Libraries
We are going to use psych
(Revelle, 2023),
lavaan
version 0.6.15 (Rosseel, Jorgensen, &
Rockwood, 2023), semTools
version 0.5.6 (Jorgensen, Pornprasertmanit, Schoemann, &
Rosseel, 2022) and semPlot
version 1.1.6 (Epskamp,
2022) in our analysis. Load the packages.
library(foreign)
library(psych)
library(lavaan)
library(semTools)
library(semPlot)
Load data
data = read.spss("Attitude_Statistics v3.sav", F, T)
dim(data)
## [1] 150 13
names(data)
## [1] "ID" "Q1" "Q2" "Q3" "Q4" "Q5" "Q6" "Q7" "Q8" "Q9" "Q10" "Q11" "Q12"
describe(data[-1])
Q1 |
1 |
150 |
3.126667 |
1.1009250 |
3 |
3.125000 |
1.4826 |
1 |
5 |
4 |
-0.0995748 |
-0.7324083 |
0.0898901 |
Q2 |
2 |
150 |
3.506667 |
1.0346135 |
3 |
3.550000 |
1.4826 |
1 |
5 |
4 |
-0.1441109 |
-0.4692084 |
0.0844758 |
Q3 |
3 |
150 |
3.180000 |
1.0302147 |
3 |
3.166667 |
1.4826 |
1 |
5 |
4 |
-0.0321343 |
-0.4202388 |
0.0841167 |
Q4 |
4 |
150 |
2.813333 |
1.1723130 |
3 |
2.775000 |
1.4826 |
1 |
5 |
4 |
0.1888890 |
-0.8077519 |
0.0957190 |
Q5 |
5 |
150 |
3.313333 |
1.0109247 |
3 |
3.316667 |
1.4826 |
1 |
5 |
4 |
-0.2242453 |
-0.4760474 |
0.0825417 |
Q6 |
6 |
150 |
3.053333 |
1.0916810 |
3 |
3.050000 |
1.4826 |
1 |
5 |
4 |
-0.0432196 |
-0.7058165 |
0.0891354 |
Q7 |
7 |
150 |
2.920000 |
1.1901159 |
3 |
2.925000 |
1.4826 |
1 |
5 |
4 |
-0.0366766 |
-1.0562073 |
0.0971726 |
Q8 |
8 |
150 |
3.326667 |
0.9999776 |
3 |
3.341667 |
1.4826 |
1 |
5 |
4 |
-0.0816209 |
-0.1204552 |
0.0816478 |
Q9 |
9 |
150 |
3.440000 |
1.0457970 |
3 |
3.483333 |
1.4826 |
1 |
5 |
4 |
-0.2091593 |
-0.3234321 |
0.0853890 |
Q10 |
10 |
150 |
3.313333 |
1.0999492 |
3 |
3.358333 |
1.4826 |
1 |
5 |
4 |
-0.2157639 |
-0.3888402 |
0.0898105 |
Q11 |
11 |
150 |
3.353333 |
0.9350496 |
3 |
3.366667 |
1.4826 |
1 |
5 |
4 |
-0.3074829 |
-0.3281186 |
0.0763465 |
Q12 |
12 |
150 |
2.826667 |
0.9813473 |
3 |
2.833333 |
1.4826 |
1 |
5 |
4 |
0.0945084 |
-0.6761637 |
0.0801267 |
Correlational &
causal
Correlational
Observed
variables
# Q4 & Q11
model.c = "
Q4 ~~ Q11
"
corr.c = sem(model.c, data = data, meanstructure = T) # meanstructure -> display mean
summary(corr.c, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 13 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 32.305
## Degrees of freedom 1
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -422.299
## Loglikelihood unrestricted model (H1) -422.299
##
## Akaike (AIC) 854.599
## Bayesian (BIC) 869.652
## Sample-size adjusted Bayesian (SABIC) 853.828
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 ~~
## Q11 0.479 0.097 4.934 0.000 0.479 0.440
##
## Intercepts:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 2.813 0.095 29.490 0.000 2.813 2.408
## Q11 3.353 0.076 44.070 0.000 3.353 3.598
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 1.365 0.158 8.660 0.000 1.365 1.000
## Q11 0.868 0.100 8.660 0.000 0.868 1.000
semPaths(corr.c, what = "path", whatLabels = "par", edge.color = "black",
edge.label.cex = 1, residuals = F, sizeInt = 4)
cor(data$Q4, data$Q11)
## [1] 0.4401738
![](data:image/png;base64,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)
Latent
variables
model.cl = "
F1 =~ Q4 + Q6 + Q7 + Q11
F2 =~ Q8 + Q9 + Q10
"
corr.cl = sem(model.cl, data = data)
summary(corr.cl, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 15
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 20.451
## Degrees of freedom 13
## P-value (Chi-square) 0.085
##
## Model Test Baseline Model:
##
## Test statistic 380.263
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.979
## Tucker-Lewis Index (TLI) 0.966
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1380.510
## Loglikelihood unrestricted model (H1) -1370.284
##
## Akaike (AIC) 2791.020
## Bayesian (BIC) 2836.179
## Sample-size adjusted Bayesian (SABIC) 2788.707
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.062
