$all
[1] 101AI
Data preparation
Import
Sample size
Pre-screener flag
surveydata$prescreener_flag <- (
(surveydata$prescreener_employment_work_role == 7 |
surveydata$prescreener_employment_work_role == 8 |
surveydata$prescreener_employer_type == 2 |
surveydata$prescreener_employer_type == 3 |
surveydata$prescreener_employer_type == 4 |
surveydata$prescreener_employer_type == 5 |
surveydata$prescreener_employer_type == 9)
)Data Quality
Manipulation, pre-screener validations and bot
Manipulation flag
FALSE TRUE
1 48 5
2 47 1Bot flag
FALSE TRUE
99 2 Pre-screener flag
prescreener_employment_work_role n
1 1 2
2 7 6
3 8 20 prescreener_employer_type n_flag
1 1 26
2 9 2Attention
Duration
Min. 1st Qu. Median Mean 3rd Qu. Max.
1.550 2.917 3.950 4.981 5.500 45.017 
Outliers defined as 3 std. deviations below or above the meanOutliers on completion time
FALSE TRUE
100 1 On scales
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.5149 1.0553 1.1645 1.2100 1.3027 2.2344 Flagged outliers based on scales
FALSE TRUE
98 3 Removing bad participants
Exclude participants
excluded <- subset(surveydata, cond.reward_flag == TRUE | prescreener_flag == TRUE | bot_flag == TRUE | outliers_completion == TRUE | outliers_scales == TRUE)| cond.reward_flag | prescreener_flag | outliers_completion | bot_flag | outliers_scales | n |
|---|---|---|---|---|---|
| TRUE | FALSE | FALSE | FALSE | FALSE | 1 |
| TRUE | FALSE | FALSE | TRUE | FALSE | 1 |
| TRUE | TRUE | FALSE | FALSE | FALSE | 4 |
| FALSE | FALSE | FALSE | FALSE | TRUE | 2 |
| FALSE | FALSE | FALSE | TRUE | FALSE | 1 |
| FALSE | FALSE | TRUE | FALSE | FALSE | 1 |
| FALSE | TRUE | FALSE | FALSE | FALSE | 23 |
| FALSE | TRUE | FALSE | FALSE | TRUE | 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 33 5.63 1.02 4.78 1.29
2 control 34 5.98 0.635 4.96 1.18
Scales
Descriptive stats on scales
all good
101 67 vars n mean sd median trimmed mad min max range skew kurtosis se
IM1 1 67 5.60 1.14 6 5.71 1.48 1 7 6 -1.29 3.17 0.14
IM2 2 67 5.96 1.09 6 6.09 1.48 1 7 6 -2.04 6.39 0.13
IM3 3 67 5.79 1.19 6 5.96 1.48 1 7 6 -1.42 2.84 0.15
EEF1 4 67 5.70 0.94 6 5.76 1.48 2 7 5 -1.13 2.68 0.11
EEF2 5 67 5.76 1.13 6 5.89 1.48 2 7 5 -0.90 0.74 0.14
EEF3 6 67 5.96 0.94 6 6.05 1.48 3 7 4 -0.76 0.20 0.12
EEC1 7 67 4.67 1.30 5 4.69 1.48 1 7 6 -0.29 -0.13 0.16
EEC2 8 67 4.97 1.39 5 5.05 1.48 2 7 5 -0.58 -0.40 0.17
EEC3 9 67 4.97 1.33 5 5.07 1.48 1 7 6 -0.79 0.27 0.16
ADT1 10 67 5.51 1.53 6 5.75 1.48 1 7 6 -1.30 1.10 0.19
ADT2 11 67 5.43 1.55 6 5.65 1.48 1 7 6 -1.16 0.70 0.19
ADT3 12 67 5.39 1.54 6 5.60 1.48 1 7 6 -1.12 0.41 0.19
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 0.85 0.86 0.72 0.78 0.93 0.87 0.84 0.88 0.78 0.82 0.82 Non-normality test across all scales
$IM1
Shapiro-Wilk normality test
data: newX[, i]
W = 0.83792, p-value = 4.492e-07
$IM2
Shapiro-Wilk normality test
data: newX[, i]
W = 0.74316, p-value = 1.697e-09
$IM3
Shapiro-Wilk normality test
data: newX[, i]
W = 0.81898, p-value = 1.286e-07
$EEF1
Shapiro-Wilk normality test
data: newX[, i]
W = 0.82878, p-value = 2.431e-07
$EEF2
Shapiro-Wilk normality test
data: newX[, i]
W = 0.86159, p-value = 2.436e-06
$EEF3
Shapiro-Wilk normality test
data: newX[, i]
W = 0.85007, p-value = 1.05e-06
$EEC1
Shapiro-Wilk normality test
data: newX[, i]
W = 0.94092, p-value = 0.00323
$EEC2
Shapiro-Wilk normality test
data: newX[, i]
W = 0.89981, p-value = 5.462e-05
$EEC3
Shapiro-Wilk normality test
data: newX[, i]
W = 0.9022, p-value = 6.757e-05
$ADT1
Shapiro-Wilk normality test
data: newX[, i]
W = 0.81774, p-value = 1.188e-07
$ADT2
Shapiro-Wilk normality test
data: newX[, i]
W = 0.83749, p-value = 4.363e-07
$ADT3
Shapiro-Wilk normality test
data: newX[, i]
W = 0.8305, p-value = 2.725e-07Descriptive on EEF composite
Shapiro-Wilk normality test
data: data_filtered$EEF_composite
W = 0.91356, p-value = 0.0001934Descriptive on EEC composite
Shapiro-Wilk normality test
data: data_filtered$EEC_composite
W = 0.95101, p-value = 0.01024DV per condition
# A tibble: 2 × 3
cond.reward n shapiro_p
