AI manipulation study


Data preparation

Import

Sample size

$all
[1] 126

Data Quality

Manipulation and bot

Manipulation flag

   
    FALSE TRUE
  1    62    5
  2    58    1

Response bias check

Total approvals
   vars   n    mean     sd median trimmed     mad min  max range skew kurtosis
X1    1 126 2457.03 1795.3   1994 2301.22 1759.85  23 8152  8129 0.73    -0.25
       se
X1 159.94

Bot flag


FALSE  TRUE 
  124     2 

Attention

Duration

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  1.550   2.921   3.967   5.049   5.583  45.017 

Outliers defined as 3 std. deviations below or above the mean
Outliers on completion time

FALSE  TRUE 
  125     1 

On scales

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5149  1.0597  1.1645  1.2190  1.3092  2.2344 
Flagged outliers based on scales

FALSE  TRUE 
  123     3 

Removing bad participants

Exclude participants

$all
[1] 11
cond.AI_flag outliers_completion bot_flag outliers_scales n
TRUE FALSE FALSE FALSE 5
TRUE FALSE TRUE FALSE 1
FALSE FALSE FALSE TRUE 3
FALSE FALSE TRUE FALSE 1
FALSE TRUE FALSE FALSE 1

Descriptive on good participants

Conditions

Group statistics

# A tibble: 2 × 6
  cond.AI     n mean_EEF sd_EEF mean_EEC sd_EEC
  <chr>   <int>    <dbl>  <dbl>    <dbl>  <dbl>
1 AI         56     5.64  0.989     4.88   1.23
2 control    59     5.82  0.641     4.93   1.11

Ease and feedback

   vars   n mean   sd median trimmed  mad min max range  skew kurtosis   se
X1    1 115 4.36 0.62    4.5    4.42 0.74   2   5     3 -0.94     0.86 0.06

Scales

Descriptive stats on scales

 all good 
 126  115 
     Variable vars   n     mean        sd median  trimmed    mad min max range
IM1       IM1    1 115 5.443478 1.1934860      5 5.569892 1.4826   1   7     6
IM2       IM2    2 115 5.852174 1.2157120      6 6.043011 1.4826   1   7     6
IM3       IM3    3 115 5.643478 1.2296862      6 5.827957 1.4826   1   7     6
EEF1     EEF1    4 115 5.591304 0.9070451      6 5.612903 1.4826   2   7     5
EEF2     EEF2    5 115 5.773913 1.0350089      6 5.870968 1.4826   2   7     5
EEF3     EEF3    6 115 5.843478 0.9513730      6 5.924731 1.4826   3   7     4
EEC1     EEC1    7 115 4.686957 1.2591087      5 4.731183 1.4826   1   7     6
EEC2     EEC2    8 115 5.000000 1.3311385      5 5.075269 1.4826   2   7     5
EEC3     EEC3    9 115 5.034783 1.2837065      5 5.150538 1.4826   1   7     6
ADT1     ADT1   10 115 5.495652 1.5007245      6 5.720430 1.4826   1   7     6
ADT2     ADT2   11 115 5.452174 1.5231747      6 5.666667 1.4826   1   7     6
ADT3     ADT3   12 115 5.391304 1.5766701      6 5.602151 1.4826   1   7     6
           skew     kurtosis         se
IM1  -1.0489429  1.751720098 0.11129314
IM2  -1.6643802  3.423150713 0.11336573
IM3  -1.3534400  2.160446783 0.11466883
EEF1 -0.6543198  1.573326278 0.08458239
EEF2 -0.7202855  0.600751369 0.09651507
EEF3 -0.5968928 -0.009295716 0.08871599
EEC1 -0.3430226 -0.308180058 0.11741249
EEC2 -0.5972380 -0.280302443 0.12412931
EEC3 -0.8287281  0.261966603 0.11970625
ADT1 -1.2111939  0.937801485 0.13994328
ADT2 -1.1058594  0.611552905 0.14203677
ADT3 -1.0129413  0.102156242 0.14702525

Assumptions

Non-normality test across all scales

$IM1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.85797, p-value = 4.083e-09


$IM2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.77939, p-value = 7.426e-12


$IM3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.8243, p-value = 2.18e-10


$EEF1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.85186, p-value = 2.326e-09


$EEF2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.86864, p-value = 1.133e-08


$EEF3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.86777, p-value = 1.04e-08


$EEC1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.93477, p-value = 2.842e-05


$EEC2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.90513, p-value = 5.784e-07


$EEC3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.89004, p-value = 1.035e-07


$ADT1

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.83474, p-value = 5.185e-10


$ADT2

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.84743, p-value = 1.561e-09


$ADT3

    Shapiro-Wilk normality test

data:  newX[, i]
W = 0.84495, p-value = 1.254e-09

Non-normality test on EEF composite


    Shapiro-Wilk normality test

data:  data_filtered$EEF_composite
W = 0.94903, p-value = 0.0002562

Non-normality test on EEC composite


    Shapiro-Wilk normality test

data:  data_filtered$EEC_composite
W = 0.94529, p-value = 0.0001403

Non-normality test on DV per condition

EEF composite

# A tibble: 2 × 3
  cond.AI     n shapiro_p
  <chr>   <int>     <dbl>
1 AI         56   0.00525
2 control    59   0.00482

EEC composite

# A tibble: 2 × 3
  cond.AI     n shapiro_p
  <chr>   <int>     <dbl>
1 AI         56 0.0000132
2 control    59 0.321    

Non-normality test on IM composite


    Shapiro-Wilk normality test

data:  data_filtered$IM_composite
W = 0.85765, p-value = 3.962e-09

Non-normality test on IM per condition

# A tibble: 2 × 3
  cond.AI     n   shapiro_p
  <chr>   <int>       <dbl>
1 AI         56 0.000000366
2 control    59 0.0000415  

Factor analyses

KMO

Kaiser-Meyer-Olkin factor adequacy
Call: KMO(r = efa_data_good)
Overall MSA =  0.84
MSA for each item = 
 IM1  IM2  IM3 EEF1 EEF2 EEF3 EEC1 EEC2 EEC3 ADT1 ADT2 ADT3 
0.88 0.84 0.89 0.84 0.84 0.90 0.86 0.83 0.85 0.77 0.81 0.83 

# A tibble: 8 × 6
  cond.AI Measure        Mean Median    SD     N
  <chr>   <chr>         <dbl>  <dbl> <dbl> <int>
1 AI      ADT_composite  5.32   6    1.63     56
2 AI      EEC_composite  4.88   5.33 1.23     56
3 AI      EEF_composite  5.64   5.83 0.989    56
4 AI      IM_composite   5.58   5.67 1.17     56
5 control ADT_composite  5.57   6    1.33     59
6 control EEC_composite  4.93   5    1.11     59
7 control EEF_composite  5.82   5.67 0.641    59
8 control IM_composite   5.71   6    1.13     59

EFA

Parallel analysis suggests that the number of factors =  4  and the number of components =  NA 
Threshold=0.40

Loadings:
     MR2   MR1   MR4   MR3  
IM1     NA 0.831    NA    NA
IM2     NA 0.867    NA    NA
IM3     NA 0.831    NA    NA
EEF1    NA    NA    NA 0.840
EEF2    NA    NA    NA 0.720
EEF3    NA    NA    NA 0.595
EEC1    NA    NA 0.763    NA
EEC2    NA    NA 0.745    NA
EEC3    NA    NA 0.787    NA
ADT1 0.956    NA    NA    NA
ADT2 0.922    NA    NA    NA
ADT3 0.890    NA    NA    NA

               MR2 MR1 MR4 MR3
SS loadings     NA  NA  NA  NA
Proportion Var  NA  NA  NA  NA
Cumulative Var  NA  NA  NA  NA
Factor Analysis using method =  minres
Call: fa(r = cor(efa_data_good, use = "pairwise.complete.obs"), nfactors = 4, 
    rotate = "varimax")
Standardized loadings (pattern matrix) based upon correlation matrix
      MR2  MR1  MR4  MR3   h2    u2 com
IM1  0.16 0.83 0.30 0.21 0.85 0.149 1.5
IM2  0.11 0.87 0.23 0.19 0.85 0.147 1.3
IM3  0.13 0.83 0.27 0.22 0.83 0.170 1.4
EEF1 0.15 0.19 0.14 0.84 0.78 0.220 1.2
EEF2 0.17 0.14 0.18 0.72 0.60 0.402 1.3
EEF3 0.14 0.29 0.30 0.59 0.55 0.455 2.1
EEC1 0.12 0.30 0.76 0.07 0.69 0.310 1.4
EEC2 0.17 0.29 0.74 0.29 0.75 0.248 1.7
EEC3 0.11 0.21 0.79 0.32 0.78 0.222 1.5
ADT1 0.96 0.09 0.12 0.11 0.95 0.051 1.1
ADT2 0.92 0.15 0.10 0.17 0.91 0.088 1.1
ADT3 0.89 0.14 0.15 0.18 0.87 0.133 1.2

                       MR2  MR1  MR4  MR3
SS loadings           2.74 2.53 2.16 1.98
Proportion Var        0.23 0.21 0.18 0.16
Cumulative Var        0.23 0.44 0.62 0.78
Proportion Explained  0.29 0.27 0.23 0.21
Cumulative Proportion 0.29 0.56 0.79 1.00

Mean item complexity =  1.4
Test of the hypothesis that 4 factors are sufficient.

df null model =  66  with the objective function =  10.79
df of  the model are 24  and the objective function was  0.3 

The root mean square of the residuals (RMSR) is  0.01 
The df corrected root mean square of the residuals is  0.02 

Fit based upon off diagonal values = 1
Measures of factor score adequacy             
                                                   MR2  MR1  MR4  MR3
Correlation of (regression) scores with factors   0.98 0.95 0.91 0.90
Multiple R square of scores with factors          0.97 0.90 0.83 0.81
Minimum correlation of possible factor scores     0.93 0.80 0.66 0.63

CFA

lavaan 0.6-19 ended normally after 44 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        30

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                68.574      60.496
  Degrees of freedom                                48          48
  P-value (Chi-square)                           0.027       0.106
  Scaling correction factor                                  1.134
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              1240.604    1042.507
  Degrees of freedom                                66          66
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.190

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.982       0.987
  Tucker-Lewis Index (TLI)                       0.976       0.982
                                                                  
  Robust Comparative Fit Index (CFI)                         0.988
  Robust Tucker-Lewis Index (TLI)                            0.983

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1655.229   -1655.229
  Scaling correction factor                                  1.399
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1620.942   -1620.942
  Scaling correction factor                                  1.235
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                3370.457    3370.457
  Bayesian (BIC)                              3452.805    3452.805
  Sample-size adjusted Bayesian (SABIC)       3357.981    3357.981

Root Mean Square Error of Approximation:

  RMSEA                                          0.061       0.048
  90 Percent confidence interval - lower         0.021       0.000
  90 Percent confidence interval - upper         0.092       0.079
  P-value H_0: RMSEA <= 0.050                    0.276       0.521
  P-value H_0: RMSEA >= 0.080                    0.169       0.047
                                                                  
  Robust RMSEA                                               0.051
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.087
  P-value H_0: Robust RMSEA <= 0.050                         0.464
  P-value H_0: Robust RMSEA >= 0.080                         0.096

Standardized Root Mean Square Residual:

