$all
[1] 126AI manipulation study
Data preparation
Import
Sample size
Data Quality
Manipulation and bot
Manipulation flag
FALSE TRUE
1 62 5
2 58 1Bot 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 meanOutliers 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.reward_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.reward 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 0.06Scales
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
$ADT3
Shapiro-Wilk normality test
data: newX[, i]
W = 0.84495, p-value = 1.254e-09Non-normality test on EEF composite
Shapiro-Wilk normality test
data: data_filtered$EEF_composite
W = 0.94903, p-value = 0.0002562Non-normality test on EEC composite
Shapiro-Wilk normality test
data: data_filtered$EEC_composite
W = 0.94529, p-value = 0.0001403Non-normality test on DV per condition
EEF composite
# A tibble: 2 × 3
cond.reward n shapiro_p
<chr> <int> <dbl>
1 AI 56 0.00525
2 control 59 0.00482EEC composite
# A tibble: 2 × 3
cond.reward n shapiro_p
<chr> <int> <dbl>
1 AI 56 0.0000132
2 control 59 0.321 Non-normality test on IM composite
Shapiro-Wilk normality test
data: data_filtered$IM_composite
W = 0.85765, p-value = 3.962e-09Non-normality test on IM per condition
# A tibble: 2 × 3
cond.reward 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.reward 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 59EFA
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 NAFactor 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 0.829Cronbach 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 0.965CFA 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 1.000Latent 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
Factor Analysis using method = minres
Call: fa(r = efa_data_good, nfactors = 1, rotate = "none")
Standardized loadings (pattern matrix) based upon correlation matrix
MR1 h2 u2 com
IM1 0.78 0.60 0.40 1
IM2 0.72 0.52 0.48 1
IM3 0.75 0.57 0.43 1
EEF1 0.61 0.37 0.63 1
EEF2 0.57 0.32 0.68 1
EEF3 0.66 0.44 0.56 1
EEC1 0.63 0.40 0.60 1
EEC2 0.75 0.57 0.43 1
EEC3 0.70 0.50 0.50 1
ADT1 0.55 0.30 0.70 1
ADT2 0.59 0.34 0.66 1
ADT3 0.60 0.36 0.64 1
MR1
SS loadings 5.29
Proportion Var 0.44
Mean item complexity = 1
Test of the hypothesis that 1 factor is sufficient.
df null model = 66 with the objective function = 10.79 with Chi Square = 1177.68
df of the model are 54 and the objective function was 5.98
The root mean square of the residuals (RMSR) is 0.17
The df corrected root mean square of the residuals is 0.19
The harmonic n.obs is 115 with the empirical chi square 462.35 with prob < 3.2e-66
The total n.obs was 115 with Likelihood Chi Square = 649.18 with prob < 5.7e-103
Tucker Lewis Index of factoring reliability = 0.341
RMSEA index = 0.309 and the 90 % confidence intervals are 0.29 0.333
BIC = 392.95
Fit based upon off diagonal values = 0.86
Measures of factor score adequacy
MR1
Correlation of (regression) scores with factors 0.95
Multiple R square of scores with factors 0.91
Minimum correlation of possible factor scores 0.82CFA with one factor