<chr> <int> <dbl>
1 AI 33 0.00763
2 control 34 0.0267 # A tibble: 2 × 3
cond.reward n shapiro_p
<chr> <int> <dbl>
1 AI 33 0.00784
2 control 34 0.294 Descriptive on IM composite
Shapiro-Wilk normality test
data: data_filtered$IM_composite
W = 0.84492, p-value = 7.291e-07IM per condition
# A tibble: 2 × 3
cond.reward n shapiro_p
<chr> <int> <dbl>
1 AI 33 0.0000421
2 control 34 0.000250 Data analysis
EFA
Parallel analysis suggests that the number of factors = 2 and the number of components = NA Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
The estimated weights for the factor scores are probably incorrect. Try a
different factor score estimation method.Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
ultra-Heywood case was detected. Examine the results carefullyFactor Analysis using method = minres
Call: fa(r = efa_data_good, nfactors = 4, rotate = "varimax")
Unstandardized loadings (pattern matrix) based upon covariance matrix
MR2 MR4 MR1 MR3 h2 u2 H2 U2
IM1 NA 0.42 0.75 NA NA 0.1335 NA NA
IM2 NA NA 0.82 NA NA 0.1687 NA NA
IM3 NA NA 0.78 NA NA 0.2265 NA NA
EEF1 NA NA NA 0.98 NA -0.0061 NA NA
EEF2 NA NA NA 0.61 NA 0.4525 NA NA
EEF3 NA 0.42 NA 0.46 NA 0.4223 NA NA
EEC1 NA 0.75 NA NA NA 0.3117 NA NA
EEC2 NA 0.80 NA NA NA 0.1533 NA NA
EEC3 NA 0.82 NA NA NA 0.1780 NA NA
ADT1 0.96 NA NA NA NA 0.0473 NA NA
ADT2 0.91 NA NA NA NA 0.0477 NA NA
ADT3 0.89 NA NA NA NA 0.1226 NA NA
MR2 MR4 MR1 MR3
SS loadings NA NA NA NA
Proportion Var NA NA NA NA
Cumulative Var NA NA NA NA
Proportion Explained NA NA NA NA
Cumulative Proportion NA NA NA NA
Standardized loadings (pattern matrix)
item MR2 MR4 MR1 MR3 h2 u2
IM1 1 NA NA NA NA NA NA
IM2 2 NA NA NA NA NA NA
IM3 3 NA NA NA NA NA NA
EEF1 4 NA NA NA NA NA NA
EEF2 5 NA NA NA NA NA NA
EEF3 6 NA NA NA NA NA NA
EEC1 7 NA NA NA NA NA NA
EEC2 8 NA NA NA NA NA NA
EEC3 9 NA NA NA NA NA NA
ADT1 10 NA NA NA NA NA NA
ADT2 11 NA NA NA NA NA NA
ADT3 12 NA NA NA NA NA NA
MR2 MR4 MR1 MR3
SS loadings NA NA NA NA
Proportion Var NA NA NA NA
Cumulative Var NA NA NA NA
Cum. factor Var NA NA NA NA
Mean item complexity = 1.6
Test of the hypothesis that 4 factors are sufficient.
df null model = 66 with the objective function = 12.29 with Chi Square = 751.43
df of the model are 24 and the objective function was 0.57
The root mean square of the residuals (RMSR) is 0.02
The df corrected root mean square of the residuals is 0.03
The harmonic n.obs is 67 with the empirical chi square 2.8 with prob < 1
The total n.obs was 67 with Likelihood Chi Square = 33.62 with prob < 0.092
Tucker Lewis Index of factoring reliability = 0.959
RMSEA index = 0.076 and the 90 % confidence intervals are 0 0.135
BIC = -67.29
Fit based upon off diagonal values = 1CFA
model1<-'
EEC =~ EEC1 + EEC2 + EEC3
EEF =~ EEF1 + EEF2 + EEF3
ADT =~ ADT1 + ADT2 + ADT3
IM =~ IM1 + IM2 + IM3'
fit1<-cfa(model1,data = efa_data_good, estimator = "MLR")
summary(fit1, ci = TRUE, fit.measures=TRUE, rsquare=TRUE,standardized=TRUE)lavaan 0.6-19 ended normally after 45 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 30
Number of observations 67
Model Test User Model:
Standard Scaled
Test Statistic 96.871 105.097
Degrees of freedom 48 48
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.922
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 823.097 823.017
Degrees of freedom 66 66
P-value 0.000 0.000
Scaling correction factor 1.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.935 0.925
Tucker-Lewis Index (TLI) 0.911 0.896
Robust Comparative Fit Index (CFI) 0.930
Robust Tucker-Lewis Index (TLI) 0.904
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -943.149 -943.149
Scaling correction factor 1.453
for the MLR correction
Loglikelihood unrestricted model (H1) -894.714 -894.714
Scaling correction factor 1.126
for the MLR correction
Akaike (AIC) 1946.299 1946.299
Bayesian (BIC) 2012.440 2012.440
Sample-size adjusted Bayesian (SABIC) 1917.980 1917.980
Root Mean Square Error of Approximation:
RMSEA 0.123 0.133
90 Percent confidence interval - lower 0.087 0.097