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.111
## P-value H_0: RMSEA <= 0.050 0.314
## P-value H_0: RMSEA >= 0.080 0.306
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## Q4 1.000 0.941 0.806
## Q6 0.830 0.103 8.040 0.000 0.781 0.718
## Q7 0.960 0.115 8.348 0.000 0.904 0.762
## Q11 0.504 0.088 5.742 0.000 0.474 0.509
## F2 =~
## Q8 1.000 0.651 0.653
## Q9 1.351 0.170 7.951 0.000 0.880 0.844
## Q10 1.444 0.182 7.927 0.000 0.940 0.858
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 ~~
## F2 0.048 0.060 0.800 0.424 0.078 0.078
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q4 0.479 0.097 4.932 0.000 0.479 0.351
## .Q6 0.574 0.088 6.530 0.000 0.574 0.485
## .Q7 0.591 0.101 5.825 0.000 0.591 0.420
## .Q11 0.644 0.081 7.997 0.000 0.644 0.741
## .Q8 0.569 0.076 7.526 0.000 0.569 0.573
## .Q9 0.313 0.077 4.054 0.000 0.313 0.288
## .Q10 0.318 0.086 3.693 0.000 0.318 0.264
## F1 0.886 0.168 5.279 0.000 1.000 1.000
## F2 0.424 0.101 4.191 0.000 1.000 1.000
semPaths(corr.cl, what = "path", whatLabels = "par", edge.color = "black",
layout = "tree2", edge.label.cex = 1, residuals = F)
![](data:image/png;base64,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)
Causal effects
Observed
variables
# Q4 & Q11
model.cs = "
Q4 ~ Q11
"
cause.cs = sem(model.cs, data = data)
summary(cause.cs, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 2
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 32.305
## Degrees of freedom 1
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -220.034
## Loglikelihood unrestricted model (H1) -220.034
##
## Akaike (AIC) 444.067
## Bayesian (BIC) 450.088
## Sample-size adjusted Bayesian (SABIC) 443.759
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 ~
## Q11 0.552 0.092 6.004 0.000 0.552 0.440
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q4 1.101 0.127 8.660 0.000 1.101 0.806
summary(lm(formula = Q4 ~ Q11, data = data)) # compare with SLR
##
## Call:
## lm(formula = Q4 ~ Q11, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.7221 -0.6183 -0.1702 0.8298 2.9335
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.96274 0.32207 2.989 0.00328 **
## Q11 0.55187 0.09254 5.964 1.74e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.056 on 148 degrees of freedom
## Multiple R-squared: 0.1938, Adjusted R-squared: 0.1883
## F-statistic: 35.57 on 1 and 148 DF, p-value: 1.737e-08
semPaths(cause.cs, what = "path", whatLabels = "par", edge.color = "black",
rotation = 2, edge.label.cex = 1, residuals = F)
![](data:image/png;base64,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)
Latent
variables
model.csl = "
F1 =~ Q4 + Q6 + Q7 + Q11
F2 =~ Q8 + Q9 + Q10
F2 ~ F1
"
cause.csl = sem(model.csl, data = data)
summary(cause.csl, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 15
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 20.451
## Degrees of freedom 13
## P-value (Chi-square) 0.085
##
## Model Test Baseline Model:
##
## Test statistic 380.263
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.979
## Tucker-Lewis Index (TLI) 0.966
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1380.510
## Loglikelihood unrestricted model (H1) -1370.284
##
## Akaike (AIC) 2791.020
## Bayesian (BIC) 2836.179
## Sample-size adjusted Bayesian (SABIC) 2788.707
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.062
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.111
## P-value H_0: RMSEA <= 0.050 0.314
## P-value H_0: RMSEA >= 0.080 0.306
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.063
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F1 =~
## Q4 1.000 0.941 0.806
## Q6 0.830 0.103 8.040 0.000 0.781 0.718
## Q7 0.960 0.115 8.348 0.000 0.904 0.762
## Q11 0.504 0.088 5.742 0.000 0.474 0.509
## F2 =~
## Q8 1.000 0.651 0.653
## Q9 1.351 0.170 7.951 0.000 0.880 0.844
## Q10 1.444 0.182 7.927 0.000 0.940 0.858
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## F2 ~