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 EEC EEF ADT IM
EEC 1.000
EEF 0.596 1.000
ADT 0.356 0.388 1.000
IM 0.633 0.538 0.328 1.000 EEC EEF ADT IM
0.9829447 0.5737160 2.0940521 1.2144506 lavaan 0.6-19 did NOT end normally after 2107 iterations
** WARNING ** Estimates below are most likely unreliable
Estimator ML
Optimization method NLMINB
Number of model parameters 37
Number of observations 115
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 0.000 0.000
EEC2 3503.705 NA 1.166 0.880
EEC3 3287.294 NA 1.094 0.856
EEF =~
EEF1 1.000 0.885 0.980
EEF2 0.865 NA 0.765 0.743
EEF3 0.784 NA 0.694 0.733
ADT =~
ADT1 1.000 1.464 0.980
ADT2 0.988 NA 1.446 0.954
ADT3 0.999 NA 1.463 0.932
IM =~
IM1 1.000 1.028 0.866
IM2 1.083 NA 1.114 0.920
IM3 1.084 NA 1.115 0.911
CMF =~
EEC1 1.000 1.000 0.799
EEF1 -0.181 NA -0.181 -0.201
ADT1 -0.046 NA -0.046 -0.031
IM1 0.101 NA 0.101 0.085
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC ~~
EEF 0.000 NA 0.714 0.714
ADT 0.000 NA 0.375 0.375
IM 0.000 NA 0.603 0.603
CMF 0.000 NA 1.004 1.004
EEF ~~
ADT 0.519 NA 0.401 0.401
IM 0.520 NA 0.571 0.571
CMF 0.458 NA 0.518 0.518
ADT ~~
IM 0.496 NA 0.329 0.329
CMF 0.510 NA 0.348 0.348
IM ~~
CMF 0.670 NA 0.651 0.651
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
CMF 1.000 1.000 1.000
.EEC1 0.565 NA 0.565 0.361
.EEC2 0.394 NA 0.394 0.225
.EEC3 0.434 NA 0.434 0.266
.EEF1 0.166 NA 0.166 0.203
.EEF2 0.475 NA 0.475 0.448
.EEF3 0.415 NA 0.415 0.463
.ADT1 0.133 NA 0.133 0.059
.ADT2 0.208 NA 0.208 0.091
.ADT3 0.324 NA 0.324 0.131
.IM1 0.207 NA 0.207 0.147
.IM2 0.224 NA 0.224 0.153
.IM3 0.255 NA 0.255 0.170
EEC 0.000 NA 1.000 1.000
EEF 0.783 NA 1.000 1.000
ADT 2.144 NA 1.000 1.000
IM 1.057 NA 1.000 1.000
R-Square:
Estimate
EEC1 0.639
EEC2 0.775
EEC3 0.734
EEF1 0.797
EEF2 0.552
EEF3 0.537
ADT1 0.941
ADT2 0.909
ADT3 0.869
IM1 0.853
IM2 0.847
IM3 0.830 EEC EEF ADT IM CMF
EEC 1.000
EEF 0.714 1.000
ADT 0.375 0.401 1.000
IM 0.603 0.571 0.329 1.000
CMF 1.004 0.518 0.348 0.651 1.000 EEC EEF ADT IM CMF
1.106582e-07 7.832044e-01 2.143783e+00 1.057486e+00 1.000000e+00 SEM
SEM with two non-connected DVs
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 ~
reward_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
reward_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
reward_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 0.004Plain - 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 ~
reward_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
reward_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 0.004SEM - 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 ~
reward_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
reward_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 0.004Partial 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 ~
reward_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
reward_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
reward_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 0.004Partial 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 ~