90 Percent confidence interval - upper 0.159 0.169
P-value H_0: RMSEA <= 0.050 0.001 0.000
P-value H_0: RMSEA >= 0.080 0.975 0.990
Robust RMSEA 0.128
90 Percent confidence interval - lower 0.095
90 Percent confidence interval - upper 0.161
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 0.989
Standardized Root Mean Square Residual:
SRMR 0.062 0.062
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 1.267 0.145 8.717 0.000 0.982 1.551
EEC3 1.131 0.125 9.026 0.000 0.885 1.377
EEF =~
EEF1 1.000 1.000 1.000
EEF2 1.189 0.228 5.216 0.000 0.742 1.636
EEF3 1.005 0.400 2.515 0.012 0.222 1.789
ADT =~
ADT1 1.000 1.000 1.000
ADT2 1.028 0.067 15.368 0.000 0.897 1.160
ADT3 0.988 0.066 15.014 0.000 0.859 1.117
IM =~
IM1 1.000 1.000 1.000
IM2 0.874 0.099 8.862 0.000 0.680 1.067
IM3 0.936 0.076 12.314 0.000 0.787 1.085
Std.lv Std.all
1.023 0.795
1.295 0.937
1.157 0.879
0.725 0.779
0.862 0.769
0.729 0.778
1.452 0.955
1.493 0.971
1.435 0.941
1.086 0.958
0.949 0.875
1.017 0.863
Covariances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
EEC ~~
EEF 0.533 0.146 3.653 0.000 0.247 0.819
ADT 0.570 0.260 2.193 0.028 0.061 1.079
IM 0.801 0.261 3.069 0.002 0.289 1.312
EEF ~~
ADT 0.433 0.164 2.641 0.008 0.112 0.754
IM 0.530 0.138 3.843 0.000 0.259 0.800
ADT ~~
IM 0.836 0.277 3.020 0.003 0.294 1.379
Std.lv Std.all
0.719 0.719
0.384 0.384
0.721 0.721
0.411 0.411
0.673 0.673
0.530 0.530
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper
.EEC1 0.608 0.112 5.433 0.000 0.389 0.827
.EEC2 0.232 0.089 2.617 0.009 0.058 0.406
.EEC3 0.393 0.107 3.683 0.000 0.184 0.602
.EEF1 0.341 0.172 1.978 0.048 0.003 0.678
.EEF2 0.513 0.244 2.105 0.035 0.035 0.991
.EEF3 0.347 0.162 2.143 0.032 0.030 0.665
.ADT1 0.202 0.086 2.347 0.019 0.033 0.370
.ADT2 0.135 0.065 2.093 0.036 0.009 0.262
.ADT3 0.268 0.086 3.106 0.002 0.099 0.437
.IM1 0.106 0.053 1.998 0.046 0.002 0.210
.IM2 0.277 0.088 3.138 0.002 0.104 0.450
.IM3 0.356 0.129 2.754 0.006 0.103 0.609
EEC 1.046 0.302 3.462 0.001 0.454 1.637
EEF 0.526 0.290 1.810 0.070 -0.043 1.095
ADT 2.108 0.517 4.078 0.000 1.095 3.121
IM 1.179 0.364 3.243 0.001 0.467 1.892
Std.lv Std.all
0.608 0.368
0.232 0.122
0.393 0.227
0.341 0.393
0.513 0.408
0.347 0.395
0.202 0.087
0.135 0.057
0.268 0.115
0.106 0.082
0.277 0.235
0.356 0.256
1.000 1.000
1.000 1.000
1.000 1.000
1.000 1.000
R-Square:
Estimate
EEC1 0.632
EEC2 0.878
EEC3 0.773
EEF1 0.607
EEF2 0.592
EEF3 0.605
ADT1 0.913
ADT2 0.943
ADT3 0.885
IM1 0.918
IM2 0.765
IM3 0.744lavaanPlot(model = fit1, node_options = list(shape = "box", fontname = "Helvetica"), edge_options = list(color = "grey"),
coefs = T, stand=T)#Construct Reliability:
semTools::compRelSEM(fit1, tau.eq=T, obs.var=T) #Cronbach Alpha EEC EEF ADT IM
0.905 0.815 0.970 0.928 semTools::compRelSEM(fit1, tau.eq=F, obs.var=T) #Omega EEC EEF ADT IM
0.905 0.816 0.969 0.921 AVE(fit1, obs.var = TRUE, omit.imps = c("no.conv", "no.se"),
omit.factors = character(0), dropSingle = TRUE, return.df = TRUE) #AVE EEC EEF ADT IM
0.767 0.600 0.914 0.808 #Standardized residuals
lavResiduals(fit1, type = "cor.bentler", custom.rmr = NULL,
se = FALSE, zstat = TRUE, summary = TRUE, h1.acov = "unstructured",
add.type = TRUE, add.labels = TRUE, add.class = TRUE,
drop.list.single.group = TRUE,
maximum.number = length(res.vech), output = "list")$type
[1] "cor.bentler"
$cov
EEC1 EEC2 EEC3 EEF1 EEF2 EEF3 ADT1 ADT2 ADT3 IM1
EEC1 0.000
EEC2 -0.003 0.000
EEC3 0.019 -0.003 0.000
EEF1 -0.228 -0.033 -0.049 0.000
EEF2 -0.049 -0.051 0.015 0.105 0.000
EEF3 0.026 0.120 0.100 -0.022 -0.083 0.000
ADT1 -0.015 -0.045 -0.039 -0.125 -0.108 0.035 0.000
ADT2 0.025 0.029 0.011 -0.002 0.004 0.138 0.000 0.000
ADT3 0.059 -0.021 0.023 -0.083 0.019 0.035 0.008 -0.005 0.000
IM1 0.046 0.031 0.005 -0.093 -0.019 0.100 -0.072 0.052 0.027 0.000
IM2 0.012 -0.074 -0.085 -0.102 0.017 0.128 -0.113 0.053 0.007 -0.003
IM3 0.002 0.009 -0.089 -0.114 0.002 0.108 -0.095 0.042 -0.053 -0.007
IM2 IM3
EEC1
EEC2
EEC3
EEF1
EEF2
EEF3
ADT1
ADT2
ADT3
IM1
IM2 0.000
IM3 0.032 0.000
$cov.z