## F1 0.054 0.067 0.803 0.422 0.078 0.078
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q4 0.479 0.097 4.932 0.000 0.479 0.351
## .Q6 0.574 0.088 6.530 0.000 0.574 0.485
## .Q7 0.591 0.101 5.825 0.000 0.591 0.420
## .Q11 0.644 0.081 7.997 0.000 0.644 0.741
## .Q8 0.569 0.076 7.526 0.000 0.569 0.573
## .Q9 0.313 0.077 4.054 0.000 0.313 0.288
## .Q10 0.318 0.086 3.693 0.000 0.318 0.264
## F1 0.886 0.168 5.279 0.000 1.000 1.000
## .F2 0.421 0.101 4.189 0.000 0.994 0.994
semPaths(cause.csl, what = "path", whatLabels = "par", edge.color = "black",
rotation = 2, edge.label.cex = 1,
sizeMan = 4, sizeLat = 6, residuals = F)
![](data:image/png;base64,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)
Multiple
variables
model.cs1 = "
Q4 ~ Q7 + Q11 + Q6
"
cause.cs1 = sem(model.cs1, data = data)
summary(cause.cs1, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 4
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 98.444
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -186.964
## Loglikelihood unrestricted model (H1) -186.964
##
## Akaike (AIC) 381.928
## Bayesian (BIC) 393.970
## Sample-size adjusted Bayesian (SABIC) 381.311
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 ~
## Q7 0.366 0.072 5.087 0.000 0.366 0.372
## Q11 0.259 0.080 3.218 0.001 0.259 0.206
## Q6 0.309 0.078 3.964 0.000 0.309 0.287
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q4 0.708 0.082 8.660 0.000 0.708 0.519
semPaths(cause.cs1, what = "path", whatLabels = "par", edge.color = "black",
rotation = 2, edge.label.cex = 1, residuals = F)
summary(lm(Q4 ~ Q7 + Q11 + Q6, data = data)) # compare with MLR
##
## Call:
## lm(formula = Q4 ~ Q7 + Q11 + Q6, data = data)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.36767 -0.61468 -0.05963 0.49242 2.42276
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.06699 0.28680 -0.234 0.81564
## Q7 0.36638 0.07301 5.018 1.49e-06 ***
## Q11 0.25881 0.08153 3.174 0.00183 **
## Q6 0.30872 0.07894 3.911 0.00014 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.853 on 146 degrees of freedom
## Multiple R-squared: 0.4812, Adjusted R-squared: 0.4706
## F-statistic: 45.15 on 3 and 146 DF, p-value: < 2.2e-16
![](data:image/png;base64,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)
Mediation
model.me = "
Q11 ~ a*Q7 # mediator
Q4 ~ c*Q7 + b*Q11
ab := a*b # indirect effect
total := c + a*b # total effect
"
med.me = sem(model.me, data = data)
summary(med.me, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 5
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 104.734
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -386.085
## Loglikelihood unrestricted model (H1) -386.085
##
## Akaike (AIC) 782.169
## Bayesian (BIC) 797.222
## Sample-size adjusted Bayesian (SABIC) 781.398
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q11 ~
## Q7 (a) 0.285 0.060 4.776 0.000 0.285 0.363
## Q4 ~
## Q7 (c) 0.511 0.065 7.811 0.000 0.511 0.518
## Q11 (b) 0.316 0.083 3.797 0.000 0.316 0.252
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q11 0.754 0.087 8.660 0.000 0.754 0.868
## .Q4 0.782 0.090 8.660 0.000 0.782 0.573
##
## Defined Parameters:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## ab 0.090 0.030 2.972 0.003 0.090 0.092
## total 0.601 0.064 9.422 0.000 0.601 0.610
semPaths(med.me, what = "path", whatLabels = "name", edge.color = "black",
layout = "spring", edge.label.cex = 1, residuals = F)
semPaths(med.me, what = "path", whatLabels = "par", edge.color = "black",
layout = "spring", edge.label.cex = 1, residuals = F)
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Compare with model without mediator. Note c = 0.51 (with mediator)
< c = 0.60 (without mediator). All a, b, and c are significant. So
this is a partial mediation.
