366  0.629  0.082  1.840  1.354
TR3.eco_Condition_eco2       -0.806 -0.991 -0.583  0.602  0.363  1.676  1.465
TR1.eco_Condition_eco3        2.120  1.542  0.183 -0.380 -0.214 -0.348 -1.299
TR2.eco_Condition_eco3        2.516  1.721  0.159 -0.472 -0.090 -1.347 -0.960
TR3.eco_Condition_eco3        2.203  1.429  0.352 -0.658 -0.174 -1.298 -0.980
                                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                           0.691  0.000                                   
BV2                          -0.238  0.003  0.000                            
BV3                          -0.190 -0.020  0.001  0.000                     
S1.BV1                        0.217 -0.191 -0.096 -0.209  0.000              
S2.BV2                        0.133  0.178  0.170  0.022 -0.026  0.000       
S3.BV3                        0.185 -0.008  0.073  0.074 -0.011  0.028  0.000
reward_Condition_reward2     -0.434 -0.095 -0.155 -0.314 -0.530 -1.068 -1.091
reward_Condition_reward3     -0.470 -0.310 -0.557 -0.461  0.907  0.687 -0.437
eco_Condition_eco2           -1.250  0.516  0.508  0.929 -0.882 -1.067 -0.527
eco_Condition_eco3            0.566  0.286  0.593 -0.082  1.044  1.622  1.021
rewardEco22                  -1.090 -0.754  0.129  0.004 -0.389 -0.548 -0.320
rewardEco33                  -0.252 -1.184 -0.398 -0.952  0.528  0.538 -0.100
TR1.reward_Condition_reward2  0.328 -0.227 -0.294  0.035 -0.123  0.030  0.149
TR2.reward_Condition_reward2  1.144  0.062 -0.815 -0.532 -0.428 -0.444 -0.404
TR3.reward_Condition_reward2  0.516  0.435 -0.285 -0.028 -0.946 -0.854 -0.768
TR1.reward_Condition_reward3  0.495  0.725  0.769 -0.038  0.045  0.121  1.345
TR2.reward_Condition_reward3  0.180 -0.367  0.229 -0.556  0.362  0.481  1.798
TR3.reward_Condition_reward3 -0.030  0.244  0.962  0.615 -0.282  0.219  1.700
TR1.eco_Condition_eco2        1.773 -1.641 -2.296 -1.953  0.415  0.524  0.236
TR2.eco_Condition_eco2        1.416 -0.516 -0.782 -0.412  0.008  0.272  0.180
TR3.eco_Condition_eco2        0.974 -0.522 -0.604 -0.505 -0.025  0.310 -0.028
TR1.eco_Condition_eco3       -1.258  1.695  2.069  1.776 -1.198 -1.165 -0.688
TR2.eco_Condition_eco3       -0.979  0.547  1.841  1.626 -0.824 -0.836 -0.062
TR3.eco_Condition_eco3       -0.568  0.651  1.596  1.670 -0.358 -0.739  0.380
                             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                    0.148
srmr.se                 0.035
srmr.exactfit.z         1.315
srmr.exactfit.pvalue    0.094
usrmr                   0.104
usrmr.se                0.031
usrmr.ci.lower          0.053
usrmr.ci.upper          0.155
usrmr.closefit.h0.value 0.050
usrmr.closefit.z        1.752
usrmr.closefit.pvalue   0.040

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. 
0.00000 0.00000 0.00000 0.01410 0.02148 0.05598 

# 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 0.02598 0.02378 0.12417 

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 132.932087 
iter  10 value 61.470565
final  value 61.470468 
converged

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

   (Intercept) EEF_composite
2 0.0548866031  4.226369e-02
3 0.0004709928  2.275653e-06

summary(model_PEB_EEF)

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

Coefficients:
  (Intercept) EEF_composite
2   -2.221832     0.5477226
3   -4.742593     1.3996746

Std. Errors:
  (Intercept) EEF_composite
2    1.157341     0.2696926
3    1.356293     0.2960856

Residual Deviance: 122.9409 
AIC: 130.9409 

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 132.932087 
iter  10 value 68.909697
final  value 68.909693 
converged

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

  (Intercept) EEC_composite
2  0.07134909  5.601241e-02
3  0.02323969  2.406828e-05

summary(model_PEB_EEC)

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

Coefficients:
  (Intercept) EEC_composite
2   -1.700239     0.5433779
3   -1.843020     1.0602229

Std. Errors:
  (Intercept) EEC_composite
2   0.9428752     0.2843512
3   0.8120921     0.2510375

Residual Deviance: 137.8194 
AIC: 145.8194 

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. 
0.00000 0.00000 0.00000 0.02804 0.02566 0.13402 

# 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 0.03469 0.03154 0.16609 

# 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. 
0.00000 0.00000 0.00000 0.02804 0.02566 0.13402 

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 132.932087 
iter  10 value 62.039245
final  value 62.038354 
converged

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

  (Intercept) IM_composite
2 0.017596683 0.0112796307
3 0.000971256 0.0000245519

summary(model_PEB_IM)

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

Coefficients:
  (Intercept) IM_composite
2   -4.626754     1.028818
3   -6.276555     1.685423

Std. Errors:
  (Intercept) IM_composite
2    1.948930    0.4060192
3    1.902722    0.3994954

Residual Deviance: 124.0767 
AIC: 132.0767 

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 132.932087 
iter  10 value 68.610028
final  value 68.556369 
converged

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

   (Intercept) IDR_composite
2 0.0509833326  4.550420e-02
3 0.0008561708  4.983655e-05

summary(model_PEB_IDR)

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

Coefficients:
  (Intercept) IDR_composite
2   -4.962159     0.8802942
3   -7.832607     1.6546782

Std. Errors:
  (Intercept) IDR_composite
2    2.542585     0.4401552
3    2.349336     0.4079187

Residual Deviance: 137.1127 
AIC: 145.1127 

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 132.932087 
iter  10 value 60.194945
final  value 60.193964 
converged

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

   (Intercept) INR_composite
2 0.0058163262  4.377189e-03
3 0.0006373509  4.747976e-06

summary(model_PEB_INR)

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

Coefficients:
  (Intercept) INR_composite
2   -2.960088     0.9990934
3   -3.392619     1.5395274

Std. Errors:
  (Intercept) INR_composite
2   1.0732890     0.3506062
3   0.9933879     0.3364627

Residual Deviance: 120.3879 
AIC: 128.3879