EEC1 EEC2 EEC3 EEF1 EEF2 EEF3 ADT1 ADT2 ADT3 IM1
EEC1 0.000
EEC2 -0.045 0.000
EEC3 0.283 -0.043 0.000
EEF1 -1.655 -0.418 -0.465 0.000
EEF2 -0.652 -0.638 0.187 1.215 0.000
EEF3 0.209 1.107 0.887 -0.181 -0.955 0.000
ADT1 -0.171 -0.611 -0.433 -1.534 -1.308 0.371 0.000
ADT2 0.276 0.426 0.128 -0.034 0.049 1.473 0.003 0.000
ADT3 0.800 -0.262 0.309 -0.810 0.306 0.330 0.131 -0.117 0.000
IM1 0.550 0.316 0.053 -0.745 -0.287 0.644 -0.768 0.596 0.303 0.000
IM2 0.129 -0.604 -0.674 -0.695 0.202 0.834 -0.927 0.518 0.077 -0.019
IM3 0.019 0.084 -0.790 -0.871 0.030 0.746 -1.035 0.512 -0.542 -0.051
IM2 IM3
EEC1
EEC2
EEC3
EEF1
EEF2
EEF3
ADT1
ADT2
ADT3
IM1
IM2 0.000
IM3 0.204 0.000
$summary
cov
srmr 0.062
srmr.se 0.038
srmr.exactfit.z 0.000
srmr.exactfit.pvalue 0.500
usrmr 0.000
usrmr.se 0.193
usrmr.ci.lower -0.318
usrmr.ci.upper 0.318
usrmr.closefit.h0.value 0.050
usrmr.closefit.z -0.259
usrmr.closefit.pvalue 0.602Common 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 0.87 0.76 0.24 1
IM2 0.77 0.60 0.40 1
IM3 0.76 0.58 0.42 1
EEF1 0.54 0.29 0.71 1
EEF2 0.61 0.37 0.63 1
EEF3 0.74 0.55 0.45 1
EEC1 0.67 0.45 0.55 1
EEC2 0.79 0.62 0.38 1
EEC3 0.73 0.54 0.46 1
ADT1 0.57 0.32 0.68 1
ADT2 0.69 0.48 0.52 1
ADT3 0.63 0.40 0.60 1
MR1
SS loadings 5.96
Proportion Var 0.50
Mean item complexity = 1
Test of the hypothesis that 1 factor is sufficient.
df null model = 66 with the objective function = 12.29 with Chi Square = 751.43
df of the model are 54 and the objective function was 6.23
The root mean square of the residuals (RMSR) is 0.16
The df corrected root mean square of the residuals is 0.17
The harmonic n.obs is 67 with the empirical chi square 220.92 with prob < 4.6e-22
The total n.obs was 67 with Likelihood Chi Square = 376.68 with prob < 6.5e-50
Tucker Lewis Index of factoring reliability = 0.418
RMSEA index = 0.298 and the 90 % confidence intervals are 0.273 0.33
BIC = 149.63
Fit based upon off diagonal values = 0.91
Measures of factor score adequacy
MR1
Correlation of (regression) scores with factors 0.97
Multiple R square of scores with factors 0.94
Minimum correlation of possible factor scores 0.87CFA with one factor
model_substantive <- '
EEC =~ EEC1 + EEC2 + EEC3
EEF =~ EEF1 + EEF2 + EEF3
ADT =~ ADT1 + ADT2 + ADT3
IM =~ IM1 + IM2 + IM3
'
# Fit the CFA model
fit_substantive <- cfa(model_substantive, data = efa_data_good, estimator = "MLR")
# Summary with fit measures and standardized estimates
summary(fit_substantive, fit.measures = TRUE, standardized = TRUE)lavaan 0.6-19 ended normally after 45 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 30
Number of observations 67
Model Test User Model:
Standard Scaled
Test Statistic 96.871 105.097
Degrees of freedom 48 48
P-value (Chi-square) 0.000 0.000
Scaling correction factor 0.922
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 823.097 823.017
Degrees of freedom 66 66
P-value 0.000 0.000
Scaling correction factor 1.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.935 0.925
Tucker-Lewis Index (TLI) 0.911 0.896
Robust Comparative Fit Index (CFI) 0.930
Robust Tucker-Lewis Index (TLI) 0.904
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -943.149 -943.149
Scaling correction factor 1.453
for the MLR correction
Loglikelihood unrestricted model (H1) -894.714 -894.714
Scaling correction factor 1.126
for the MLR correction
Akaike (AIC) 1946.299 1946.299
Bayesian (BIC) 2012.440 2012.440
Sample-size adjusted Bayesian (SABIC) 1917.980 1917.980
Root Mean Square Error of Approximation:
RMSEA 0.123 0.133
90 Percent confidence interval - lower 0.087 0.097
90 Percent confidence interval - upper 0.159 0.169
P-value H_0: RMSEA <= 0.050 0.001 0.000
P-value H_0: RMSEA >= 0.080 0.975 0.990
Robust RMSEA 0.128
90 Percent confidence interval - lower 0.095
90 Percent confidence interval - upper 0.161
P-value H_0: Robust RMSEA <= 0.050 0.000
P-value H_0: Robust RMSEA >= 0.080 0.989
Standardized Root Mean Square Residual:
SRMR 0.062 0.062
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 1.023 0.795