reward_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
reward_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
reward_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 0.004With moderation
lavaan 0.6-19 ended normally after 46 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 37
Number of observations 115
Model Test User Model:
Standard Scaled
Test Statistic 142.934 131.540
Degrees of freedom 98 98
P-value (Chi-square) 0.002 0.013
Scaling correction factor 1.087
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) 0.969 0.971
Tucker-Lewis Index (TLI) 0.962 0.965
Robust Comparative Fit Index (CFI) 0.974
Robust Tucker-Lewis Index (TLI) 0.968
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -2301.256 -2301.256
Scaling correction factor 2.278
for the MLR correction
Loglikelihood unrestricted model (H1) -2229.789 -2229.789
Scaling correction factor 1.413
for the MLR correction
Akaike (AIC) 4676.512 4676.512
Bayesian (BIC) 4778.074 4778.074
Sample-size adjusted Bayesian (SABIC) 4661.124 4661.124
Root Mean Square Error of Approximation:
RMSEA 0.063 0.055
90 Percent confidence interval - lower 0.039 0.028
90 Percent confidence interval - upper 0.085 0.077
P-value H_0: RMSEA <= 0.050 0.169 0.361
P-value H_0: RMSEA >= 0.080 0.104 0.027
Robust RMSEA 0.057
90 Percent confidence interval - lower 0.027
90 Percent confidence interval - upper 0.081
P-value H_0: Robust RMSEA <= 0.050 0.317
P-value H_0: Robust RMSEA >= 0.080 0.056
Standardized Root Mean Square Residual:
SRMR 0.076 0.076
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 0.792
EEC2 1.192 0.107 11.132 0.000 1.182 0.892
EEC3 1.099 0.099 11.054 0.000 1.091 0.854
EEF =~
EEF1 1.000 0.757 0.838
EEF2 1.058 0.154 6.848 0.000 0.800 0.777
EEF3 0.930 0.158 5.867 0.000 0.704 0.743
ADT =~
ADT1 1.000 1.448 0.969
ADT2 1.000 0.041 24.338 0.000 1.448 0.955
ADT3 1.010 0.049 20.688 0.000 1.462 0.931
IM =~
IM1 1.000 1.100 0.927
IM2 1.007 0.058 17.248 0.000 1.108 0.916
IM3 1.009 0.057 17.649 0.000 1.111 0.908
IM_ADT =~
IM1.ADT1 1.000 1.644 0.851
IM2.ADT2 1.365 0.339 4.027 0.000 2.244 0.896
IM3.ADT3 1.195 0.371 3.220 0.001 1.966 0.869
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IM ~
reward_2 -0.060 0.184 -0.325 0.745 -0.054 -0.027
ADT 0.192 0.055 3.497 0.000 0.253 0.253
IM_ADT -0.261 0.117 -2.237 0.025 -0.391 -0.391
EEF ~
IM 0.372 0.063 5.930 0.000 0.542 0.542
EEC ~
IM 0.573 0.083 6.903 0.000 0.636 0.636
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC ~~
.EEF 0.189 0.061 3.100 0.002 0.389 0.389
ADT ~~
IM_ADT -0.514 0.417 -1.232 0.218 -0.216 -0.216
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.586 0.100 5.881 0.000 0.586 0.373
.EEC2 0.358 0.102 3.500 0.000 0.358 0.204
.EEC3 0.443 0.108 4.118 0.000 0.443 0.271
.EEF1 0.242 0.083 2.913 0.004 0.242 0.297
.EEF2 0.421 0.094 4.491 0.000 0.421 0.396
.EEF3 0.402 0.107 3.757 0.000 0.402 0.448
.ADT1 0.137 0.062 2.211 0.027 0.137 0.061
.ADT2 0.204 0.055 3.693 0.000 0.204 0.089
.ADT3 0.327 0.085 3.861 0.000 0.327 0.133