model.me1 = "
Q4 ~ c*Q7
"
med.me1 = sem(model.me1, data = data)
summary(med.me1, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 2
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 69.738
## Degrees of freedom 1
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -201.317
## Loglikelihood unrestricted model (H1) -201.317
##
## Akaike (AIC) 406.634
## Bayesian (BIC) 412.655
## Sample-size adjusted Bayesian (SABIC) 406.326
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 ~
## Q7 (c) 0.601 0.064 9.422 0.000 0.601 0.610
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q4 0.858 0.099 8.660 0.000 0.858 0.628
semPaths(med.me1, what = "path", whatLabels = "par", edge.color = "black",
rotation = 2, edge.label.cex = 1, residuals = F)
![](data:image/png;base64,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)
Moderation/Interaction
data$Q7.Q8 = data$Q7*data$Q8 # create interaction
head(data)
1 |
2 |
3 |
3 |
3 |
4 |
4 |
3 |
3 |
3 |
3 |
4 |
2 |
9 |
2 |
3 |
2 |
3 |
3 |
4 |
4 |
4 |
3 |
3 |
3 |
4 |
2 |
12 |
3 |
5 |
4 |
5 |
1 |
1 |
1 |
1 |
4 |
4 |
5 |
1 |
4 |
4 |
4 |
2 |
2 |
2 |
4 |
3 |
2 |
2 |
2 |
2 |
2 |
3 |
3 |
4 |
5 |
4 |
1 |
4 |
2 |
5 |
1 |
4 |
5 |
5 |
3 |
4 |
4 |
20 |
6 |
4 |
4 |
4 |
3 |
4 |
4 |
4 |
3 |
4 |
4 |
4 |
4 |
12 |
model.mo = "
Q4 ~ Q7 + Q8 + Q7.Q8
"
mod.mo = sem(model.mo, data = data)
summary(mod.mo, fit.measures = T, standardized = T) # complete moderation
## lavaan 0.6.15 ended normally after 1 iteration
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 4
##
## Number of observations 150
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 76.491
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -197.940
## Loglikelihood unrestricted model (H1) -197.940
##
## Akaike (AIC) 403.880
## Bayesian (BIC) 415.923
## Sample-size adjusted Bayesian (SABIC) 403.264
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Q4 ~
## Q7 0.179 0.196 0.914 0.361 0.179 0.182
## Q8 -0.207 0.164 -1.260 0.207 -0.207 -0.176
## Q7.Q8 0.124 0.057 2.179 0.029 0.124 0.549
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .Q4 0.820 0.095 8.660 0.000 0.820 0.601
semPaths(mod.mo, what = "path", whatLabels = "par", edge.color = "black",
edge.label.cex = 1, residuals = F)
lm(Q4 ~ Q7 + Q8 + Q7*Q8, data = data)
##
## Call:
## lm(formula = Q4 ~ Q7 + Q8 + Q7 * Q8, data = data)
##
## Coefficients:
## (Intercept) Q7 Q8 Q7:Q8
## 1.7515 0.1793 -0.2069 0.1236
![](data:image/png;base64,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)
Exercise
Use built-in data sets:
data("HolzingerSwineford1939")
data("PoliticalDemocracy")
Mental ability test
data set
Descriptive
data1 = HolzingerSwineford1939
dim(data1)
## [1] 301 15
names(data1)
## [1] "id" "sex" "ageyr" "agemo" "school" "grade" "x1" "x2" "x3"
## [10] "x4" "x5" "x6" "x7" "x8" "x9"
head(data1)
1 |
1 |
13 |
1 |
Pasteur |
7 |
3.333333 |
7.75 |
0.375 |
2.333333 |
5.75 |
1.2857143 |
3.391304 |
5.75 |
6.361111 |
2 |
2 |
13 |
7 |
Pasteur |
7 |
5.333333 |
5.25 |
2.125 |
1.666667 |
3.00 |
1.2857143 |
3.782609 |
6.25 |
7.916667 |
3 |
2 |
13 |
1 |
Pasteur |
7 |
4.500000 |
5.25 |
1.875 |
1.000000 |
1.75 |
0.4285714 |
3.260870 |
3.90 |
4.416667 |
4 |
1 |
13 |
2 |
Pasteur |
7 |
5.333333 |
7.75 |
3.000 |
2.666667 |
4.50 |
2.4285714 |
3.000000 |
5.30 |
4.861111 |
5 |
2 |
12 |
2 |
Pasteur |
7 |
4.833333 |
4.75 |
0.875 |
2.666667 |
4.00 |
2.5714286 |
3.695652 |
6.30 |
5.916667 |
6 |
2 |
14 |
1 |
Pasteur |
7 |
5.333333 |
5.00 |
2.250 |
1.000000 |
3.00 |
0.8571429 |
4.347826 |
6.65 |
7.500000 |
str(data1)