EEC2 1.267 0.145 8.717 0.000 1.295 0.937
EEC3 1.131 0.125 9.026 0.000 1.157 0.879
EEF =~
EEF1 1.000 0.725 0.779
EEF2 1.189 0.228 5.216 0.000 0.862 0.769
EEF3 1.005 0.400 2.515 0.012 0.729 0.778
ADT =~
ADT1 1.000 1.452 0.955
ADT2 1.028 0.067 15.368 0.000 1.493 0.971
ADT3 0.988 0.066 15.014 0.000 1.435 0.941
IM =~
IM1 1.000 1.086 0.958
IM2 0.874 0.099 8.862 0.000 0.949 0.875
IM3 0.936 0.076 12.314 0.000 1.017 0.863
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC ~~
EEF 0.533 0.146 3.653 0.000 0.719 0.719
ADT 0.570 0.260 2.193 0.028 0.384 0.384
IM 0.801 0.261 3.069 0.002 0.721 0.721
EEF ~~
ADT 0.433 0.164 2.641 0.008 0.411 0.411
IM 0.530 0.138 3.843 0.000 0.673 0.673
ADT ~~
IM 0.836 0.277 3.020 0.003 0.530 0.530
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.608 0.112 5.433 0.000 0.608 0.368
.EEC2 0.232 0.089 2.617 0.009 0.232 0.122
.EEC3 0.393 0.107 3.683 0.000 0.393 0.227
.EEF1 0.341 0.172 1.978 0.048 0.341 0.393
.EEF2 0.513 0.244 2.105 0.035 0.513 0.408
.EEF3 0.347 0.162 2.143 0.032 0.347 0.395
.ADT1 0.202 0.086 2.347 0.019 0.202 0.087
.ADT2 0.135 0.065 2.093 0.036 0.135 0.057
.ADT3 0.268 0.086 3.106 0.002 0.268 0.115
.IM1 0.106 0.053 1.998 0.046 0.106 0.082
.IM2 0.277 0.088 3.138 0.002 0.277 0.235
.IM3 0.356 0.129 2.754 0.006 0.356 0.256
EEC 1.046 0.302 3.462 0.001 1.000 1.000
EEF 0.526 0.290 1.810 0.070 1.000 1.000
ADT 2.108 0.517 4.078 0.000 1.000 1.000
IM 1.179 0.364 3.243 0.001 1.000 1.000# Inspect latent correlations
lavInspect(fit_substantive, "cor.lv") EEC EEF ADT IM
EEC 1.000
EEF 0.719 1.000
ADT 0.384 0.411 1.000
IM 0.721 0.673 0.530 1.000# Inspect latent variances (diagonal of covariance matrix)
cov_lv <- lavInspect(fit_substantive, "cov.lv")
diag(cov_lv) EEC EEF ADT IM
1.0455834 0.5255262 2.1080381 1.1794917 # CFA with a marker-variable CMF
model_marker <- '
# Substantive factors
EEC =~ EEC1 + EEC2 + EEC3
EEF =~ EEF1 + EEF2 + EEF3
ADT =~ ADT1 + ADT2 + ADT3
IM =~ IM1 + IM2 + IM3
# Common method factor (marker variable approach)
CMF =~ EEC1 + EEF1 + ADT1 + IM1
# Fix CMF variance for identification
CMF ~~ 1*CMF
'
# Fit the model
fit_marker <- cfa(model_marker, data = efa_data_good, estimator = "MLR")Warning: lavaan->lav_object_post_check():
some estimated ov variances are negativeWarning: lavaan->lav_object_post_check():
covariance matrix of latent variables is not positive definite ; use
lavInspect(fit, "cov.lv") to investigate.# Summary with fit measures and standardized estimates
summary(fit_marker, fit.measures = TRUE, standardized = TRUE)lavaan 0.6-19 ended normally after 341 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 37
Number of observations 67
Model Test User Model:
Standard Scaled
Test Statistic 70.321 78.288
Degrees of freedom 41 41
P-value (Chi-square) 0.003 0.000
Scaling correction factor 0.898
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 823.097 823.017
Degrees of freedom 66 66
P-value 0.000 0.000
Scaling correction factor 1.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.961 0.951
Tucker-Lewis Index (TLI) 0.938 0.921
Robust Comparative Fit Index (CFI) 0.956
Robust Tucker-Lewis Index (TLI) 0.929
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -929.874 -929.874
Scaling correction factor 1.378
for the MLR correction
Loglikelihood unrestricted model (H1) -894.714 -894.714
Scaling correction factor 1.126
for the MLR correction
Akaike (AIC) 1933.748 1933.748
Bayesian (BIC) 2015.322 2015.322
Sample-size adjusted Bayesian (SABIC) 1898.822 1898.822
Root Mean Square Error of Approximation:
RMSEA 0.103 0.117
90 Percent confidence interval - lower 0.060 0.074
90 Percent confidence interval - upper 0.143 0.157
P-value H_0: RMSEA <= 0.050 0.025 0.008
P-value H_0: RMSEA >= 0.080 0.832 0.926
Robust RMSEA 0.110
90 Percent confidence interval - lower 0.073
90 Percent confidence interval - upper 0.147
P-value H_0: Robust RMSEA <= 0.050 0.007
P-value H_0: Robust RMSEA >= 0.080 0.912
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 0.027 0.020
EEC2 48.425 332.375 0.146 0.884 1.294 0.923