.IM1 0.199 0.043 4.604 0.000 0.199 0.141
.IM2 0.235 0.057 4.101 0.000 0.235 0.160
.IM3 0.263 0.075 3.496 0.000 0.263 0.176
.IM1.ADT1 1.029 0.408 2.525 0.012 1.029 0.276
.IM2.ADT2 1.243 0.712 1.746 0.081 1.243 0.198
.IM3.ADT3 1.254 0.541 2.320 0.020 1.254 0.245
.EEC 0.586 0.144 4.067 0.000 0.596 0.596
.EEF 0.405 0.137 2.951 0.003 0.707 0.707
ADT 2.096 0.365 5.749 0.000 1.000 1.000
.IM 0.896 0.203 4.420 0.000 0.740 0.740
IM_ADT 2.704 1.257 2.151 0.032 1.000 1.000
R-Square:
Estimate
EEC1 0.627
EEC2 0.796
EEC3 0.729
EEF1 0.703
EEF2 0.604
EEF3 0.552
ADT1 0.939
ADT2 0.911
ADT3 0.867
IM1 0.859
IM2 0.840
IM3 0.824
IM1.ADT1 0.724
IM2.ADT2 0.802
IM3.ADT3 0.755
EEC 0.404
EEF 0.293
IM 0.260R square EEC1 EEC2 EEC3 EEF1 EEF2 EEF3 ADT1 ADT2
0.627 0.796 0.729 0.703 0.604 0.552 0.939 0.911
ADT3 IM1 IM2 IM3 IM1.ADT1 IM2.ADT2 IM3.ADT3 EEC
0.867 0.859 0.840 0.824 0.724 0.802 0.755 0.404
EEF IM
0.293 0.260 IM
lavaan 0.6-19 ended normally after 28 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 21
Number of observations 115
Model Test User Model:
Standard Scaled
Test Statistic 36.948 33.118
Degrees of freedom 24 24
P-value (Chi-square) 0.044 0.102
Scaling correction factor 1.116
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 758.745 652.866
Degrees of freedom 36 36
P-value 0.000 0.000
Scaling correction factor 1.162
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.982 0.985
Tucker-Lewis Index (TLI) 0.973 0.978
Robust Comparative Fit Index (CFI) 0.986
Robust Tucker-Lewis Index (TLI) 0.979
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1244.881 -1244.881
Scaling correction factor 1.379
for the MLR correction
Loglikelihood unrestricted model (H1) -1226.407 -1226.407
Scaling correction factor 1.239
for the MLR correction
Akaike (AIC) 2531.762 2531.762
Bayesian (BIC) 2589.406 2589.406
Sample-size adjusted Bayesian (SABIC) 2523.029 2523.029
Root Mean Square Error of Approximation:
RMSEA 0.068 0.057
90 Percent confidence interval - lower 0.011 0.000
90 Percent confidence interval - upper 0.110 0.099
P-value H_0: RMSEA <= 0.050 0.228 0.364
P-value H_0: RMSEA >= 0.080 0.357 0.209
Robust RMSEA 0.061
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.107
P-value H_0: Robust RMSEA <= 0.050 0.336
P-value H_0: Robust RMSEA >= 0.080 0.278
Standardized Root Mean Square Residual:
SRMR 0.054 0.054
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 1.193 0.107 11.143 0.000 1.183 0.893
EEC3 1.100 0.099 11.075 0.000 1.091 0.854
EEF =~
EEF1 1.000 0.758 0.839
EEF2 1.056 0.153 6.904 0.000 0.800 0.777
EEF3 0.928 0.157 5.894 0.000 0.703 0.742
IM =~
IM1 1.000 1.101 0.927
IM2 1.006 0.061 16.562 0.000 1.108 0.915
IM3 1.012 0.060 16.935 0.000 1.115 0.910
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEF ~
IM 0.371 0.062 5.959 0.000 0.539 0.539
EEC ~
IM 0.395 0.101 3.905 0.000 0.439 0.439
EEF 0.471 0.154 3.070 0.002 0.360 0.360
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.588 0.100 5.896 0.000 0.588 0.374
.EEC2 0.357 0.102 3.496 0.000 0.357 0.203
.EEC3 0.443 0.108 4.118 0.000 0.443 0.271