  SRMR                                           0.046       0.046

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
  EEC =~                                                                
    EEC1              1.000                               1.000    1.000
    EEC2              1.196    0.107   11.193    0.000    0.987    1.406
    EEC3              1.098    0.099   11.031    0.000    0.903    1.293
  EEF =~                                                                
    EEF1              1.000                               1.000    1.000
    EEF2              1.059    0.153    6.908    0.000    0.759    1.360
    EEF3              0.927    0.156    5.959    0.000    0.622    1.231
  ADT =~                                                                
    ADT1              1.000                               1.000    1.000
    ADT2              1.001    0.041   24.537    0.000    0.921    1.081
    ADT3              1.011    0.049   20.766    0.000    0.915    1.106
  IM =~                                                                 
    IM1               1.000                               1.000    1.000
    IM2               1.005    0.061   16.507    0.000    0.886    1.124
    IM3               1.011    0.060   16.914    0.000    0.894    1.129
   Std.lv  Std.all
                  
    0.991    0.791
    1.186    0.895
    1.088    0.851
                  
    0.757    0.839
    0.802    0.779
    0.702    0.741
                  
    1.447    0.968
    1.448    0.955
    1.463    0.932
                  
    1.102    0.927
    1.107    0.915
    1.114    0.910

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
  EEC ~~                                                                
    EEF               0.448    0.094    4.784    0.000    0.264    0.631
    ADT               0.510    0.169    3.014    0.003    0.178    0.842
    IM                0.692    0.185    3.745    0.000    0.330    1.054
  EEF ~~                                                                
    ADT               0.426    0.121    3.531    0.000    0.189    0.662
    IM                0.449    0.099    4.521    0.000    0.255    0.644
  ADT ~~                                                                
    IM                0.523    0.185    2.826    0.005    0.160    0.886
   Std.lv  Std.all
                  
    0.596    0.596
    0.356    0.356
    0.633    0.633
                  
    0.388    0.388
    0.538    0.538
                  
    0.328    0.328

Variances:
                   Estimate  Std.Err  z-value  P(>|z|) ci.lower ci.upper
   .EEC1              0.589    0.100    5.905    0.000    0.393    0.784
   .EEC2              0.350    0.101    3.462    0.001    0.152    0.548
   .EEC3              0.450    0.109    4.107    0.000    0.235    0.664
   .EEF1              0.242    0.082    2.959    0.003    0.082    0.402
   .EEF2              0.418    0.092    4.544    0.000    0.238    0.598
   .EEF3              0.405    0.104    3.880    0.000    0.200    0.609
   .ADT1              0.139    0.060    2.304    0.021    0.021    0.256
   .ADT2              0.203    0.055    3.690    0.000    0.095    0.311
   .ADT3              0.324    0.084    3.866    0.000    0.160    0.489
   .IM1               0.198    0.045    4.417    0.000    0.110    0.285
   .IM2               0.239    0.059    4.082    0.000    0.124    0.354
   .IM3               0.257    0.075    3.431    0.001    0.110    0.404
    EEC               0.983    0.215    4.576    0.000    0.562    1.404
    EEF               0.574    0.155    3.712    0.000    0.271    0.877
    ADT               2.094    0.364    5.745    0.000    1.380    2.808
    IM                1.214    0.262    4.644    0.000    0.702    1.727
   Std.lv  Std.all
    0.589    0.375
    0.350    0.199
    0.450    0.275
    0.242    0.297
    0.418    0.394
    0.405    0.451
    0.139    0.062
    0.203    0.088
    0.324    0.132
    0.198    0.140
    0.239    0.163
    0.257    0.171
    1.000    1.000
    1.000    1.000
    1.000    1.000
    1.000    1.000

R-Square:
                   Estimate
    EEC1              0.625
    EEC2              0.801
    EEC3              0.725
    EEF1              0.703
    EEF2              0.606
    EEF3              0.549
    ADT1              0.938
    ADT2              0.912
    ADT3              0.868
    IM1               0.860
    IM2               0.837
    IM3               0.829
Cronbach Alpha
  EEC   EEF   ADT    IM 
0.884 0.823 0.966 0.941 
Omega
  EEC   EEF   ADT    IM 
0.883 0.832 0.967 0.941 
AVE
  EEC   EEF   ADT    IM 
0.720 0.616 0.905 0.842 
$type
[1] "cor.bentler"

$cov
       EEC1   EEC2   EEC3   EEF1   EEF2   EEF3   ADT1   ADT2   ADT3    IM1
EEC1  0.000                                                               
EEC2 -0.001  0.000                                                        
EEC3  0.017 -0.007  0.000                                                 
EEF1 -0.163  0.003 -0.007  0.000                                          
EEF2 -0.099 -0.008  0.007  0.032  0.000                                   
EEF3 -0.003  0.076  0.174 -0.015 -0.034  0.000                            
ADT1 -0.036  0.012 -0.034 -0.043 -0.034 -0.009  0.000                     
ADT2 -0.034  0.042 -0.041  0.014  0.027  0.023  0.001  0.000              
ADT3  0.039  0.021  0.036  0.012  0.074  0.042  0.001 -0.003  0.000       
IM1   0.037  0.049 -0.018 -0.015 -0.044  0.101 -0.012  0.042  0.052  0.000
IM2   0.016 -0.041 -0.057 -0.039 -0.062  0.077 -0.063  0.006  0.016  0.001
IM3   0.021  0.015 -0.022 -0.024 -0.046  0.136 -0.022  0.017  0.029 -0.006
        IM2    IM3
EEC1              
EEC2              
EEC3              
EEF1              
EEF2              
EEF3              
ADT1              
ADT2              
ADT3              
IM1               
IM2   0.000       
IM3   0.006  0.000

$cov.z
       EEC1   EEC2   EEC3   EEF1   EEF2   EEF3   ADT1   ADT2   ADT3    IM1
EEC1  0.000                                                               
EEC2 -0.030  0.000                                                        
EEC3  0.320 -0.153  0.000                                                 
EEF1 -2.639  0.069 -0.126  0.000                                          
EEF2 -1.841 -0.173  0.119  0.716  0.000                                   
EEF3 -0.030  0.824  2.321 -0.405 -0.639  0.000                            
ADT1 -0.652  0.333 -0.647 -1.001 -0.607 -0.120  0.000                     
ADT2 -0.569  0.948 -0.700  0.362  0.480  0.290  0.030  0.000              
ADT3  0.766  0.445  0.742  0.216  1.541  0.584  0.053 -0.176  0.000       
IM1   0.628  1.005 -0.292 -0.231 -0.840  1.115 -0.269  1.041  0.971  0.000
IM2   0.286 -0.722 -0.909 -0.581 -0.977  0.810 -1.157  0.095  0.320  0.020
IM3   0.343  0.278 -0.330 -0.379 -0.778  1.758 -0.499  0.321  0.517 -0.112
        IM2    IM3
EEC1              
EEC2              
EEC3              
EEF1              
EEF2              
EEF3              
ADT1              
ADT2              
ADT3              
IM1               
IM2   0.000       
IM3   0.099  0.000

$summary
                           cov
srmr                     0.046
srmr.se                  0.015
srmr.exactfit.z          0.000
srmr.exactfit.pvalue     0.500
usrmr                    0.000
usrmr.se                 0.028
usrmr.ci.lower          -0.045
usrmr.ci.upper           0.045
usrmr.closefit.h0.value  0.050
usrmr.closefit.z        -1.812
usrmr.closefit.pvalue    0.965

CFA with correlation matrix

lavaan 0.6-19 ended normally after 44 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        30

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                68.574      60.496
  Degrees of freedom                                48          48
  P-value (Chi-square)                           0.027       0.106
  Scaling correction factor                                  1.134
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              1240.604    1042.507
  Degrees of freedom                                66          66
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.190

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.982       0.987
  Tucker-Lewis Index (TLI)                       0.976       0.982
                                                                  
  Robust Comparative Fit Index (CFI)                         0.988
  Robust Tucker-Lewis Index (TLI)                            0.983

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1655.229   -1655.229
  Scaling correction factor                                  1.399
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1620.942   -1620.942
  Scaling correction factor                                  1.235
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                3370.457    3370.457
  Bayesian (BIC)                              3452.805    3452.805
  Sample-size adjusted Bayesian (SABIC)       3357.981    3357.981

Root Mean Square Error of Approximation:

  RMSEA                                          0.061       0.048
  90 Percent confidence interval - lower         0.021       0.000
  90 Percent confidence interval - upper         0.092       0.079
  P-value H_0: RMSEA <= 0.050                    0.276       0.521
  P-value H_0: RMSEA >= 0.080                    0.169       0.047
                                                                  
  Robust RMSEA                                               0.051
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.087
  P-value H_0: Robust RMSEA <= 0.050                         0.464
  P-value H_0: Robust RMSEA >= 0.080                         0.096

Standardized Root Mean Square Residual:

  SRMR                                           0.046       0.046

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
  EEC =~                                                                
    EEC1              1.000                               0.991    0.791
    EEC2              1.196    0.107   11.193    0.000    1.186    0.895
    EEC3              1.098    0.099   11.031    0.000    1.088    0.851
  EEF =~                                                                
    EEF1              1.000                               0.757    0.839
    EEF2              1.059    0.153    6.908    0.000    0.802    0.779
    EEF3              0.927    0.156    5.959    0.000    0.702    0.741
  ADT =~                                                                
    ADT1              1.000                               1.447    0.968
    ADT2              1.001    0.041   24.537    0.000    1.448    0.955
    ADT3              1.011    0.049   20.766    0.000    1.463    0.932
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.005    0.061   16.507    0.000    1.107    0.915
    IM3               1.011    0.060   16.914    0.000    1.114    0.910

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEC ~~                                                                
    EEF               0.448    0.094    4.784    0.000    0.596    0.596
    ADT               0.510    0.169    3.014    0.003    0.356    0.356
    IM                0.692    0.185    3.745    0.000    0.633    0.633
  EEF ~~                                                                
    ADT               0.426    0.121    3.531    0.000    0.388    0.388
    IM                0.449    0.099    4.521    0.000    0.538    0.538
  ADT ~~                                                                
    IM                0.523    0.185    2.826    0.005    0.328    0.328

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.100    5.905    0.000    0.589    0.375
   .EEC2              0.350    0.101    3.462    0.001    0.350    0.199
   .EEC3              0.450    0.109    4.107    0.000    0.450    0.275
   .EEF1              0.242    0.082    2.959    0.003    0.242    0.297
   .EEF2              0.418    0.092    4.544    0.000    0.418    0.394
   .EEF3              0.405    0.104    3.880    0.000    0.405    0.451
   .ADT1              0.139    0.060    2.304    0.021    0.139    0.062
   .ADT2              0.203    0.055    3.690    0.000    0.203    0.088
   .ADT3              0.324    0.084    3.866    0.000    0.324    0.132
   .IM1               0.198    0.045    4.417    0.000    0.198    0.140
   .IM2               0.239    0.059    4.082    0.000    0.239    0.163
   .IM3               0.257    0.075    3.431    0.001    0.257    0.171
    EEC               0.983    0.215    4.576    0.000    1.000    1.000
    EEF               0.574    0.155    3.712    0.000    1.000    1.000
    ADT               2.094    0.364    5.745    0.000    1.000    1.000
    IM                1.214    0.262    4.644    0.000    1.000    1.000
Latent factor correlation matrix with p-values:
    IM             ADT            EEF        EEC       
IM  "1"            "0.33 (0.001)" "0.54 (0)" "0.63 (0)"
ADT "0.33 (0.001)" "1"            "0.39 (0)" "0.36 (0)"
EEF "0.54 (0)"     "0.39 (0)"     "1"        "0.6 (0)" 
EEC "0.63 (0)"     "0.36 (0)"     "0.6 (0)"  "1"       

Common method bias

Harman’s test

CFA with one factor

SEM

SEM with two non-connected DVs

No mediation

lavaan 0.6-19 ended normally after 29 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        21