EEC3 44.639 305.165 0.146 0.884 1.193 0.895
EEF =~
EEF1 1.000 1.787 1.916
EEF2 0.437 0.444 0.983 0.325 0.781 0.693
EEF3 0.374 0.365 1.025 0.305 0.669 0.709
ADT =~
ADT1 1.000 1.551 1.017
ADT2 0.966 0.053 18.341 0.000 1.499 0.970
ADT3 0.929 0.051 18.161 0.000 1.440 0.940
IM =~
IM1 1.000 0.802 0.698
IM2 1.243 0.356 3.493 0.000 0.996 0.909
IM3 1.294 0.325 3.982 0.000 1.038 0.872
CMF =~
EEC1 1.000 1.000 0.760
EEF1 -1.133 1.737 -0.652 0.514 -1.133 -1.215
ADT1 -0.168 0.155 -1.084 0.278 -0.168 -0.110
IM1 0.307 0.198 1.554 0.120 0.307 0.268
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC ~~
EEF 0.044 0.323 0.135 0.892 0.916 0.916
ADT 0.017 0.125 0.139 0.890 0.419 0.419
IM 0.014 0.097 0.143 0.886 0.646 0.646
CMF 0.027 0.186 0.145 0.885 1.007 1.007
EEF ~~
ADT 1.306 1.691 0.773 0.440 0.471 0.471
IM 1.079 1.257 0.858 0.391 0.753 0.753
CMF 1.475 1.757 0.839 0.401 0.825 0.825
ADT ~~
IM 0.669 0.235 2.848 0.004 0.538 0.538
CMF 0.831 0.334 2.491 0.013 0.536 0.536
IM ~~
CMF 0.693 0.168 4.118 0.000 0.865 0.865
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
CMF 1.000 1.000 1.000
.EEC1 0.678 0.144 4.725 0.000 0.678 0.391
.EEC2 0.291 0.108 2.684 0.007 0.291 0.148
.EEC3 0.355 0.101 3.514 0.000 0.355 0.200
.EEF1 -0.265 0.883 -0.300 0.764 -0.265 -0.305
.EEF2 0.661 0.187 3.531 0.000 0.661 0.520
.EEF3 0.442 0.154 2.865 0.004 0.442 0.497
.ADT1 0.170 0.071 2.407 0.016 0.170 0.073
.ADT2 0.140 0.060 2.337 0.019 0.140 0.059
.ADT3 0.272 0.082 3.331 0.001 0.272 0.116
.IM1 0.155 0.051 3.040 0.002 0.155 0.117
.IM2 0.209 0.078 2.666 0.008 0.209 0.174
.IM3 0.338 0.115 2.955 0.003 0.338 0.239
EEC 0.001 0.010 0.072 0.943 1.000 1.000
EEF 3.194 6.002 0.532 0.595 1.000 1.000
ADT 2.404 0.632 3.804 0.000 1.000 1.000
IM 0.643 0.249 2.582 0.010 1.000 1.000# Inspect latent correlations
lavInspect(fit_marker, "cor.lv") EEC EEF ADT IM CMF
EEC 1.000
EEF 0.916 1.000
ADT 0.419 0.471 1.000
IM 0.646 0.753 0.538 1.000
CMF 1.007 0.825 0.536 0.865 1.000# Inspect latent variances
diag(lavInspect(fit_marker, "cov.lv")) EEC EEF ADT IM CMF
0.0007140811 3.1943385481 2.4044230046 0.6429758039 1.0000000000 SEM
SEM with two non-connected DVs
Warning: lavaan->lav_model_nvcov_bootstrap():
1 bootstrap runs failed or did not converge.Warning: lavaan->lav_model_nvcov_bootstrap():
159 bootstrap runs resulted in nonadmissible solutions.lavaan 0.6-19 ended normally after 41 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 29
Number of observations 67
Model Test User Model:
Test statistic 158.030
Degrees of freedom 61
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 836.264
Degrees of freedom 78
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.872
Tucker-Lewis Index (TLI) 0.836
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -967.145
Loglikelihood unrestricted model (H1) -888.130
Akaike (AIC) 1992.291
Bayesian (BIC) 2056.227
Sample-size adjusted Bayesian (SABIC) 1964.917
Root Mean Square Error of Approximation:
RMSEA 0.154
90 Percent confidence interval - lower 0.125
90 Percent confidence interval - upper 0.184
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 1.000
Standardized Root Mean Square Residual:
SRMR 0.269
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 5000
Number of successful bootstrap draws 4999
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC =~
EEC1 1.000 1.005 0.791
EEC2 1.244 0.155 8.012 0.000 1.249 0.919
EEC3 1.152 0.144 8.015 0.000 1.157 0.893
EEF =~
EEF1 1.000 0.686 0.779
EEF2 1.206 0.285 4.226 0.000 0.828 0.780
EEF3 0.917 0.390 2.351 0.019 0.629 0.702
ADT =~
ADT1 1.000 1.461 0.961
ADT2 1.016 0.065 15.585 0.000 1.484 0.965
ADT3 0.984 0.070 14.127 0.000 1.437 0.942
IM =~
IM1 1.000 1.055 0.930
IM2 0.924 0.093 9.936 0.000 0.975 0.898
IM3 0.981 0.085 11.597 0.000 1.035 0.878
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IM ~
reward_2 -0.338 0.262 -1.290 0.197 -0.321 -0.160
EEF ~
IM 0.293 0.115 2.546 0.011 0.450 0.450
reward_2 -0.261 0.208 -1.256 0.209 -0.380 -0.190
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC ~~