.EEF1 0.241 0.083 2.919 0.004 0.241 0.296
.EEF2 0.421 0.094 4.496 0.000 0.421 0.397
.EEF3 0.403 0.107 3.754 0.000 0.403 0.449
.IM1 0.199 0.044 4.489 0.000 0.199 0.141
.IM2 0.238 0.057 4.138 0.000 0.238 0.162
.IM3 0.257 0.075 3.442 0.001 0.257 0.171
.EEC 0.499 0.139 3.599 0.000 0.507 0.507
.EEF 0.408 0.137 2.965 0.003 0.710 0.710
IM 1.213 0.261 4.641 0.000 1.000 1.000
R-Square:
Estimate
EEC1 0.626
EEC2 0.797
EEC3 0.729
EEF1 0.704
EEF2 0.603
EEF3 0.551
IM1 0.859
IM2 0.838
IM3 0.829
EEC 0.493
EEF 0.290ADT and full mediation by IM
lavaan 0.6-19 ended normally after 39 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 29
Number of observations 115
Model Test User Model:
Standard Scaled
Test Statistic 72.082 64.074
Degrees of freedom 49 49
P-value (Chi-square) 0.018 0.073
Scaling correction factor 1.125
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) 0.980 0.985
Tucker-Lewis Index (TLI) 0.974 0.979
Robust Comparative Fit Index (CFI) 0.985
Robust Tucker-Lewis Index (TLI) 0.980
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1656.983 -1656.983
Scaling correction factor 1.422
for the MLR correction
Loglikelihood unrestricted model (H1) -1620.942 -1620.942
Scaling correction factor 1.235
for the MLR correction
Akaike (AIC) 3371.965 3371.965
Bayesian (BIC) 3451.569 3451.569
Sample-size adjusted Bayesian (SABIC) 3359.905 3359.905
Root Mean Square Error of Approximation:
RMSEA 0.064 0.052
90 Percent confidence interval - lower 0.028 0.000
90 Percent confidence interval - upper 0.094 0.082
P-value H_0: RMSEA <= 0.050 0.225 0.443
P-value H_0: RMSEA >= 0.080 0.206 0.067
Robust RMSEA 0.055
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.089
P-value H_0: Robust RMSEA <= 0.050 0.393
P-value H_0: Robust RMSEA >= 0.080 0.125
Standardized Root Mean Square Residual:
SRMR 0.060 0.060
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 0.989 0.789
EEC2 1.200 0.107 11.206 0.000 1.187 0.896
EEC3 1.100 0.099 11.071 0.000 1.088 0.851
EEF =~
EEF1 1.000 0.758 0.839
EEF2 1.056 0.153 6.908 0.000 0.800 0.777
EEF3 0.928 0.157 5.896 0.000 0.703 0.743
IM =~
IM1 1.000 1.102 0.927
IM2 1.005 0.061 16.542 0.000 1.107 0.915
IM3 1.011 0.060 16.946 0.000 1.114 0.910
ADT =~
ADT1 1.000 1.448 0.969
ADT2 0.999 0.041 24.397 0.000 1.447 0.954
ADT3 1.009 0.049 20.684 0.000 1.462 0.931
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEF ~
IM 0.183 0.092 1.984 0.047 0.266 0.266
EEC 0.332 0.125 2.669 0.008 0.434 0.434
EEC ~
IM 0.516 0.081 6.337 0.000 0.576 0.576
ADT 0.119 0.062 1.936 0.053 0.175 0.175
IM ~
ADT 0.251 0.091 2.764 0.006 0.330 0.330
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.594 0.100 5.949 0.000 0.594 0.378
.EEC2 0.348 0.100 3.464 0.001 0.348 0.198
.EEC3 0.451 0.108 4.160 0.000 0.451 0.276
.EEF1 0.241 0.083 2.921 0.003 0.241 0.296
.EEF2 0.421 0.094 4.494 0.000 0.421 0.397
.EEF3 0.403 0.107 3.761 0.000 0.403 0.449
.IM1 0.197 0.045 4.424 0.000 0.197 0.140
.IM2 0.239 0.059 4.083 0.000 0.239 0.163
.IM3 0.257 0.075 3.432 0.001 0.257 0.171