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                93.818      85.693
  Degrees of freedom                                33          33
  P-value (Chi-square)                           0.000       0.000
  Scaling correction factor                                  1.095
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               762.973     680.484
  Degrees of freedom                                45          45
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.121

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.915       0.917
  Tucker-Lewis Index (TLI)                       0.884       0.887
                                                                  
  Robust Comparative Fit Index (CFI)                         0.919
  Robust Tucker-Lewis Index (TLI)                            0.890

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1271.202   -1271.202
  Scaling correction factor                                  1.344
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1224.293   -1224.293
  Scaling correction factor                                  1.192
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2584.404    2584.404
  Bayesian (BIC)                              2642.048    2642.048
  Sample-size adjusted Bayesian (SABIC)       2575.671    2575.671

Root Mean Square Error of Approximation:

  RMSEA                                          0.127       0.118
  90 Percent confidence interval - lower         0.097       0.089
  90 Percent confidence interval - upper         0.157       0.147
  P-value H_0: RMSEA <= 0.050                    0.000       0.000
  P-value H_0: RMSEA >= 0.080                    0.994       0.983
                                                                  
  Robust RMSEA                                               0.123
  90 Percent confidence interval - lower                     0.092
  90 Percent confidence interval - upper                     0.156
  P-value H_0: Robust RMSEA <= 0.050                         0.000
  P-value H_0: Robust RMSEA >= 0.080                         0.986

Standardized Root Mean Square Residual:

  SRMR                                           0.261       0.261

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                               0.762    0.844
    EEF2              1.064    0.146    7.294    0.000    0.811    0.787
    EEF3              0.903    0.143    6.333    0.000    0.688    0.727
  EEC =~                                                                
    EEC1              1.000                               0.982    0.784
    EEC2              1.195    0.107   11.125    0.000    1.174    0.886
    EEC3              1.128    0.105   10.765    0.000    1.108    0.867
  IM =~                                                                 
    IM1               1.000                               1.095    0.921
    IM2               1.020    0.061   16.670    0.000    1.116    0.922
    IM3               1.017    0.060   17.062    0.000    1.113    0.909

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    AI_2             -0.196    0.158   -1.242    0.214   -0.257   -0.129
  EEC ~                                                                 
    AI_2              0.112    0.167    0.671    0.502    0.114    0.057
    EEF               0.775    0.191    4.063    0.000    0.601    0.601

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEF1              0.234    0.077    3.059    0.002    0.234    0.287
   .EEF2              0.403    0.090    4.471    0.000    0.403    0.380
   .EEF3              0.423    0.109    3.893    0.000    0.423    0.472
   .EEC1              0.607    0.099    6.128    0.000    0.607    0.386
   .EEC2              0.379    0.121    3.138    0.002    0.379    0.216
   .EEC3              0.406    0.107    3.798    0.000    0.406    0.249
   .IM1               0.214    0.046    4.674    0.000    0.214    0.151
   .IM2               0.219    0.061    3.582    0.000    0.219    0.149
   .IM3               0.259    0.075    3.469    0.001    0.259    0.173
   .EEF               0.572    0.143    3.992    0.000    0.983    0.983
   .EEC               0.621    0.161    3.867    0.000    0.644    0.644
    IM                1.199    0.262    4.579    0.000    1.000    1.000

R-Square:
                   Estimate
    EEF1              0.713
    EEF2              0.620
    EEF3              0.528
    EEC1              0.614
    EEC2              0.784
    EEC3              0.751
    IM1               0.849
    IM2               0.851
    IM3               0.827
    EEF               0.017
    EEC               0.356

With mediation

Plain - both DVs

lavaan 0.6-19 ended normally after 31 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        24

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                39.268      36.279
  Degrees of freedom                                30          30
  P-value (Chi-square)                           0.120       0.199
  Scaling correction factor                                  1.082
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               762.973     680.484
  Degrees of freedom                                45          45
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.121

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.987       0.990
  Tucker-Lewis Index (TLI)                       0.981       0.985
                                                                  
  Robust Comparative Fit Index (CFI)                         0.990
  Robust Tucker-Lewis Index (TLI)                            0.986

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1243.927   -1243.927
  Scaling correction factor                                  1.329
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1224.293   -1224.293
  Scaling correction factor                                  1.192
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2535.854    2535.854
  Bayesian (BIC)                              2601.732    2601.732
  Sample-size adjusted Bayesian (SABIC)       2525.873    2525.873

Root Mean Square Error of Approximation:

  RMSEA                                          0.052       0.043
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.093       0.085
  P-value H_0: RMSEA <= 0.050                    0.442       0.570
  P-value H_0: RMSEA >= 0.080                    0.143       0.077
                                                                  
  Robust RMSEA                                               0.044
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.090
  P-value H_0: Robust RMSEA <= 0.050                         0.538
  P-value H_0: Robust RMSEA >= 0.080                         0.109

Standardized Root Mean Square Residual:

  SRMR                                           0.051       0.051

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                               0.759    0.841
    EEF2              1.058    0.157    6.750    0.000    0.803    0.780
    EEF3              0.921    0.155    5.953    0.000    0.699    0.738
  EEC =~                                                                
    EEC1              1.000                               0.991    0.791
    EEC2              1.194    0.107   11.143    0.000    1.184    0.893
    EEC3              1.101    0.099   11.071    0.000    1.091    0.854
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.006    0.061   16.564    0.000    1.108    0.915
    IM3               1.012    0.060   16.976    0.000    1.115    0.910

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  IM ~                                                                  
    AI_2             -0.136    0.212   -0.643    0.521   -0.124   -0.062
  EEF ~                                                                 
    IM                0.366    0.061    6.010    0.000    0.531    0.531
    AI_2             -0.143    0.143   -1.000    0.317   -0.188   -0.094
  EEC ~                                                                 
    IM                0.396    0.100    3.956    0.000    0.440    0.440
    AI_2              0.105    0.149    0.707    0.480    0.106    0.053
    EEF               0.478    0.151    3.153    0.002    0.366    0.366

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEF1              0.239    0.081    2.933    0.003    0.239    0.293
   .EEF2              0.417    0.093    4.476    0.000    0.417    0.392
   .EEF3              0.408    0.108    3.777    0.000    0.408    0.455
   .EEC1              0.589    0.100    5.909    0.000    0.589    0.375
   .EEC2              0.355    0.101    3.525    0.000    0.355    0.202
   .EEC3              0.443    0.108    4.110    0.000    0.443    0.271
   .IM1               0.199    0.044    4.475    0.000    0.199    0.141
   .IM2               0.238    0.057    4.138    0.000    0.238    0.162
   .IM3               0.257    0.074    3.453    0.001    0.257    0.171
   .EEF               0.405    0.133    3.044    0.002    0.703    0.703
   .EEC               0.496    0.141    3.523    0.000    0.505    0.505
   .IM                1.209    0.258    4.689    0.000    0.996    0.996

R-Square:
                   Estimate
    EEF1              0.707
    EEF2              0.608
    EEF3              0.545
    EEC1              0.625
    EEC2              0.798
    EEC3              0.729
    IM1               0.859
    IM2               0.838
    IM3               0.829
    EEF               0.297
    EEC               0.495
    IM                0.004

Plain - only EEF

lavaan 0.6-19 ended normally after 27 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        15

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                11.353       9.792
  Degrees of freedom                                12          12
  P-value (Chi-square)                           0.499       0.634
  Scaling correction factor                                  1.159
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               484.153     421.834
  Degrees of freedom                                21          21
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.148

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    1.000       1.000
  Tucker-Lewis Index (TLI)                       1.002       1.010
                                                                  
  Robust Comparative Fit Index (CFI)                         1.000
  Robust Tucker-Lewis Index (TLI)                            1.010

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)               -793.240    -793.240
  Scaling correction factor                                  1.412
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)       -787.564    -787.564
  Scaling correction factor                                  1.300
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                1616.480    1616.480
  Bayesian (BIC)                              1657.654    1657.654
  Sample-size adjusted Bayesian (SABIC)       1610.242    1610.242

Root Mean Square Error of Approximation:

  RMSEA                                          0.000       0.000
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.091       0.075
  P-value H_0: RMSEA <= 0.050                    0.726       0.845
  P-value H_0: RMSEA >= 0.080                    0.090       0.036
                                                                  
  Robust RMSEA                                               0.000
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.086
  P-value H_0: Robust RMSEA <= 0.050                         0.803
  P-value H_0: Robust RMSEA >= 0.080                         0.067

Standardized Root Mean Square Residual:

  SRMR                                           0.047       0.047

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                               0.772    0.855
    EEF2              1.040    0.167    6.236    0.000    0.804    0.780
    EEF3              0.886    0.151    5.884    0.000    0.684    0.722
  IM =~                                                                 
    IM1               1.000                               1.096    0.923
    IM2               1.015    0.059   17.090    0.000    1.113    0.920
    IM3               1.017    0.059   17.215    0.000    1.115    0.911

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  IM ~                                                                  
    AI_2             -0.135    0.211   -0.638    0.523   -0.123   -0.062
  EEF ~                                                                 
    IM                0.369    0.063    5.871    0.000    0.524    0.524
    AI_2             -0.149    0.144   -1.032    0.302   -0.192   -0.096

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEF1              0.219    0.083    2.653    0.008    0.219    0.268
   .EEF2              0.416    0.090    4.644    0.000    0.416    0.392
   .EEF3              0.429    0.109    3.933    0.000    0.429    0.478
   .IM1               0.210    0.044    4.819    0.000    0.210    0.149
   .IM2               0.226    0.057    3.947    0.000    0.226    0.154
   .IM3               0.256    0.073    3.519    0.000    0.256    0.171
   .EEF               0.423    0.137    3.088    0.002    0.710    0.710
   .IM                1.198    0.258    4.636    0.000    0.996    0.996

R-Square:
                   Estimate
    EEF1              0.732
    EEF2              0.608
    EEF3              0.522
    IM1               0.851
    IM2               0.846
    IM3               0.829
    EEF               0.290
    IM                0.004

SEM - only EEC

lavaan 0.6-19 ended normally after 28 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        15

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                 8.181       8.038
  Degrees of freedom                                12          12
  P-value (Chi-square)                           0.771       0.782
  Scaling correction factor                                  1.018
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               557.292     530.997
  Degrees of freedom                                21          21
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.050

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    1.000       1.000
  Tucker-Lewis Index (TLI)                       1.012       1.014
                                                                  
  Robust Comparative Fit Index (CFI)                         1.000
  Robust Tucker-Lewis Index (TLI)                            1.013

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)               -856.192    -856.192
  Scaling correction factor                                  1.303
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)       -852.102    -852.102
  Scaling correction factor                                  1.176
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                1742.385    1742.385
  Bayesian (BIC)                              1783.559    1783.559
  Sample-size adjusted Bayesian (SABIC)       1736.146    1736.146

Root Mean Square Error of Approximation:

  RMSEA                                          0.000       0.000
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.066       0.064
  P-value H_0: RMSEA <= 0.050                    0.903       0.911
  P-value H_0: RMSEA >= 0.080                    0.023       0.020
                                                                  
  Robust RMSEA                                               0.000
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.065
  P-value H_0: Robust RMSEA <= 0.050                         0.907
  P-value H_0: Robust RMSEA >= 0.080                         0.022

Standardized Root Mean Square Residual:

  SRMR                                           0.019       0.019

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
  EEC =~                                                                
    EEC1              1.000                               1.011    0.806
    EEC2              1.164    0.100   11.649    0.000    1.177    0.888
    EEC3              1.070    0.098   10.966    0.000    1.082    0.846
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.006    0.062   16.240    0.000    1.108    0.916
    IM3               1.011    0.060   16.848    0.000    1.114    0.910