## 'data.frame': 301 obs. of 15 variables:
## $ id : int 1 2 3 4 5 6 7 8 9 11 ...
## $ sex : int 1 2 2 1 2 2 1 2 2 2 ...
## $ ageyr : int 13 13 13 13 12 14 12 12 13 12 ...
## $ agemo : int 1 7 1 2 2 1 1 2 0 5 ...
## $ school: Factor w/ 2 levels "Grant-White",..: 2 2 2 2 2 2 2 2 2 2 ...
## $ grade : int 7 7 7 7 7 7 7 7 7 7 ...
## $ x1 : num 3.33 5.33 4.5 5.33 4.83 ...
## $ x2 : num 7.75 5.25 5.25 7.75 4.75 5 6 6.25 5.75 5.25 ...
## $ x3 : num 0.375 2.125 1.875 3 0.875 ...
## $ x4 : num 2.33 1.67 1 2.67 2.67 ...
## $ x5 : num 5.75 3 1.75 4.5 4 3 6 4.25 5.75 5 ...
## $ x6 : num 1.286 1.286 0.429 2.429 2.571 ...
## $ x7 : num 3.39 3.78 3.26 3 3.7 ...
## $ x8 : num 5.75 6.25 3.9 5.3 6.3 6.65 6.2 5.15 4.65 4.55 ...
## $ x9 : num 6.36 7.92 4.42 4.86 5.92 ...
Need to recode sex
variable from {1,2} to {0,1}
i.e. dummy variable,
data1$sex1 = data1$sex - 1
head(data1)
1 |
1 |
13 |
1 |
Pasteur |
7 |
3.333333 |
7.75 |
0.375 |
2.333333 |
5.75 |
1.2857143 |
3.391304 |
5.75 |
6.361111 |
0 |
2 |
2 |
13 |
7 |
Pasteur |
7 |
5.333333 |
5.25 |
2.125 |
1.666667 |
3.00 |
1.2857143 |
3.782609 |
6.25 |
7.916667 |
1 |
3 |
2 |
13 |
1 |
Pasteur |
7 |
4.500000 |
5.25 |
1.875 |
1.000000 |
1.75 |
0.4285714 |
3.260870 |
3.90 |
4.416667 |
1 |
4 |
1 |
13 |
2 |
Pasteur |
7 |
5.333333 |
7.75 |
3.000 |
2.666667 |
4.50 |
2.4285714 |
3.000000 |
5.30 |
4.861111 |
0 |
5 |
2 |
12 |
2 |
Pasteur |
7 |
4.833333 |
4.75 |
0.875 |
2.666667 |
4.00 |
2.5714286 |
3.695652 |
6.30 |
5.916667 |
1 |
6 |
2 |
14 |
1 |
Pasteur |
7 |
5.333333 |
5.00 |
2.250 |
1.000000 |
3.00 |
0.8571429 |
4.347826 |
6.65 |
7.500000 |
1 |
describe(data1)
id |
1 |
301 |
176.5548173 |
105.9384781 |
163.000000 |
176.7759336 |
140.847000 |
1.0000000 |
351.000000 |
350.000000 |
-0.0085838 |
-1.3626249 |
6.1061924 |
sex |
2 |
301 |
1.5149502 |
0.5006087 |
2.000000 |
1.5186722 |
0.000000 |
1.0000000 |
2.000000 |
1.000000 |
-0.0595295 |
-2.0030779 |
0.0288546 |
ageyr |
3 |
301 |
12.9966777 |
1.0503915 |
13.000000 |
12.8879668 |
1.482600 |
11.0000000 |
16.000000 |
5.000000 |
0.6945948 |
0.2045723 |
0.0605436 |
agemo |
4 |
301 |
5.3754153 |
3.4518488 |
5.000000 |
5.3195021 |
4.447800 |
0.0000000 |
11.000000 |
11.000000 |
0.0892744 |
-1.2186405 |
0.1989613 |
school* |
5 |
301 |
1.5182724 |
0.5004981 |
2.000000 |
1.5228216 |
0.000000 |
1.0000000 |
2.000000 |
1.000000 |
-0.0727744 |
-2.0013197 |
0.0288482 |
grade |
6 |
300 |
7.4766667 |
0.5002898 |
7.000000 |
7.4708333 |
0.000000 |
7.0000000 |
8.000000 |
1.000000 |
0.0929683 |
-1.9979835 |
0.0288842 |
x1 |
7 |
301 |
4.9357697 |
1.1674321 |
5.000000 |
4.9647303 |
1.235500 |
0.6666667 |
8.500000 |
7.833333 |
-0.2543455 |
0.3075338 |
0.0672897 |
x2 |
8 |
301 |
6.0880399 |
1.1774506 |
6.000000 |
6.0176349 |
1.111950 |
2.2500000 |
9.250000 |
7.000000 |
0.4700766 |
0.3323940 |
0.0678671 |
x3 |
9 |
301 |
2.2504153 |
1.1309794 |
2.125000 |
2.1991701 |
1.297275 |
0.2500000 |
4.500000 |
4.250000 |
0.3834294 |
-0.9075264 |
0.0651886 |
x4 |
10 |
301 |
3.0609081 |
1.1641163 |