.ADT1 0.135 0.061 2.207 0.027 0.135 0.060
.ADT2 0.206 0.056 3.699 0.000 0.206 0.090
.ADT3 0.326 0.085 3.843 0.000 0.326 0.132
.EEC 0.559 0.145 3.856 0.000 0.572 0.572
.EEF 0.342 0.118 2.890 0.004 0.595 0.595
.IM 1.082 0.215 5.036 0.000 0.891 0.891
ADT 2.098 0.364 5.762 0.000 1.000 1.000
R-Square:
Estimate
EEC1 0.622
EEC2 0.802
EEC3 0.724
EEF1 0.704
EEF2 0.603
EEF3 0.551
IM1 0.860
IM2 0.837
IM3 0.829
ADT1 0.940
ADT2 0.910
ADT3 0.868
EEC 0.428
EEF 0.405
IM 0.109Multigroup analysis on ADT
Interaction effect between ADT and reward groups
continous variablelavaan 0.6-19 ended normally after 56 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 82
Number of observations per group:
AI 56
control 59
Model Test User Model:
Standard Scaled
Test Statistic 144.775 153.957
Degrees of freedom 98 98
P-value (Chi-square) 0.002 0.000
Scaling correction factor 0.940
Yuan-Bentler correction (Mplus variant)
Test statistic for each group:
AI 87.258 87.258
control 66.699 66.699
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) 0.961 0.949
Tucker-Lewis Index (TLI) 0.947 0.931
Robust Comparative Fit Index (CFI) 0.955
Robust Tucker-Lewis Index (TLI) 0.940
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -1636.906 -1636.906
Scaling correction factor 1.288
for the MLR correction
Loglikelihood unrestricted model (H1) -1564.518 -1564.518
Scaling correction factor 1.099
for the MLR correction
Akaike (AIC) 3437.812 3437.812
Bayesian (BIC) 3662.897 3662.897
Sample-size adjusted Bayesian (SABIC) 3403.710 3403.710
Root Mean Square Error of Approximation:
RMSEA 0.091 0.100
90 Percent confidence interval - lower 0.057 0.067
90 Percent confidence interval - upper 0.121 0.130
P-value H_0: RMSEA <= 0.050 0.027 0.010
P-value H_0: RMSEA >= 0.080 0.729 0.852
Robust RMSEA 0.097
90 Percent confidence interval - lower 0.066
90 Percent confidence interval - upper 0.125
P-value H_0: Robust RMSEA <= 0.050 0.009
P-value H_0: Robust RMSEA >= 0.080 0.829
Standardized Root Mean Square Residual:
SRMR 0.059 0.059
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 1.052 0.826
EEC2 1.155 0.150 7.718 0.000 1.215 0.914
EEC3 1.143 0.155 7.350 0.000 1.202 0.869
EEF =~
EEF1 1.000 0.918 0.859
EEF2 1.115 0.200 5.567 0.000 1.023 0.872
EEF3 0.909 0.150 6.051 0.000 0.834 0.833
IM =~
IM1 1.000 1.129 0.940
IM2 0.976 0.090 10.811 0.000 1.102 0.892
IM3 1.012 0.062 16.268 0.000 1.142 0.913
ADT =~
ADT1 1.000 1.600 0.980
ADT2 0.996 0.057 17.442 0.000 1.593 0.969
ADT3 0.997 0.066 15.095 0.000 1.595 0.946
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEF ~
IM 0.084 0.166 0.505 0.614 0.103 0.103
EEC 0.508 0.212 2.396 0.017 0.582 0.582
EEC ~
IM 0.577 0.137 4.213 0.000 0.619 0.619
ADT 0.089 0.080 1.119 0.263 0.135 0.135
IM ~
ADT 0.235 0.129 1.816 0.069 0.332 0.332
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 0.517 0.149 3.465 0.001 0.517 0.318
.EEC2 0.291 0.141 2.064 0.039 0.291 0.165
.EEC3 0.467 0.183 2.555 0.011 0.467 0.244
.EEF1 0.300 0.128 2.347 0.019 0.300 0.263
.EEF2 0.330 0.146 2.270 0.023 0.330 0.240
.EEF3 0.308 0.131 2.358 0.018 0.308 0.307