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  IM ~                                                                  
    AI_2             -0.137    0.212   -0.643    0.520   -0.124   -0.062
  EEC ~                                                                 
    IM                0.583    0.083    6.989    0.000    0.635    0.635
    AI_2              0.037    0.161    0.227    0.820    0.036    0.018

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.550    0.098    5.600    0.000    0.550    0.350
   .EEC2              0.371    0.103    3.605    0.000    0.371    0.211
   .EEC3              0.463    0.119    3.889    0.000    0.463    0.284
   .IM1               0.198    0.046    4.328    0.000    0.198    0.140
   .IM2               0.237    0.059    4.005    0.000    0.237    0.162
   .IM3               0.259    0.076    3.424    0.001    0.259    0.173
   .EEC               0.610    0.145    4.219    0.000    0.597    0.597
   .IM                1.210    0.258    4.696    0.000    0.996    0.996

R-Square:
                   Estimate
    EEC1              0.650
    EEC2              0.789
    EEC3              0.716
    IM1               0.860
    IM2               0.838
    IM3               0.827
    EEC               0.403
    IM                0.004

Partial mediation EEF -> EEC

lavaan 0.6-19 ended normally after 31 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        24

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                39.268      36.279
  Degrees of freedom                                30          30
  P-value (Chi-square)                           0.120       0.199
  Scaling correction factor                                  1.082
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               762.973     680.484
  Degrees of freedom                                45          45
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.121

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.987       0.990
  Tucker-Lewis Index (TLI)                       0.981       0.985
                                                                  
  Robust Comparative Fit Index (CFI)                         0.990
  Robust Tucker-Lewis Index (TLI)                            0.986

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1243.927   -1243.927
  Scaling correction factor                                  1.329
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1224.293   -1224.293
  Scaling correction factor                                  1.192
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2535.854    2535.854
  Bayesian (BIC)                              2601.732    2601.732
  Sample-size adjusted Bayesian (SABIC)       2525.873    2525.873

Root Mean Square Error of Approximation:

  RMSEA                                          0.052       0.043
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.093       0.085
  P-value H_0: RMSEA <= 0.050                    0.442       0.570
  P-value H_0: RMSEA >= 0.080                    0.143       0.077
                                                                  
  Robust RMSEA                                               0.044
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.090
  P-value H_0: Robust RMSEA <= 0.050                         0.538
  P-value H_0: Robust RMSEA >= 0.080                         0.109

Standardized Root Mean Square Residual:

  SRMR                                           0.051       0.051

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
  EEC =~                                                                
    EEC1              1.000                               0.991    0.791
    EEC2              1.194    0.107   11.143    0.000    1.184    0.893
    EEC3              1.101    0.099   11.071    0.000    1.091    0.854
  EEF =~                                                                
    EEF1              1.000                               0.759    0.841
    EEF2              1.058    0.157    6.750    0.000    0.803    0.780
    EEF3              0.921    0.155    5.953    0.000    0.699    0.738
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.006    0.061   16.564    0.000    1.108    0.915
    IM3               1.012    0.060   16.976    0.000    1.115    0.910

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  IM ~                                                                  
    AI_2             -0.136    0.212   -0.643    0.521   -0.124   -0.062
  EEF ~                                                                 
    IM                0.366    0.061    6.010    0.000    0.531    0.531
    AI_2             -0.143    0.143   -1.000    0.317   -0.188   -0.094
  EEC ~                                                                 
    IM                0.396    0.100    3.956    0.000    0.440    0.440
    EEF               0.478    0.151    3.153    0.002    0.366    0.366
    AI_2              0.105    0.149    0.707    0.480    0.106    0.053

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.100    5.909    0.000    0.589    0.375
   .EEC2              0.355    0.101    3.525    0.000    0.355    0.202
   .EEC3              0.443    0.108    4.110    0.000    0.443    0.271
   .EEF1              0.239    0.081    2.933    0.003    0.239    0.293
   .EEF2              0.417    0.093    4.476    0.000    0.417    0.392
   .EEF3              0.408    0.108    3.777    0.000    0.408    0.455
   .IM1               0.199    0.044    4.475    0.000    0.199    0.141
   .IM2               0.238    0.057    4.138    0.000    0.238    0.162
   .IM3               0.257    0.074    3.453    0.001    0.257    0.171
   .EEC               0.496    0.141    3.523    0.000    0.505    0.505
   .EEF               0.405    0.133    3.044    0.002    0.703    0.703
   .IM                1.209    0.258    4.689    0.000    0.996    0.996

R-Square:
                   Estimate
    EEC1              0.625
    EEC2              0.798
    EEC3              0.729
    EEF1              0.707
    EEF2              0.608
    EEF3              0.545
    IM1               0.859
    IM2               0.838
    IM3               0.829
    EEC               0.495
    EEF               0.297
    IM                0.004

Partial mediation EEC -> EEF

lavaan 0.6-19 ended normally after 31 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        24

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                39.268      36.279
  Degrees of freedom                                30          30
  P-value (Chi-square)                           0.120       0.199
  Scaling correction factor                                  1.082
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               762.973     680.484
  Degrees of freedom                                45          45
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.121

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.987       0.990
  Tucker-Lewis Index (TLI)                       0.981       0.985
                                                                  
  Robust Comparative Fit Index (CFI)                         0.990
  Robust Tucker-Lewis Index (TLI)                            0.986

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1243.927   -1243.927
  Scaling correction factor                                  1.329
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1224.293   -1224.293
  Scaling correction factor                                  1.192
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2535.854    2535.854
  Bayesian (BIC)                              2601.732    2601.732
  Sample-size adjusted Bayesian (SABIC)       2525.873    2525.873

Root Mean Square Error of Approximation:

  RMSEA                                          0.052       0.043
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.093       0.085
  P-value H_0: RMSEA <= 0.050                    0.442       0.570
  P-value H_0: RMSEA >= 0.080                    0.143       0.077
                                                                  
  Robust RMSEA                                               0.044
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.090
  P-value H_0: Robust RMSEA <= 0.050                         0.538
  P-value H_0: Robust RMSEA >= 0.080                         0.109

Standardized Root Mean Square Residual:

  SRMR                                           0.051       0.051

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
  EEC =~                                                                
    EEC1              1.000                               0.991    0.791
    EEC2              1.194    0.107   11.143    0.000    1.184    0.893
    EEC3              1.101    0.099   11.071    0.000    1.091    0.854
  EEF =~                                                                
    EEF1              1.000                               0.759    0.841
    EEF2              1.058    0.157    6.750    0.000    0.803    0.780
    EEF3              0.921    0.155    5.953    0.000    0.699    0.738
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.006    0.061   16.564    0.000    1.108    0.915
    IM3               1.012    0.060   16.976    0.000    1.115    0.910

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  IM ~                                                                  
    AI_2             -0.136    0.212   -0.643    0.521   -0.124   -0.062
  EEF ~                                                                 
    IM                0.179    0.090    1.978    0.048    0.260    0.260
    AI_2             -0.155    0.136   -1.136    0.256   -0.204   -0.102
    EEC               0.329    0.122    2.686    0.007    0.429    0.429
  EEC ~                                                                 
    IM                0.570    0.082    6.995    0.000    0.634    0.634
    AI_2              0.037    0.158    0.234    0.815    0.037    0.019

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.100    5.909    0.000    0.589    0.375
   .EEC2              0.355    0.101    3.525    0.000    0.355    0.202
   .EEC3              0.443    0.108    4.110    0.000    0.443    0.271
   .EEF1              0.239    0.081    2.933    0.003    0.239    0.293
   .EEF2              0.417    0.093    4.476    0.000    0.417    0.392
   .EEF3              0.408    0.108    3.777    0.000    0.408    0.455
   .IM1               0.199    0.044    4.475    0.000    0.199    0.141
   .IM2               0.238    0.057    4.138    0.000    0.238    0.162
   .IM3               0.257    0.074    3.453    0.001    0.257    0.171
   .EEC               0.589    0.146    4.038    0.000    0.599    0.599
   .EEF               0.342    0.115    2.974    0.003    0.592    0.592
   .IM                1.209    0.258    4.689    0.000    0.996    0.996

R-Square:
                   Estimate
    EEC1              0.625
    EEC2              0.798
    EEC3              0.729
    EEF1              0.707
    EEF2              0.608
    EEF3              0.545
    IM1               0.859
    IM2               0.838
    IM3               0.829
    EEC               0.401
    EEF               0.408
    IM                0.004

With moderation

With latent interactions

Based on ADT as a latent variable
lavaan 0.6-19 ended normally after 48 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        41

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               133.998     122.878
  Degrees of freedom                                94          94
  P-value (Chi-square)                           0.004       0.024
  Scaling correction factor                                  1.090
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              1552.498    1293.066
  Degrees of freedom                               120         120
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.201

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.972       0.975
  Tucker-Lewis Index (TLI)                       0.964       0.969
                                                                  
  Robust Comparative Fit Index (CFI)                         0.978
  Robust Tucker-Lewis Index (TLI)                            0.971

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -2296.788   -2296.788
  Scaling correction factor                                  2.153
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -2229.789   -2229.789
  Scaling correction factor                                  1.413
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                4675.576    4675.576
  Bayesian (BIC)                              4788.118    4788.118
  Sample-size adjusted Bayesian (SABIC)       4658.525    4658.525

Root Mean Square Error of Approximation:

  RMSEA                                          0.061       0.052
  90 Percent confidence interval - lower         0.035       0.022
  90 Percent confidence interval - upper         0.083       0.075
  P-value H_0: RMSEA <= 0.050                    0.219       0.438
  P-value H_0: RMSEA >= 0.080                    0.082       0.019
                                                                  
  Robust RMSEA                                               0.054
  90 Percent confidence interval - lower                     0.021
  90 Percent confidence interval - upper                     0.079
  P-value H_0: Robust RMSEA <= 0.050                         0.388
  P-value H_0: Robust RMSEA >= 0.080                         0.042

Standardized Root Mean Square Residual:

  SRMR                                           0.055       0.055

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
  EEC =~                                                                
    EEC1              1.000                               0.992    0.791
    EEC2              1.196    0.107   11.189    0.000    1.186    0.895
    EEC3              1.098    0.100   11.011    0.000    1.089    0.852
  EEF =~                                                                
    EEF1              1.000                               0.756    0.839
    EEF2              1.063    0.158    6.731    0.000    0.803    0.781
    EEF3              0.922    0.154    5.989    0.000    0.696    0.736
  ADT =~                                                                
    ADT1              1.000                               1.447    0.968
    ADT2              1.001    0.041   24.365    0.000    1.448    0.955
    ADT3              1.011    0.049   20.682    0.000    1.463    0.932
  IM =~                                                                 
    IM1               1.000                               1.100    0.926
    IM2               1.009    0.059   17.240    0.000    1.110    0.918
    IM3               1.010    0.057   17.608    0.000    1.111    0.908
  IM_ADT =~                                                             
    IM1.ADT1          1.000                               1.644    0.851
    IM2.ADT2          1.364    0.339    4.029    0.000    2.244    0.895
    IM3.ADT3          1.196    0.371    3.220    0.001    1.966    0.869

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  IM ~                                                                  
    AI_2             -0.058    0.185   -0.316    0.752   -0.053   -0.027
    ADT               0.183    0.054    3.387    0.001    0.241    0.241
    IM_ADT           -0.263    0.117   -2.237    0.025   -0.393   -0.393
  EEF ~                                                                 
    IM                0.312    0.058    5.402    0.000    0.455    0.455
    AI_2             -0.121    0.140   -0.864    0.388   -0.160   -0.080
    ADT               0.122    0.056    2.187    0.029    0.234    0.234
  EEC ~                                                                 
    IM                0.522    0.082    6.388    0.000    0.578    0.578
    AI_2              0.058    0.152    0.383    0.702    0.059    0.029
    ADT               0.115    0.060    1.925    0.054    0.168    0.168