3.000000 |
3.0248963 |
0.988400 |
0.0000000 |
6.333333 |
6.333333 |
0.2674867 |
0.0801268 |
0.0670985 |
x5 |
11 |
301 |
4.3405316 |
1.2904722 |
4.500000 |
4.3952282 |
1.482600 |
1.0000000 |
7.000000 |
6.000000 |
-0.3497961 |
-0.5525369 |
0.0743816 |
x6 |
12 |
301 |
2.1855719 |
1.0956031 |
2.000000 |
2.0883225 |
1.059000 |
0.1428571 |
6.142857 |
6.000000 |
0.8579486 |
0.8165572 |
0.0631495 |
x7 |
13 |
301 |
4.1859021 |
1.0895335 |
4.086957 |
4.1636298 |
1.095835 |
1.3043478 |
7.434783 |
6.130435 |
0.2490881 |
-0.3074039 |
0.0627997 |
x8 |
14 |
301 |
5.5270764 |
1.0126151 |
5.500000 |
5.4929461 |
0.963690 |
3.0500000 |
10.000000 |
6.950000 |
0.5252580 |
1.1715556 |
0.0583662 |
x9 |
15 |
301 |
5.3741233 |
1.0091517 |
5.416667 |
5.3660673 |
0.988400 |
2.7777778 |
9.250000 |
6.472222 |
0.2038709 |
0.2899079 |
0.0581665 |
sex1 |
16 |
301 |
0.5149502 |
0.5006087 |
1.000000 |
0.5186722 |
0.000000 |
0.0000000 |
1.000000 |
1.000000 |
-0.0595295 |
-2.0030779 |
0.0288546 |
Categorical
variable
sex.model = "
visual =~ x1 + x2 + x3
visual ~ sex1
"
sem.sex = sem(sex.model, data = data1)
summary(sem.sex, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 25 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 1.818
## Degrees of freedom 2
## P-value (Chi-square) 0.403
##
## Model Test Baseline Model:
##
## Test statistic 122.574
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.005
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1352.235
## Loglikelihood unrestricted model (H1) -1351.326
##
## Akaike (AIC) 2718.470
## Bayesian (BIC) 2744.420
## Sample-size adjusted Bayesian (SABIC) 2722.220
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.111
## P-value H_0: RMSEA <= 0.050 0.628
## P-value H_0: RMSEA >= 0.080 0.172
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.018
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## visual =~
## x1 1.000 0.695 0.596
## x2 0.804 0.142 5.645 0.000 0.558 0.475
## x3 1.198 0.222 5.392 0.000 0.832 0.737
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## visual ~
## sex1 -0.302 0.103 -2.929 0.003 -0.435 -0.217
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.876 0.111 7.903 0.000 0.876 0.645
## .x2 1.070 0.104 10.284 0.000 1.070 0.774
## .x3 0.582 0.129 4.498 0.000 0.582 0.457
## .visual 0.460 0.114 4.026 0.000 0.953 0.953
semPaths(sem.sex, what = "path", whatLabels = "par", edge.color = "black",
edge.label.cex = 1, residuals = F, rotation = 2)
![](data:image/png;base64,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)
Numerical
variable
age.model = "
speed =~ x7 + x8 + x9
speed ~ ageyr
"
sem.age = sem(age.model, data = data1)
summary(sem.age, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 23 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 7
##
## Number of observations 301
##
## Model Test User Model:
##
## Test statistic 2.415
## Degrees of freedom 2
## P-value (Chi-square) 0.299
##
## Model Test Baseline Model:
##
## Test statistic 174.223
## Degrees of freedom 6
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.998