.IM1 0.169 0.070 2.421 0.015 0.169 0.117
.IM2 0.312 0.110 2.832 0.005 0.312 0.204
.IM3 0.259 0.126 2.062 0.039 0.259 0.166
.ADT1 0.108 0.088 1.228 0.219 0.108 0.040
.ADT2 0.168 0.069 2.425 0.015 0.168 0.062
.ADT3 0.296 0.107 2.760 0.006 0.296 0.104
.EEC 0.600 0.215 2.787 0.005 0.542 0.542
.EEF 0.481 0.179 2.691 0.007 0.571 0.571
.IM 1.134 0.360 3.147 0.002 0.890 0.890
ADT 2.559 0.566 4.524 0.000 1.000 1.000
R-Square:
Estimate
EEC1 0.682
EEC2 0.835
EEC3 0.756
EEF1 0.737
EEF2 0.760
EEF3 0.693
IM1 0.883
IM2 0.796
IM3 0.834
ADT1 0.960
ADT2 0.938
ADT3 0.896
EEC 0.458
EEF 0.429
IM 0.110
Group 2 [control]:
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC =~
EEC1 1.000 0.926 0.751
EEC2 1.252 0.155 8.055 0.000 1.159 0.878
EEC3 1.051 0.131 8.035 0.000 0.972 0.831
EEF =~
EEF1 1.000 0.452 0.650
EEF2 0.893 0.170 5.253 0.000 0.403 0.475
EEF3 1.501 0.722 2.078 0.038 0.678 0.760
IM =~
IM1 1.000 1.075 0.919
IM2 1.030 0.088 11.765 0.000 1.108 0.936
IM3 1.008 0.107 9.431 0.000 1.084 0.906
ADT =~
ADT1 1.000 1.283 0.956
ADT2 0.992 0.053 18.859 0.000 1.274 0.933
ADT3 1.024 0.065 15.803 0.000 1.314 0.911
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEF ~
IM 0.246 0.099 2.491 0.013 0.586 0.586
EEC 0.137 0.100 1.374 0.170 0.282 0.282
EEC ~
IM 0.440 0.089 4.929 0.000 0.511 0.511
ADT 0.164 0.083 1.969 0.049 0.227 0.227
IM ~
ADT 0.278 0.120 2.314 0.021 0.332 0.332
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 0.663 0.136 4.874 0.000 0.663 0.436
.EEC2 0.401 0.150 2.681 0.007 0.401 0.230
.EEC3 0.425 0.140 3.032 0.002 0.425 0.310
.EEF1 0.279 0.114 2.450 0.014 0.279 0.578
.EEF2 0.559 0.128 4.368 0.000 0.559 0.775
.EEF3 0.335 0.110 3.051 0.002 0.335 0.422
.IM1 0.212 0.052 4.104 0.000 0.212 0.155
.IM2 0.173 0.044 3.884 0.000 0.173 0.123
.IM3 0.258 0.086 3.014 0.003 0.258 0.180
.ADT1 0.153 0.081 1.898 0.058 0.153 0.085
.ADT2 0.243 0.086 2.816 0.005 0.243 0.130
.ADT3 0.355 0.131 2.717 0.007 0.355 0.171
.EEC 0.523 0.199 2.634 0.008 0.610 0.610
.EEF 0.078 0.076 1.028 0.304 0.384 0.384
.IM 1.029 0.232 4.441 0.000 0.890 0.890
ADT 1.647 0.436 3.781 0.000 1.000 1.000
R-Square:
Estimate
EEC1 0.564
EEC2 0.770
EEC3 0.690
EEF1 0.422
EEF2 0.225
EEF3 0.578
IM1 0.845
IM2 0.877
IM3 0.820
ADT1 0.915
ADT2 0.870
ADT3 0.829
EEC 0.390
EEF 0.616
IM 0.110`geom_smooth()` using formula = 'y ~ x'
`geom_smooth()` using formula = 'y ~ x'
- as categorical variables of ADT
high >5dummies where high as above 5lavaan 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
Composite variables
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 freedomChecks 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: 0.11
Bootstrap CI: [0.01; 0.27]##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 freedomCall:
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: 0.18
Bootstrap CI: [0.01; 0.43]##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 freedomCall:
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: 0.17
Bootstrap CI: [0.02; 0.45]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