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .EEC ~~                                                                
   .EEF               0.168    0.056    3.003    0.003    0.364    0.364
  ADT ~~                                                                
    IM_ADT           -0.513    0.416   -1.233    0.218   -0.216   -0.216

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.100    5.910    0.000    0.589    0.374
   .EEC2              0.351    0.100    3.500    0.000    0.351    0.199
   .EEC3              0.449    0.110    4.094    0.000    0.449    0.274
   .EEF1              0.241    0.081    2.968    0.003    0.241    0.297
   .EEF2              0.413    0.092    4.513    0.000    0.413    0.390
   .EEF3              0.409    0.106    3.880    0.000    0.409    0.458
   .ADT1              0.139    0.061    2.296    0.022    0.139    0.062
   .ADT2              0.203    0.055    3.697    0.000    0.203    0.088
   .ADT3              0.324    0.084    3.861    0.000    0.324    0.131
   .IM1               0.200    0.043    4.618    0.000    0.200    0.142
   .IM2               0.230    0.057    4.052    0.000    0.230    0.158
   .IM3               0.262    0.075    3.500    0.000    0.262    0.175
   .IM1.ADT1          1.030    0.408    2.526    0.012    1.030    0.276
   .IM2.ADT2          1.244    0.712    1.747    0.081    1.244    0.198
   .IM3.ADT3          1.253    0.541    2.319    0.020    1.253    0.245
   .EEC               0.565    0.145    3.890    0.000    0.574    0.574
   .EEF               0.378    0.126    3.005    0.003    0.661    0.661
    ADT               2.093    0.365    5.737    0.000    1.000    1.000
   .IM                0.902    0.203    4.448    0.000    0.746    0.746
    IM_ADT            2.704    1.257    2.151    0.032    1.000    1.000

R-Square:
                   Estimate
    EEC1              0.626
    EEC2              0.801
    EEC3              0.726
    EEF1              0.703
    EEF2              0.610
    EEF3              0.542
    ADT1              0.938
    ADT2              0.912
    ADT3              0.869
    IM1               0.858
    IM2               0.842
    IM3               0.825
    IM1.ADT1          0.724
    IM2.ADT2          0.802
    IM3.ADT3          0.755
    EEC               0.426
    EEF               0.339
    IM                0.254
R square
    EEC1     EEC2     EEC3     EEF1     EEF2     EEF3     ADT1     ADT2 
   0.626    0.801    0.726    0.703    0.610    0.542    0.938    0.912 
    ADT3      IM1      IM2      IM3 IM1.ADT1 IM2.ADT2 IM3.ADT3      EEC 
   0.869    0.858    0.842    0.825    0.724    0.802    0.755    0.426 
     EEF       IM 
   0.339    0.254 
high >5

Full model based on the moderator as a dummy

Based on ADT as a dummy variable
lavaan 0.6-19 ended normally after 45 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        30

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                44.120      42.295
  Degrees of freedom                                42          42
  P-value (Chi-square)                           0.382       0.458
  Scaling correction factor                                  1.043
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               786.673     729.650
  Degrees of freedom                                63          63
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.078

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.997       1.000
  Tucker-Lewis Index (TLI)                       0.996       0.999
                                                                  
  Robust Comparative Fit Index (CFI)                         1.000
  Robust Tucker-Lewis Index (TLI)                            0.999

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1234.503   -1234.503
  Scaling correction factor                                  1.267
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1212.443   -1212.443
  Scaling correction factor                                  1.137
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2529.006    2529.006
  Bayesian (BIC)                              2611.354    2611.354
  Sample-size adjusted Bayesian (SABIC)       2516.530    2516.530

Root Mean Square Error of Approximation:

  RMSEA                                          0.021       0.008
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.068       0.063
  P-value H_0: RMSEA <= 0.050                    0.803       0.856
  P-value H_0: RMSEA >= 0.080                    0.012       0.007
                                                                  
  Robust RMSEA                                               0.008
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.065
  P-value H_0: Robust RMSEA <= 0.050                         0.840
  P-value H_0: Robust RMSEA >= 0.080                         0.010

Standardized Root Mean Square Residual:

  SRMR                                           0.043       0.043

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
  EEC =~                                                                
    EEC1              1.000                               0.991    0.791
    EEC2              1.196    0.106   11.273    0.000    1.185    0.894
    EEC3              1.099    0.100   11.045    0.000    1.089    0.852
  EEF =~                                                                
    EEF1              1.000                               0.757    0.839
    EEF2              1.065    0.158    6.746    0.000    0.807    0.783
    EEF3              0.921    0.155    5.946    0.000    0.698    0.737
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.005    0.061   16.476    0.000    1.107    0.915
    IM3               1.011    0.060   16.824    0.000    1.115    0.910

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.320    0.054    5.940    0.000    0.466    0.466
    ADT_high          0.416    0.135    3.093    0.002    0.550    0.259
    AI_2             -0.138    0.257   -0.537    0.592   -0.182   -0.091
    AI2_ADT          -0.006    0.295   -0.021    0.984   -0.008   -0.004
  EEC ~                                                                 
    IM                0.534    0.078    6.805    0.000    0.594    0.594
    ADT_high          0.511    0.197    2.593    0.010    0.515    0.242
    AI_2              0.238    0.245    0.974    0.330    0.240    0.120
    AI2_ADT          -0.298    0.317   -0.941    0.347   -0.301   -0.141
  IM ~                                                                  
    AI_2             -0.281    0.425   -0.661    0.509   -0.255   -0.127
    AI2_ADT           0.231    0.478    0.483    0.629    0.210    0.098
    ADT_high          0.484    0.325    1.488    0.137    0.439    0.207

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .EEC ~~                                                                
   .EEF               0.162    0.059    2.738    0.006    0.357    0.357

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.098    5.998    0.000    0.589    0.375
   .EEC2              0.352    0.100    3.527    0.000    0.352    0.200
   .EEC3              0.447    0.111    4.030    0.000    0.447    0.274
   .EEF1              0.242    0.079    3.046    0.002    0.242    0.296
   .EEF2              0.411    0.092    4.479    0.000    0.411    0.387
   .EEF3              0.410    0.108    3.794    0.000    0.410    0.457
   .IM1               0.198    0.045    4.384    0.000    0.198    0.140
   .IM2               0.239    0.058    4.119    0.000    0.239    0.163
   .IM3               0.257    0.075    3.426    0.001    0.257    0.171
   .EEC               0.556    0.145    3.844    0.000    0.566    0.566
   .EEF               0.368    0.122    3.012    0.003    0.641    0.641
   .IM                1.128    0.232    4.854    0.000    0.929    0.929

R-Square:
                   Estimate
    EEC1              0.625
    EEC2              0.800
    EEC3              0.726
    EEF1              0.704
    EEF2              0.613
    EEF3              0.543
    IM1               0.860
    IM2               0.837
    IM3               0.829
    EEC               0.434
    EEF               0.359
    IM                0.071

ADT as an IV

Based on ADT as a dummy variable
lavaan 0.6-19 ended normally after 32 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        26

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                52.532      50.200
  Degrees of freedom                                46          46
  P-value (Chi-square)                           0.236       0.311
  Scaling correction factor                                  1.046
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               786.673     729.650
  Degrees of freedom                                63          63
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.078

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.991       0.994
  Tucker-Lewis Index (TLI)                       0.988       0.991
                                                                  
  Robust Comparative Fit Index (CFI)                         0.994
  Robust Tucker-Lewis Index (TLI)                            0.992

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1238.709   -1238.709
  Scaling correction factor                                  1.296
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1212.443   -1212.443
  Scaling correction factor                                  1.137
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2529.419    2529.419
  Bayesian (BIC)                              2600.787    2600.787
  Sample-size adjusted Bayesian (SABIC)       2518.606    2518.606

Root Mean Square Error of Approximation:

  RMSEA                                          0.035       0.028
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.074       0.069
  P-value H_0: RMSEA <= 0.050                    0.695       0.771
  P-value H_0: RMSEA >= 0.080                    0.023       0.012
                                                                  
  Robust RMSEA                                               0.029
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.071
  P-value H_0: Robust RMSEA <= 0.050                         0.750
  P-value H_0: Robust RMSEA >= 0.080                         0.018

Standardized Root Mean Square Residual:

  SRMR                                           0.081       0.081

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
  EEC =~                                                                
    EEC1              1.000                               0.965    0.783
    EEC2              1.196    0.107   11.224    0.000    1.154    0.890
    EEC3              1.098    0.100   11.001    0.000    1.061    0.846
  EEF =~                                                                
    EEF1              1.000                               0.734    0.830
    EEF2              1.065    0.157    6.790    0.000    0.782    0.773
    EEF3              0.924    0.153    6.019    0.000    0.678    0.728
  IM =~                                                                 
    IM1               1.000                               1.100    0.926
    IM2               1.008    0.061   16.603    0.000    1.109    0.916
    IM3               1.014    0.060   16.921    0.000    1.115    0.911

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.319    0.053    5.987    0.000    0.478    0.478
    ADT_high          0.425    0.150    2.831    0.005    0.579    0.273
    AI_2             -0.142    0.139   -1.020    0.308   -0.193   -0.096
    AI2_ADT           0.000                               0.000    0.000
  EEC ~                                                                 
    IM                0.529    0.081    6.557    0.000    0.603    0.603
    ADT_high          0.386    0.160    2.421    0.015    0.400    0.188
    AI_2              0.038    0.154    0.245    0.807    0.039    0.020
    AI2_ADT           0.000                               0.000    0.000
  IM ~                                                                  
    AI_2             -0.136    0.212   -0.641    0.521   -0.124   -0.062
    AI2_ADT           0.000                               0.000    0.000
    ADT_high          0.000                               0.000    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .EEC ~~                                                                
   .EEF               0.162    0.058    2.789    0.005    0.357    0.357

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.099    5.949    0.000    0.589    0.387
   .EEC2              0.351    0.099    3.554    0.000    0.351    0.209
   .EEC3              0.448    0.111    4.029    0.000    0.448    0.285
   .EEF1              0.243    0.079    3.054    0.002    0.243    0.310
   .EEF2              0.412    0.092    4.464    0.000    0.412    0.402
   .EEF3              0.408    0.107    3.809    0.000    0.408    0.470
   .IM1               0.202    0.045    4.522    0.000    0.202    0.143
   .IM2               0.236    0.057    4.153    0.000    0.236    0.161
   .IM3               0.255    0.073    3.477    0.001    0.255    0.170
   .EEC               0.561    0.146    3.845    0.000    0.602    0.602
   .EEF               0.367    0.121    3.034    0.002    0.681    0.681
   .IM                1.206    0.258    4.673    0.000    0.996    0.996

R-Square:
                   Estimate
    EEC1              0.613
    EEC2              0.791
    EEC3              0.715
    EEF1              0.690
    EEF2              0.598
    EEF3              0.530
    IM1               0.857
    IM2               0.839
    IM3               0.830
    EEC               0.398
    EEF               0.319
    IM                0.004

Derived model

Based on ADT as a dummy variable
lavaan 0.6-19 ended normally after 31 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        23

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                54.475      52.266
  Degrees of freedom                                49          49
  P-value (Chi-square)                           0.274       0.348
  Scaling correction factor                                  1.042
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                               786.673     729.650
  Degrees of freedom                                63          63
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.078

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.992       0.995
  Tucker-Lewis Index (TLI)                       0.990       0.994
                                                                  