.EEF 0.280 0.109 2.571 0.010 0.474 0.474
ADT 0.481 0.240 2.003 0.045 0.328 0.328
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.605 0.114 5.295 0.000 0.605 0.375
.EEC2 0.289 0.132 2.178 0.029 0.289 0.156
.EEC3 0.339 0.120 2.837 0.005 0.339 0.202
.EEF1 0.305 0.121 2.522 0.012 0.305 0.393
.EEF2 0.441 0.160 2.757 0.006 0.441 0.391
.EEF3 0.407 0.156 2.605 0.009 0.407 0.507
.ADT1 0.175 0.078 2.255 0.024 0.175 0.076
.ADT2 0.163 0.062 2.641 0.008 0.163 0.069
.ADT3 0.261 0.080 3.255 0.001 0.261 0.112
.IM1 0.173 0.051 3.427 0.001 0.173 0.135
.IM2 0.227 0.080 2.839 0.005 0.227 0.193
.IM3 0.318 0.111 2.863 0.004 0.318 0.229
EEC 1.009 0.272 3.707 0.000 1.000 1.000
.EEF 0.345 0.196 1.764 0.078 0.734 0.734
ADT 2.134 0.505 4.223 0.000 1.000 1.000
.IM 1.083 0.353 3.070 0.002 0.974 0.974SEM - only EEF
Warning: lavaan->lav_model_nvcov_bootstrap():
1 bootstrap runs failed or did not converge.Warning: lavaan->lav_model_nvcov_bootstrap():
150 bootstrap runs resulted in nonadmissible solutions.lavaan 0.6-19 ended normally after 37 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 21
Number of observations 67
Model Test User Model:
Test statistic 87.694
Degrees of freedom 33
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 614.042
Degrees of freedom 45
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.904
Tucker-Lewis Index (TLI) 0.869
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -700.996
Loglikelihood unrestricted model (H1) -657.149
Akaike (AIC) 1443.992
Bayesian (BIC) 1490.291
Sample-size adjusted Bayesian (SABIC) 1424.169
Root Mean Square Error of Approximation:
RMSEA 0.157
90 Percent confidence interval - lower 0.118
90 Percent confidence interval - upper 0.198
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 0.999
Standardized Root Mean Square Residual:
SRMR 0.232
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 5000
Number of successful bootstrap draws 4999
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEF =~
EEF1 1.000 0.761 0.817
EEF2 1.205 0.300 4.019 0.000 0.917 0.818
EEF3 0.875 0.374 2.337 0.019 0.665 0.710
ADT =~
ADT1 1.000 1.463 0.962
ADT2 1.014 0.063 15.994 0.000 1.483 0.964
ADT3 0.983 0.069 14.219 0.000 1.437 0.942
IM =~
IM1 1.000 1.060 0.935
IM2 0.915 0.094 9.702 0.000 0.970 0.894
IM3 0.974 0.084 11.646 0.000 1.033 0.876
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IM ~
reward_2 -0.340 0.264 -1.286 0.198 -0.320 -0.160
EEF ~
IM 0.440 0.134 3.287 0.001 0.613 0.613
reward_2 -0.222 0.206 -1.082 0.279 -0.292 -0.146
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEF1 0.288 0.129 2.224 0.026 0.288 0.332
.EEF2 0.416 0.156 2.662 0.008 0.416 0.331
.EEF3 0.436 0.157 2.785 0.005 0.436 0.496
.ADT1 0.171 0.076 2.244 0.025 0.171 0.074
.ADT2 0.167 0.063 2.639 0.008 0.167 0.070
.ADT3 0.262 0.080 3.285 0.001 0.262 0.113
.IM1 0.162 0.049 3.301 0.001 0.162 0.126
.IM2 0.236 0.077 3.051 0.002 0.236 0.200
.IM3 0.323 0.113 2.858 0.004 0.323 0.232
.EEF 0.332 0.186 1.785 0.074 0.574 0.574
ADT 2.139 0.504 4.241 0.000 1.000 1.000
.IM 1.095 0.351 3.117 0.002 0.974 0.974SEM - only EEC
Warning: lavaan->lav_model_nvcov_bootstrap():
339 bootstrap runs resulted in nonadmissible solutions.lavaan 0.6-19 ended normally after 35 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 21
Number of observations 67
Model Test User Model:
Test statistic 71.031
Degrees of freedom 33
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 669.268
Degrees of freedom 45
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.939
Tucker-Lewis Index (TLI) 0.917
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -723.442
Loglikelihood unrestricted model (H1) -687.926
Akaike (AIC) 1488.884
Bayesian (BIC) 1535.182
Sample-size adjusted Bayesian (SABIC) 1469.061
Root Mean Square Error of Approximation:
RMSEA 0.131
90 Percent confidence interval - lower 0.089
90 Percent confidence interval - upper 0.173
P-value H_0: RMSEA <= 0.050 0.002
P-value H_0: RMSEA >= 0.080 0.975
Standardized Root Mean Square Residual:
SRMR 0.232