## Tucker-Lewis Index (TLI) 0.993
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1226.221
## Loglikelihood unrestricted model (H1) -1225.014
##
## Akaike (AIC) 2466.442
## Bayesian (BIC) 2492.392
## Sample-size adjusted Bayesian (SABIC) 2470.192
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.026
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.121
## P-value H_0: RMSEA <= 0.050 0.532
## P-value H_0: RMSEA >= 0.080 0.237
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.021
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## speed =~
## x7 1.000 0.634 0.583
## x8 1.340 0.205 6.543 0.000 0.850 0.841
## x9 0.857 0.122 6.998 0.000 0.543 0.539
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## speed ~
## ageyr 0.155 0.043 3.615 0.000 0.245 0.257
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x7 0.781 0.084 9.302 0.000 0.781 0.660
## .x8 0.300 0.099 3.019 0.003 0.300 0.293
## .x9 0.720 0.071 10.079 0.000 0.720 0.709
## .speed 0.376 0.084 4.448 0.000 0.934 0.934
semPaths(sem.age, what = "path", whatLabels = "par", edge.color = "black",
edge.label.cex = 1, residuals = F, rotation = 2)
![](data:image/png;base64,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)
Polical Democracy
data set
Descriptive
data2 = PoliticalDemocracy
dim(data2)
## [1] 75 11
names(data2)
## [1] "y1" "y2" "y3" "y4" "y5" "y6" "y7" "y8" "x1" "x2" "x3"
CFA model Y
model.y = "
Y =~ y1 + y2 + y3 + y4 + y5 + y6 + y7
"
cfa.y = cfa(model.y, data2)
summary(cfa.y, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 27 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 14
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 31.150
## Degrees of freedom 14
## P-value (Chi-square) 0.005
##
## Model Test Baseline Model:
##
## Test statistic 367.244
## Degrees of freedom 21
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.950
## Tucker-Lewis Index (TLI) 0.926
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1180.866
## Loglikelihood unrestricted model (H1) -1165.292
##
## Akaike (AIC) 2389.733
## Bayesian (BIC) 2422.178
## Sample-size adjusted Bayesian (SABIC) 2378.053
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.128
## 90 Percent confidence interval - lower 0.067
## 90 Percent confidence interval - upper 0.189
## P-value H_0: RMSEA <= 0.050 0.023
## P-value H_0: RMSEA >= 0.080 0.910
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.050
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Y =~
## y1 1.000 2.230 0.856
## y2 1.327 0.171 7.756 0.000 2.958 0.755
## y3 1.050 0.146 7.212 0.000 2.341 0.718
## y4 1.263 0.136 9.320 0.000 2.816 0.846
## y5 0.930 0.110 8.473 0.000 2.073 0.799
## y6 1.140 0.146 7.819 0.000 2.541 0.759
## y7 1.190 0.137 8.716 0.000 2.653 0.813
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .y1 1.816 0.380 4.780 0.000 1.816 0.268