  Robust Comparative Fit Index (CFI)                         0.995
  Robust Tucker-Lewis Index (TLI)                            0.994

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1239.681   -1239.681
  Scaling correction factor                                  1.337
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1212.443   -1212.443
  Scaling correction factor                                  1.137
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2525.361    2525.361
  Bayesian (BIC)                              2588.495    2588.495
  Sample-size adjusted Bayesian (SABIC)       2515.796    2515.796

Root Mean Square Error of Approximation:

  RMSEA                                          0.031       0.024
  90 Percent confidence interval - lower         0.000       0.000
  90 Percent confidence interval - upper         0.070       0.066
  P-value H_0: RMSEA <= 0.050                    0.746       0.811
  P-value H_0: RMSEA >= 0.080                    0.015       0.008
                                                                  
  Robust RMSEA                                               0.025
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.068
  P-value H_0: Robust RMSEA <= 0.050                         0.792
  P-value H_0: Robust RMSEA >= 0.080                         0.011

Standardized Root Mean Square Residual:

  SRMR                                           0.080       0.080

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
  EEC =~                                                                
    EEC1              1.000                               0.966    0.783
    EEC2              1.194    0.106   11.225    0.000    1.154    0.889
    EEC3              1.098    0.100   11.004    0.000    1.061    0.846
  EEF =~                                                                
    EEF1              1.000                               0.732    0.829
    EEF2              1.063    0.153    6.947    0.000    0.779    0.770
    EEF3              0.931    0.156    5.958    0.000    0.682    0.732
  IM =~                                                                 
    IM1               1.000                               1.100    0.926
    IM2               1.008    0.061   16.599    0.000    1.109    0.916
    IM3               1.014    0.060   16.879    0.000    1.115    0.911

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.324    0.054    6.046    0.000    0.486    0.486
    ADT_high          0.425    0.150    2.838    0.005    0.580    0.273
    AI_2              0.000                               0.000    0.000
    AI2_ADT           0.000                               0.000    0.000
  EEC ~                                                                 
    IM                0.528    0.082    6.482    0.000    0.602    0.602
    ADT_high          0.386    0.160    2.416    0.016    0.400    0.188
    AI_2              0.000                               0.000    0.000
    AI2_ADT           0.000                               0.000    0.000
  IM ~                                                                  
    AI_2              0.000                               0.000    0.000
    AI2_ADT           0.000                               0.000    0.000
    ADT_high          0.000                               0.000    0.000

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .EEC ~~                                                                
   .EEF               0.161    0.059    2.733    0.006    0.352    0.352

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.588    0.099    5.934    0.000    0.588    0.386
   .EEC2              0.353    0.100    3.525    0.000    0.353    0.209
   .EEC3              0.448    0.111    4.036    0.000    0.448    0.285
   .EEF1              0.245    0.081    3.039    0.002    0.245    0.313
   .EEF2              0.417    0.093    4.486    0.000    0.417    0.408
   .EEF3              0.403    0.106    3.791    0.000    0.403    0.464
   .IM1               0.202    0.045    4.536    0.000    0.202    0.143
   .IM2               0.236    0.057    4.153    0.000    0.236    0.161
   .IM3               0.255    0.073    3.465    0.001    0.255    0.170
   .EEC               0.563    0.145    3.876    0.000    0.603    0.603
   .EEF               0.370    0.126    2.945    0.003    0.689    0.689
   .IM                1.210    0.262    4.626    0.000    1.000    1.000

R-Square:
                   Estimate
    EEC1              0.614
    EEC2              0.791
    EEC3              0.715
    EEF1              0.687
    EEF2              0.592
    EEF3              0.536
    IM1               0.857
    IM2               0.839
    IM3               0.830
    EEC               0.397
    EEF               0.311
    IM                0.000

IM

ADT and full mediation by IM
lavaan 0.6-19 ended normally after 39 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        30

  Number of observations                           115

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                68.574      60.496
  Degrees of freedom                                48          48
  P-value (Chi-square)                           0.027       0.106
  Scaling correction factor                                  1.134
    Yuan-Bentler correction (Mplus variant)                       

Model Test Baseline Model:

  Test statistic                              1240.604    1042.507
  Degrees of freedom                                66          66
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.190

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.982       0.987
  Tucker-Lewis Index (TLI)                       0.976       0.982
                                                                  
  Robust Comparative Fit Index (CFI)                         0.988
  Robust Tucker-Lewis Index (TLI)                            0.983

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1655.229   -1655.229
  Scaling correction factor                                  1.399
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1620.942   -1620.942
  Scaling correction factor                                  1.235
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                3370.457    3370.457
  Bayesian (BIC)                              3452.805    3452.805
  Sample-size adjusted Bayesian (SABIC)       3357.981    3357.981

Root Mean Square Error of Approximation:

  RMSEA                                          0.061       0.048
  90 Percent confidence interval - lower         0.021       0.000
  90 Percent confidence interval - upper         0.092       0.079
  P-value H_0: RMSEA <= 0.050                    0.276       0.521
  P-value H_0: RMSEA >= 0.080                    0.169       0.047
                                                                  
  Robust RMSEA                                               0.051
  90 Percent confidence interval - lower                     0.000
  90 Percent confidence interval - upper                     0.087
  P-value H_0: Robust RMSEA <= 0.050                         0.464
  P-value H_0: Robust RMSEA >= 0.080                         0.096

Standardized Root Mean Square Residual:

  SRMR                                           0.046       0.046

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
  EEC =~                                                                
    EEC1              1.000                               0.991    0.791
    EEC2              1.196    0.107   11.193    0.000    1.186    0.895
    EEC3              1.098    0.099   11.032    0.000    1.088    0.851
  EEF =~                                                                
    EEF1              1.000                               0.757    0.839
    EEF2              1.059    0.153    6.908    0.000    0.802    0.779
    EEF3              0.927    0.156    5.959    0.000    0.702    0.741
  IM =~                                                                 
    IM1               1.000                               1.102    0.927
    IM2               1.005    0.061   16.507    0.000    1.107    0.915
    IM3               1.011    0.060   16.914    0.000    1.114    0.910
  ADT =~                                                                
    ADT1              1.000                               1.447    0.968
    ADT2              1.001    0.041   24.537    0.000    1.448    0.955
    ADT3              1.011    0.049   20.766    0.000    1.463    0.932

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.164    0.084    1.957    0.050    0.239    0.239
    EEC               0.293    0.115    2.546    0.011    0.383    0.383
    ADT               0.091    0.050    1.816    0.069    0.174    0.174
  EEC ~                                                                 
    IM                0.521    0.082    6.364    0.000    0.579    0.579
    ADT               0.113    0.061    1.858    0.063    0.166    0.166
  IM ~                                                                  
    ADT               0.250    0.091    2.751    0.006    0.328    0.328

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.589    0.100    5.905    0.000    0.589    0.375
   .EEC2              0.350    0.101    3.462    0.001    0.350    0.199
   .EEC3              0.450    0.109    4.107    0.000    0.450    0.275
   .EEF1              0.242    0.082    2.959    0.003    0.242    0.297
   .EEF2              0.418    0.092    4.544    0.000    0.418    0.394
   .EEF3              0.405    0.104    3.880    0.000    0.405    0.451
   .IM1               0.198    0.045    4.417    0.000    0.198    0.140
   .IM2               0.239    0.059    4.082    0.000    0.239    0.163
   .IM3               0.257    0.075    3.431    0.001    0.257    0.171
   .ADT1              0.139    0.060    2.304    0.021    0.139    0.062
   .ADT2              0.203    0.055    3.690    0.000    0.203    0.088
   .ADT3              0.324    0.084    3.866    0.000    0.324    0.132
   .EEC               0.565    0.144    3.923    0.000    0.575    0.575
   .EEF               0.330    0.115    2.867    0.004    0.575    0.575
   .IM                1.084    0.215    5.041    0.000    0.892    0.892
    ADT               2.094    0.364    5.745    0.000    1.000    1.000

R-Square:
                   Estimate
    EEC1              0.625
    EEC2              0.801
    EEC3              0.725
    EEF1              0.703
    EEF2              0.606
    EEF3              0.549
    IM1               0.860
    IM2               0.837
    IM3               0.829
    ADT1              0.938
    ADT2              0.912
    ADT3              0.868
    EEC               0.425
    EEF               0.425
    IM                0.108

Multigroup analysis on ADT

Interaction effect between ADT and AI groups
continous variable
lavaan 0.6-19 ended normally after 54 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        84

  Number of observations per group:                   
    AI                                              56
    control                                         59

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                               141.060     150.565
  Degrees of freedom                                96          96
  P-value (Chi-square)                           0.002       0.000
  Scaling correction factor                                  0.937
    Yuan-Bentler correction (Mplus variant)                       
  Test statistic for each group:
    AI                                          86.003      86.003
    control                                     64.562      64.562

Model Test Baseline Model:

  Test statistic                              1321.078    1231.518
  Degrees of freedom                               132         132
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.073

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.962       0.950
  Tucker-Lewis Index (TLI)                       0.948       0.932
                                                                  
  Robust Comparative Fit Index (CFI)                         0.957
  Robust Tucker-Lewis Index (TLI)                            0.940

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1635.048   -1635.048
  Scaling correction factor                                  1.283
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1564.518   -1564.518
  Scaling correction factor                                  1.099
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                3438.096    3438.096
  Bayesian (BIC)                              3668.671    3668.671
  Sample-size adjusted Bayesian (SABIC)       3403.162    3403.162

Root Mean Square Error of Approximation:

  RMSEA                                          0.090       0.099
  90 Percent confidence interval - lower         0.056       0.066
  90 Percent confidence interval - upper         0.121       0.130
  P-value H_0: RMSEA <= 0.050                    0.030       0.011
  P-value H_0: RMSEA >= 0.080                    0.714       0.846
                                                                  
  Robust RMSEA                                               0.096
  90 Percent confidence interval - lower                     0.065
  90 Percent confidence interval - upper                     0.125
  P-value H_0: Robust RMSEA <= 0.050                         0.010
  P-value H_0: Robust RMSEA >= 0.080                         0.821

Standardized Root Mean Square Residual:

  SRMR                                           0.048       0.048

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian


Group 1 [AI]:

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEC =~                                                                
    EEC1              1.000                               1.053    0.827
    EEC2              1.153    0.150    7.679    0.000    1.214    0.913
    EEC3              1.141    0.156    7.314    0.000    1.202    0.870
  EEF =~                                                                
    EEF1              1.000                               0.919    0.860
    EEF2              1.115    0.201    5.533    0.000    1.024    0.873
    EEF3              0.905    0.148    6.109    0.000    0.832    0.830
  IM =~                                                                 
    IM1               1.000                               1.129    0.940
    IM2               0.976    0.091   10.764    0.000    1.102    0.892
    IM3               1.011    0.062   16.280    0.000    1.142    0.913
  ADT =~                                                                
    ADT1              1.000                               1.598    0.979
    ADT2              0.997    0.057   17.519    0.000    1.594    0.969
    ADT3              0.998    0.066   15.125    0.000    1.595    0.947

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.060    0.152    0.394    0.694    0.073    0.073
    EEC               0.478    0.201    2.383    0.017    0.548    0.548
    ADT               0.087    0.068    1.282    0.200    0.151    0.151
  EEC ~                                                                 
    IM                0.581    0.138    4.219    0.000    0.623    0.623
    ADT               0.082    0.079    1.039    0.299    0.125    0.125
  IM ~                                                                  
    ADT               0.235    0.129    1.827    0.068    0.333    0.333