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 5000
Number of successful bootstrap draws 5000
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC =~
EEC1 1.000 1.038 0.807
EEC2 1.241 0.158 7.857 0.000 1.287 0.932
EEC3 1.113 0.129 8.614 0.000 1.155 0.878
ADT =~
ADT1 1.000 1.463 0.962
ADT2 1.014 0.063 15.995 0.000 1.483 0.964
ADT3 0.983 0.069 14.220 0.000 1.437 0.942
IM =~
IM1 1.000 1.088 0.960
IM2 0.870 0.109 7.947 0.000 0.946 0.872
IM3 0.934 0.091 10.299 0.000 1.016 0.862
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IM ~
reward_2 -0.345 0.269 -1.285 0.199 -0.317 -0.159
EEC ~
IM 0.694 0.092 7.551 0.000 0.728 0.728
reward_2 0.060 0.197 0.303 0.762 0.058 0.029
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.577 0.107 5.368 0.000 0.577 0.349
.EEC2 0.253 0.102 2.479 0.013 0.253 0.132
.EEC3 0.397 0.113 3.513 0.000 0.397 0.229
.ADT1 0.171 0.076 2.244 0.025 0.171 0.074
.ADT2 0.167 0.063 2.640 0.008 0.167 0.070
.ADT3 0.262 0.080 3.285 0.001 0.262 0.113
.IM1 0.102 0.058 1.750 0.080 0.102 0.079
.IM2 0.281 0.087 3.217 0.001 0.281 0.239
.IM3 0.357 0.129 2.757 0.006 0.357 0.257
.EEC 0.513 0.157 3.259 0.001 0.477 0.477
ADT 2.139 0.504 4.241 0.000 1.000 1.000
.IM 1.154 0.352 3.273 0.001 0.975 0.975SEM with partial mediation EEF -> EEC
Warning: lavaan->lav_model_nvcov_bootstrap():
6 bootstrap runs failed or did not converge.Warning: lavaan->lav_model_nvcov_bootstrap():
299 bootstrap runs resulted in nonadmissible solutions.lavaan 0.6-19 ended normally after 44 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 31
Number of observations 67
Model Test User Model:
Test statistic 126.396
Degrees of freedom 59
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 836.264
Degrees of freedom 78
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.911
Tucker-Lewis Index (TLI) 0.882
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -951.328
Loglikelihood unrestricted model (H1) -888.130
Akaike (AIC) 1964.657
Bayesian (BIC) 2033.002
Sample-size adjusted Bayesian (SABIC) 1935.394
Root Mean Square Error of Approximation:
RMSEA 0.131
90 Percent confidence interval - lower 0.099
90 Percent confidence interval - upper 0.162
P-value H_0: RMSEA <= 0.050 0.000
P-value H_0: RMSEA >= 0.080 0.995
Standardized Root Mean Square Residual:
SRMR 0.207
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 5000
Number of successful bootstrap draws 4994
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
EEC =~
EEC1 1.000 1.015 0.794
EEC2 1.261 0.169 7.455 0.000 1.280 0.933
EEC3 1.133 0.132 8.574 0.000 1.150 0.880
EEF =~
EEF1 1.000 0.745 0.800
EEF2 1.196 0.278 4.306 0.000 0.891 0.795
EEF3 0.938 0.420 2.231 0.026 0.698 0.745
ADT =~
ADT1 1.000 1.463 0.962
ADT2 1.013 0.063 15.991 0.000 1.482 0.964
ADT3 0.982 0.069 14.219 0.000 1.437 0.942
IM =~
IM1 1.000 1.082 0.954
IM2 0.880 0.107 8.220 0.000 0.952 0.877
IM3 0.943 0.090 10.475 0.000 1.021 0.866
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
IM ~
reward_2 -0.344 0.268 -1.286 0.198 -0.318 -0.159
EEF ~
IM 0.435 0.128 3.404 0.001 0.632 0.632
reward_2 -0.201 0.208 -0.964 0.335 -0.269 -0.135
EEC ~
IM 0.424 0.180 2.360 0.018 0.452 0.452
EEF 0.575 0.644 0.893 0.372 0.422 0.422
reward_2 0.184 0.192 0.954 0.340 0.181 0.090
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC ~~
ADT 0.039 0.157 0.246 0.805 0.042 0.042
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.EEC1 0.605 0.111 5.426 0.000 0.605 0.370
.EEC2 0.242 0.098 2.475 0.013 0.242 0.129
.EEC3 0.385 0.109 3.525 0.000 0.385 0.225
.EEF1 0.311 0.129 2.416 0.016 0.311 0.359
.EEF2 0.462 0.171 2.705 0.007 0.462 0.368
.EEF3 0.391 0.155 2.526 0.012 0.391 0.445
.ADT1 0.170 0.076 2.236 0.025 0.170 0.074
.ADT2 0.167 0.064 2.630 0.009 0.167 0.071
.ADT3 0.262 0.080 3.280 0.001 0.262 0.113
.IM1 0.115 0.055 2.087 0.037 0.115 0.090
.IM2 0.271 0.083 3.248 0.001 0.271 0.230
.IM3 0.348 0.124 2.803 0.005 0.348 0.250
.EEC 0.403 0.134 3.002 0.003 0.392 0.392
.EEF 0.308 0.181 1.702 0.089 0.555 0.555
ADT 2.140 0.504 4.247 0.000 1.000 1.000
.IM 1.141 0.351 3.251 0.001 0.975 0.975