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              4.643    0.170   27.277    0.000    4.643    3.645
   .EEC2              4.982    0.178   28.043    0.000    4.982    3.747
   .EEC3              5.018    0.185   27.168    0.000    5.018    3.630
   .EEF1              5.482    0.143   38.380    0.000    5.482    5.129
   .EEF2              5.625    0.157   35.868    0.000    5.625    4.793
   .EEF3              5.821    0.134   43.480    0.000    5.821    5.810
   .IM1               5.357    0.161   33.363    0.000    5.357    4.458
   .IM2               5.786    0.165   35.054    0.000    5.786    4.684
   .IM3               5.589    0.167   33.451    0.000    5.589    4.470
   .ADT1              5.393    0.218   24.711    0.000    5.393    3.302
   .ADT2              5.286    0.220   24.054    0.000    5.286    3.214
   .ADT3              5.268    0.225   23.396    0.000    5.268    3.126

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.513    0.150    3.416    0.001    0.513    0.316
   .EEC2              0.293    0.142    2.057    0.040    0.293    0.166
   .EEC3              0.465    0.184    2.533    0.011    0.465    0.244
   .EEF1              0.298    0.128    2.320    0.020    0.298    0.261
   .EEF2              0.328    0.141    2.326    0.020    0.328    0.238
   .EEF3              0.312    0.130    2.407    0.016    0.312    0.311
   .IM1               0.169    0.070    2.408    0.016    0.169    0.117
   .IM2               0.311    0.111    2.814    0.005    0.311    0.204
   .IM3               0.260    0.125    2.070    0.038    0.260    0.166
   .ADT1              0.112    0.087    1.288    0.198    0.112    0.042
   .ADT2              0.165    0.068    2.420    0.016    0.165    0.061
   .ADT3              0.294    0.106    2.784    0.005    0.294    0.104
   .EEC               0.604    0.214    2.820    0.005    0.545    0.545
   .EEF               0.469    0.176    2.664    0.008    0.555    0.555
   .IM                1.134    0.360    3.151    0.002    0.889    0.889
    ADT               2.555    0.566    4.515    0.000    1.000    1.000

R-Square:
                   Estimate
    EEC1              0.684
    EEC2              0.834
    EEC3              0.756
    EEF1              0.739
    EEF2              0.762
    EEF3              0.689
    IM1               0.883
    IM2               0.796
    IM3               0.834
    ADT1              0.958
    ADT2              0.939
    ADT3              0.896
    EEC               0.455
    EEF               0.445
    IM                0.111


Group 2 [control]:

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEC =~                                                                
    EEC1              1.000                               0.930    0.755
    EEC2              1.245    0.155    8.014    0.000    1.158    0.877
    EEC3              1.046    0.130    8.019    0.000    0.973    0.831
  EEF =~                                                                
    EEF1              1.000                               0.452    0.651
    EEF2              0.907    0.166    5.450    0.000    0.410    0.483
    EEF3              1.492    0.735    2.029    0.043    0.675    0.756
  IM =~                                                                 
    IM1               1.000                               1.076    0.920
    IM2               1.029    0.088   11.658    0.000    1.107    0.936
    IM3               1.008    0.108    9.375    0.000    1.084    0.906
  ADT =~                                                                
    ADT1              1.000                               1.283    0.956
    ADT2              0.993    0.053   18.649    0.000    1.274    0.933
    ADT3              1.024    0.065   15.727    0.000    1.314    0.911

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.236    0.098    2.418    0.016    0.561    0.561
    EEC               0.101    0.096    1.058    0.290    0.208    0.208
    ADT               0.071    0.063    1.128    0.260    0.201    0.201
  EEC ~                                                                 
    IM                0.445    0.090    4.965    0.000    0.515    0.515
    ADT               0.160    0.084    1.905    0.057    0.221    0.221
  IM ~                                                                  
    ADT               0.272    0.120    2.274    0.023    0.325    0.325

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              4.729    0.160   29.465    0.000    4.729    3.836
   .EEC2              5.017    0.172   29.168    0.000    5.017    3.797
   .EEC3              5.051    0.152   33.142    0.000    5.051    4.315
   .EEF1              5.695    0.090   62.929    0.000    5.695    8.193
   .EEF2              5.915    0.111   53.486    0.000    5.915    6.963
   .EEF3              5.864    0.116   50.515    0.000    5.864    6.576
   .IM1               5.525    0.152   36.287    0.000    5.525    4.724
   .IM2               5.915    0.154   38.406    0.000    5.915    5.000
   .IM3               5.695    0.156   36.550    0.000    5.695    4.758
   .ADT1              5.593    0.175   32.017    0.000    5.593    4.168
   .ADT2              5.610    0.178   31.555    0.000    5.610    4.108
   .ADT3              5.508    0.188   29.335    0.000    5.508    3.819

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.655    0.134    4.888    0.000    0.655    0.431
   .EEC2              0.404    0.154    2.633    0.008    0.404    0.232
   .EEC3              0.424    0.141    3.010    0.003    0.424    0.309
   .EEF1              0.279    0.115    2.428    0.015    0.279    0.577
   .EEF2              0.553    0.131    4.226    0.000    0.553    0.767
   .EEF3              0.340    0.116    2.937    0.003    0.340    0.428
   .IM1               0.211    0.052    4.045    0.000    0.211    0.154
   .IM2               0.174    0.043    4.016    0.000    0.174    0.124
   .IM3               0.256    0.085    3.008    0.003    0.256    0.179
   .ADT1              0.155    0.079    1.970    0.049    0.155    0.086
   .ADT2              0.241    0.086    2.807    0.005    0.241    0.129
   .ADT3              0.354    0.131    2.713    0.007    0.354    0.170
   .EEC               0.530    0.196    2.710    0.007    0.612    0.612
   .EEF               0.073    0.072    1.012    0.311    0.359    0.359
   .IM                1.035    0.232    4.453    0.000    0.894    0.894
    ADT               1.645    0.437    3.764    0.000    1.000    1.000

R-Square:
                   Estimate
    EEC1              0.569
    EEC2              0.768
    EEC3              0.691
    EEF1              0.423
    EEF2              0.233
    EEF3              0.572
    IM1               0.846
    IM2               0.876
    IM3               0.821
    ADT1              0.914
    ADT2              0.871
    ADT3              0.830
    EEC               0.388
    EEF               0.641
    IM                0.106
`geom_smooth()` using formula = 'y ~ x'

`geom_smooth()` using formula = 'y ~ x'

- as categorical variables of ADT

dummies where high as above 5
lavaan 0.6-19 ended normally after 87 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        66

  Number of observations per group:                   
    AI                                              56
    control                                         59

Model Test User Model:
                                              Standard      Scaled
  Test Statistic                                81.559      86.041
  Degrees of freedom                                60          60
  P-value (Chi-square)                           0.034       0.015
  Scaling correction factor                                  0.948
    Yuan-Bentler correction (Mplus variant)                       
  Test statistic for each group:
    AI                                          45.433      45.433
    control                                     40.608      40.608

Model Test Baseline Model:

  Test statistic                               835.666     784.979
  Degrees of freedom                                90          90
  P-value                                        0.000       0.000
  Scaling correction factor                                  1.065

User Model versus Baseline Model:

  Comparative Fit Index (CFI)                    0.971       0.963
  Tucker-Lewis Index (TLI)                       0.957       0.944
                                                                  
  Robust Comparative Fit Index (CFI)                         0.967
  Robust Tucker-Lewis Index (TLI)                            0.950

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -1216.586   -1216.586
  Scaling correction factor                                  1.232
      for the MLR correction                                      
  Loglikelihood unrestricted model (H1)      -1175.806   -1175.806
  Scaling correction factor                                  1.097
      for the MLR correction                                      
                                                                  
  Akaike (AIC)                                2565.171    2565.171
  Bayesian (BIC)                              2746.337    2746.337
  Sample-size adjusted Bayesian (SABIC)       2537.723    2537.723

Root Mean Square Error of Approximation:

  RMSEA                                          0.079       0.087
  90 Percent confidence interval - lower         0.023       0.038
  90 Percent confidence interval - upper         0.120       0.127
  P-value H_0: RMSEA <= 0.050                    0.149       0.093
  P-value H_0: RMSEA >= 0.080                    0.508       0.626
                                                                  
  Robust RMSEA                                               0.085
  90 Percent confidence interval - lower                     0.038
  90 Percent confidence interval - upper                     0.123
  P-value H_0: Robust RMSEA <= 0.050                         0.094
  P-value H_0: Robust RMSEA >= 0.080                         0.596

Standardized Root Mean Square Residual:

  SRMR                                           0.049       0.049

Parameter Estimates:

  Standard errors                             Sandwich
  Information bread                           Observed
  Observed information based on                Hessian


Group 1 [AI]:

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEC =~                                                                
    EEC1              1.000                               1.054    0.827
    EEC2              1.152    0.150    7.673    0.000    1.214    0.913
    EEC3              1.141    0.156    7.293    0.000    1.203    0.870
  EEF =~                                                                
    EEF1              1.000                               0.918    0.859
    EEF2              1.118    0.203    5.521    0.000    1.027    0.875
    EEF3              0.904    0.148    6.098    0.000    0.830    0.829
  IM =~                                                                 
    IM1               1.000                               1.129    0.940
    IM2               0.976    0.091   10.782    0.000    1.103    0.893
    IM3               1.011    0.062   16.283    0.000    1.141    0.913

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.056    0.155    0.363    0.717    0.069    0.069
    EEC               0.488    0.199    2.454    0.014    0.560    0.560
    ADT_high          0.295    0.243    1.215    0.224    0.322    0.152
  EEC ~                                                                 
    IM                0.600    0.135    4.455    0.000    0.642    0.642
    ADT_high          0.163    0.240    0.678    0.498    0.154    0.073
  IM ~                                                                  
    ADT_high          0.731    0.352    2.078    0.038    0.648    0.307

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              4.246    0.300   14.174    0.000    4.246    3.333
   .EEC2              4.525    0.305   14.837    0.000    4.525    3.403
   .EEC3              4.565    0.320   14.253    0.000    4.565    3.302
   .EEF1              5.066    0.256   19.783    0.000    5.066    4.739
   .EEF2              5.160    0.286   18.028    0.000    5.160    4.397
   .EEF3              5.445    0.219   24.873    0.000    5.445    5.435
   .IM1               4.874    0.319   15.301    0.000    4.874    4.056
   .IM2               5.314    0.344   15.470    0.000    5.314    4.302
   .IM3               5.101    0.332   15.351    0.000    5.101    4.079

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.512    0.150    3.404    0.001    0.512    0.316
   .EEC2              0.295    0.143    2.059    0.040    0.295    0.167
   .EEC3              0.464    0.184    2.521    0.012    0.464    0.243
   .EEF1              0.299    0.127    2.358    0.018    0.299    0.262
   .EEF2              0.323    0.140    2.305    0.021    0.323    0.234
   .EEF3              0.315    0.130    2.427    0.015    0.315    0.313
   .IM1               0.169    0.069    2.435    0.015    0.169    0.117
   .IM2               0.310    0.110    2.819    0.005    0.310    0.203
   .IM3               0.261    0.126    2.070    0.038    0.261    0.167
   .EEC               0.614    0.217    2.825    0.005    0.553    0.553
   .EEF               0.468    0.169    2.772    0.006    0.555    0.555
   .IM                1.155    0.385    3.004    0.003    0.906    0.906

R-Square:
                   Estimate
    EEC1              0.684
    EEC2              0.833
    EEC3              0.757
    EEF1              0.738
    EEF2              0.766
    EEF3              0.687
    IM1               0.883
    IM2               0.797
    IM3               0.833
    EEC               0.447
    EEF               0.445
    IM                0.094


Group 2 [control]:

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEC =~                                                                
    EEC1              1.000                               0.934    0.758
    EEC2              1.231    0.153    8.067    0.000    1.150    0.871
    EEC3              1.048    0.130    8.054    0.000    0.979    0.836
  EEF =~                                                                
    EEF1              1.000                               0.449    0.645
    EEF2              0.915    0.170    5.391    0.000    0.411    0.483
    EEF3              1.510    0.622    2.428    0.015    0.677    0.760
  IM =~                                                                 
    IM1               1.000                               1.075    0.919
    IM2               1.028    0.089   11.501    0.000    1.105    0.934
    IM3               1.010    0.110    9.189    0.000    1.087    0.908

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    IM                0.252    0.094    2.686    0.007    0.603    0.603
    EEC               0.061    0.095    0.638    0.524    0.127    0.127
    ADT_high          0.334    0.147    2.267    0.023    0.746    0.348
  EEC ~                                                                 
    IM                0.460    0.092    4.979    0.000    0.529    0.529
    ADT_high          0.551    0.202    2.734    0.006    0.590    0.276
  IM ~                                                                  
    ADT_high          0.479    0.328    1.459    0.144    0.445    0.208

Intercepts:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              4.206    0.219   19.235    0.000    4.206    3.412
   .EEC2              4.373    0.231   18.967    0.000    4.373    3.310
   .EEC3              4.503    0.199   22.590    0.000    4.503    3.847
   .EEF1              5.355    0.110   48.583    0.000    5.355    7.703
   .EEF2              5.604    0.123   45.415    0.000    5.604    6.597
   .EEF3              5.351    0.201   26.625    0.000    5.351    6.000
   .IM1               5.201    0.280   18.542    0.000    5.201    4.446
   .IM2               5.582    0.296   18.826    0.000    5.582    4.718
   .IM3               5.367    0.276   19.458    0.000    5.367    4.484

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.647    0.130    4.964    0.000    0.647    0.426
   .EEC2              0.423    0.155    2.727    0.006    0.423    0.242
   .EEC3              0.412    0.143    2.874    0.004    0.412    0.301
   .EEF1              0.282    0.095    2.957    0.003    0.282    0.584
   .EEF2              0.553    0.119    4.653    0.000    0.553    0.766
   .EEF3              0.336    0.100    3.354    0.001    0.336    0.423
   .IM1               0.211    0.054    3.884    0.000    0.211    0.155
   .IM2               0.178    0.041    4.306    0.000    0.178    0.128
   .IM3               0.251    0.085    2.972    0.003    0.251    0.176
   .EEC               0.509    0.188    2.705    0.007    0.583    0.583
   .EEF               0.058    0.055    1.056    0.291    0.288    0.288
   .IM                1.107    0.269    4.117    0.000    0.957    0.957

R-Square:
                   Estimate
    EEC1              0.574
    EEC2              0.758
    EEC3              0.699
    EEF1              0.416
    EEF2              0.234
    EEF3              0.577
    IM1               0.845
    IM2               0.872
    IM3               0.824
    EEC               0.417
    EEF               0.712
    IM                0.043

GG plot

EEF

EEC

IM

Differential effect of ADT on DVs

lavaan 0.6-19 ended normally after 28 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        15

  Number of observations                           115

Model Test User Model:
                                                      
  Test statistic                                21.938
  Degrees of freedom                                12
  P-value (Chi-square)                           0.038

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEC =~                                                                
    EEC1              1.000                               0.983    0.784
    EEC2              1.196    0.120   10.004    0.000    1.176    0.888
    EEC3              1.123    0.114    9.823    0.000    1.105    0.864
  EEF =~                                                                
    EEF1              1.000                               0.758    0.840
    EEF2              1.070    0.127    8.415    0.000    0.812    0.788
    EEF3              0.913    0.116    7.878    0.000    0.693    0.731

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  EEF ~                                                                 
    ADT_high          0.609    0.158    3.856    0.000    0.802    0.377
  EEC ~                                                                 
    ADT_high          0.676    0.203    3.337    0.001    0.688    0.323

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
 .EEC ~~                                                                
   .EEF               0.353    0.085    4.133    0.000    0.541    0.541

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
   .EEC1              0.605    0.099    6.098    0.000    0.605    0.385
   .EEC2              0.373    0.093    3.995    0.000    0.373    0.212
   .EEC3              0.414    0.089    4.640    0.000    0.414    0.253
   .EEF1              0.240    0.057    4.181    0.000    0.240    0.295
   .EEF2              0.403    0.078    5.197    0.000    0.403    0.380
   .EEF3              0.417    0.070    5.960    0.000    0.417    0.465
   .EEC               0.866    0.180    4.800    0.000    0.895    0.895
   .EEF               0.493    0.099    4.963    0.000    0.858    0.858
[1] "Standardized coefficient for EEF: 0.377429934835339"
[1] "Standardized coefficient for EEC: 0.32347352853529"
Statical differential effect from ADT of the DVs

Chi-Squared Difference Test

                  Df    AIC    BIC  Chisq Chisq diff RMSEA Df diff Pr(>Chisq)
fit_unconstrained 12 1758.8 1799.9 21.938                                    
fit_constrained   13 1756.9 1795.3 22.060    0.12188     0       1      0.727

Control (company size)

lavaan 0.6-19 ended normally after 32 iterations

  Estimator                                         ML
  Optimization method                           NLMINB
  Number of model parameters                        24

  Number of observations                           115

Model Test User Model:
                                                      
  Test statistic                                42.058
  Degrees of freedom                                30
  P-value (Chi-square)                           0.071

Parameter Estimates:

  Standard errors                             Standard
  Information                                 Expected
  Information saturated (h1) model          Structured

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)
  EEC =~                                              
    EEC1              1.000                           
    EEC2              1.186    0.115   10.320    0.000
    EEC3              1.101    0.110    9.971    0.000
  EEF =~                                              
    EEF1              1.000                           
    EEF2              1.057    0.126    8.373    0.000
    EEF3              0.920    0.115    7.968    0.000
  IM =~                                               
    IM1               1.000                           
    IM2               1.007    0.061   16.498    0.000
    IM3               1.013    0.062   16.278    0.000

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)
  EEF ~                                               
    IM                0.373    0.069    5.426    0.000
    Cmpny_sz_ctgry    0.018    0.061    0.296    0.767
  EEC ~                                               
    IM                0.556    0.087    6.407    0.000
    Cmpny_sz_ctgry   -0.099    0.071   -1.385    0.166
  IM ~                                                
    Cmpny_sz_ctgry   -0.144    0.093   -1.557    0.119

Covariances:
                   Estimate  Std.Err  z-value  P(>|z|)
 .EEC ~~                                              
   .EEF               0.195    0.064    3.065    0.002

Variances:
                   Estimate  Std.Err  z-value  P(>|z|)
   .EEC1              0.584    0.096    6.087    0.000
   .EEC2              0.366    0.088    4.169    0.000
   .EEC3              0.437    0.087    5.046    0.000
   .EEF1              0.238    0.057    4.171    0.000
   .EEF2              0.417    0.078    5.345    0.000
   .EEF3              0.409    0.069    5.895    0.000
   .IM1               0.200    0.043    4.595    0.000
   .IM2               0.237    0.047    5.028    0.000
   .IM3               0.256    0.049    5.199    0.000
   .EEC               0.580    0.125    4.640    0.000
   .EEF               0.410    0.086    4.761    0.000
   .IM                1.186    0.184    6.456    0.000

Nested SEM - doesnt work for Quarto

Moderation

ANOVA

EEF

Robost one-way ANOVA


Call: rlm(formula = EEF_composite ~ Condition, data = data_with_dummies)
Residuals:
     Min       1Q   Median       3Q      Max 
-2.74938 -0.48067 -0.08272  0.51933  1.25062 

Coefficients:
            Value   Std. Error t value
(Intercept)  5.8140  0.1082    53.7381
Condition2  -0.0646  0.1550    -0.4168

Residual standard error: 0.7699 on 113 degrees of freedom

Checks assumptions

One-way ANOVA using trimmed means

Call:
t1way(formula = EEF_composite ~ Condition, data = data_with_dummies, 
    tr = 0.2)

Test statistic: F = 0.0668 
Degrees of freedom 1: 1 
Degrees of freedom 2: 62.91 
p-value: 0.79692 

Explanatory measure of effect size: 0.12 
Bootstrap CI: [0.01; 0.37]

##EEC ### One-way ANOVA using trimmed means


Call: rlm(formula = EEC_composite ~ Condition, data = data_with_dummies)
Residuals:
     Min       1Q   Median       3Q      Max 
-3.40617 -0.61602  0.05065  0.59383  2.05065 

Coefficients:
            Value   Std. Error t value
(Intercept)  4.9494  0.1383    35.7832
Condition2   0.1235  0.1982     0.6230

Residual standard error: 0.9133 on 113 degrees of freedom
Call:
t1way(formula = EEC_composite ~ Condition, data = data_with_dummies, 
    tr = 0.2)

Test statistic: F = 0.9456 
Degrees of freedom 1: 1 
Degrees of freedom 2: 68.99 
p-value: 0.33424 

Explanatory measure of effect size: 0.14 
Bootstrap CI: [0.01; 0.44]

##IM ### Robost one-way ANOVA


Call: rlm(formula = IM_composite ~ Condition, data = data_with_dummies)
Residuals:
    Min      1Q  Median      3Q     Max 
-4.7117 -0.6319  0.1145  0.4478  1.2883 

Coefficients:
            Value   Std. Error t value
(Intercept)  5.8855  0.1303    45.1635
Condition2  -0.1738  0.1867    -0.9308

Residual standard error: 0.8185 on 113 degrees of freedom
Call:
t1way(formula = IM_composite ~ Condition, data = data_with_dummies, 
    tr = 0.2)

Test statistic: F = 0.9048 
Degrees of freedom 1: 1 
Degrees of freedom 2: 68.54 
p-value: 0.34483 

Explanatory measure of effect size: 0.11 
Bootstrap CI: [0.01; 0.32]

AI interaction with ADT


Call: rlm(formula = EEF_composite ~ Condition * ADT_high, data = data_with_dummies)
Residuals:
     Min       1Q   Median       3Q      Max 
-2.37744 -0.58570  0.08097  0.62256  1.08097 

Coefficients:
                    Value   Std. Error t value
(Intercept)          5.4211  0.1701    31.8786
Condition2          -0.0436  0.2405    -0.1814
ADT_high             0.5956  0.2065     2.8839
Condition2:ADT_high -0.0540  0.2940    -0.1838

Residual standard error: 0.8684 on 111 degrees of freedom

Call: rlm(formula = EEC_composite ~ Condition * ADT_high, data = data_with_dummies)
Residuals:
    Min      1Q  Median      3Q     Max 
-3.2203 -0.8082  0.1130  0.7716  1.7797 

Coefficients:
                    Value   Std. Error t value
(Intercept)          4.3960  0.2439    18.0230
Condition2           0.2113  0.3449     0.6127
ADT_high             0.8324  0.2962     2.8101
Condition2:ADT_high -0.2194  0.4217    -0.5204

Residual standard error: 1.144 on 111 degrees of freedom

Call: rlm(formula = IM_composite ~ Condition * ADT_high, data = data_with_dummies)
Residuals:
    Min      1Q  Median      3Q     Max 
-4.3333 -0.6155  0.1024  0.4616  1.6667 

Coefficients:
                    Value   Std. Error t value
(Intercept)          5.5384  0.1944    28.4932
Condition2          -0.2051  0.2749    -0.7461
ADT_high             0.4722  0.2361     2.0004
Condition2:ADT_high  0.0920  0.3360     0.2739

Residual standard error: 0.8366 on 111 degrees of freedom