## .y2 6.620 1.208 5.480 0.000 6.620 0.431
## .y3 5.141 0.917 5.606 0.000 5.141 0.484
## .y4 3.140 0.643 4.885 0.000 3.140 0.284
## .y5 2.438 0.463 5.263 0.000 2.438 0.362
## .y6 4.765 0.872 5.464 0.000 4.765 0.425
## .y7 3.616 0.699 5.171 0.000 3.616 0.339
## Y 4.971 1.094 4.544 0.000 1.000 1.000
semPaths(cfa.y, what = "path", whatLabels = "std", rotation = 2,
edge.color = "black", edge.label.cex = 1, residuals = F)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkAAAAJACAMAAABSRCkEAAAC31BMVEUAAAABAQECAgIDAwMEBAQFBQUGBgYICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUWFhYXFxcYGBgZGRkbGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJycoKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6Ojo7Ozs8PDw9PT0+Pj4/Pz9AQEBCQkJDQ0NERERFRUVGRkZHR0dISEhJSUlKSkpLS0tMTExNTU1OTk5PT09QUFBRUVFSUlJTU1NUVFRVVVVWVlZXV1dYWFhZWVlaWlpbW1tcXFxdXV1eXl5fX19gYGBhYWFiYmJkZGRlZWVmZmZnZ2doaGhpaWlra2tsbGxtbW1ubm5vb29wcHBxcXFycnJzc3N0dHR1dXV2dnZ3d3d4eHh5eXl6enp7e3t8fHx9fX1+fn5/f3+AgICBgYGCgoKDg4OEhISFhYWGhoaHh4eIiIiJiYmLi4uMjIyNjY2Ojo6Pj4+QkJCRkZGSkpKUlJSVlZWWlpaXl5eYmJiZmZmampqbm5ucnJydnZ2enp6fn5+goKChoaGioqKjo6OkpKSlpaWmpqanp6eoqKipqamqqqqrq6usrKytra2urq6vr6+wsLCysrKzs7O0tLS1tbW2tra3t7e4uLi5ubm6urq7u7u8vLy9vb2+vr7AwMDCwsLDw8PExMTFxcXGxsbHx8fIyMjJycnKysrLy8vMzMzOzs7Pz8/Q0NDR0dHS0tLT09PU1NTV1dXW1tbX19fY2NjZ2dna2trb29vc3Nzd3d3e3t7f39/g4ODh4eHi4uLj4+Pk5OTl5eXm5ubn5+fo6Ojp6enq6urr6+vs7Ozt7e3u7u7v7+/w8PDx8fHy8vLz8/P09PT19fX29vb39/f4+Pj5+fn6+vr7+/v8/Pz9/f3+/v7///8ROE4KAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAaXklEQVR4nO3d/39U1Z3H8dlWqhSQAlZYhGIgElCxy7paK8ouEzEKa4kYkKDiFrogfmF3W76JlLhi625XKitotQ20lK5EUMku2EoGEZGgARFZvxVBgUQBN2K+ff6AnTuTmZzM3Jm5937OufecmffrhzBzZ5IZzfORe+/Mnc8NEUKMQkE/AWR2AIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAedaTU7P2pOzHA6A8a+r6PVlaP1X24wFQnjX1jWy3vgFAKHsAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWKUCqho4cOB51YlrAIRyZPMXqHncF4mLAIRyJACqrKWD46L/Ln0uuQiAUI4EQDVzaPlqohPf77oVgFCOBEDNRR1jThAt+1XXrQCEciRuA5WvKYt+veyTriUAhHIkAlrfZx3R+98VbgUglCMRUFPPM0SP/0S4FYBQjkRAtRWptwIQypEAqLrkUOqtAIRyhLcyECsAQl4KJQIg5KWEH/wFQt7q9ANAyFN1nX4ACHmoLlz6OgAhj+28+do/xtZh1hUAQu6K86HErxLDFZCbknwSYbwLcl4aH/8DIHPTgA8AmZsWfADI1DThA0Bmpg0fADIxjfgAkHlpxQeATEszPgBkVtrxASCT0pAPAJmTlnwAyJQ05QNAZqQtHwAyIY35AJD+ac0HgHRPcz4ApHfa8wEgnTOADwDpmxF8AEjXDOEDQHpmDB8A0jGD+ACQfhnFB4B0yzA+AKRXxvEBIJ0ykA8A6ZORfABIlwzlA0B6ZCwfANIhg/kAUPAZzQeAgs5wPgAUbAr4YMBU4aTkrw9G3BVKilZeGLJZGCnb9gGgQkjhpjMA5X9K97wAKN9TvOMOQPmd8td9ACif8+FlQwDK33x51RmA8jWf3rQAoPzMt/e8ACgf8/Et0zRAz185bGPyCgCZmK/vuKcCOjHy1PGSlsQ1ADIvnw/YEABV1tLBcU8vIvqqI7EIgEzL9+N9BEA1c2j56oemXDbkieQiADKrAA4XEwA1F3WMOfEvf3Pm029/kFgEQCYVyNGG4jZQ+Zoy+tlSorJtiSUAZE4BHawqAlrfZx01jD199MJjiSUAZEqBHessAmrqeYboZ8UjNiSXAJAZ+c8nlPhFioBqK1LvBkAmFMRfn1AiAVB1yaHUuwGQ/gWz8kr4wVsZhhfQtk/L9k4/AGR0wfBp2Xp30axOPwBkcIHwadsxv3jm5q+o0w8AGVsQfBJ6rDr3wwDIzALgI+rpCoBMzH8+9noIgEzMdz4Z9RAAmZfffLLpIQxXMC2f+eTQQxjvYlb+8smtJ4AAyHu+8tFSDwGQ9/zko6seAiCv+chHYz0EQN7yj4/eegiAvOQbH+31EAC5zy8+JughAHKbT3wM0UMA5C5/+JijhwAoQ6fv6D/6D52XD97Qe2hV7NLeKeof2Sg9BEAZun18w7pv7Itd7Bg+tX5T76ejF/ZfN17xw5qmhwDIvqPnNBDN+GH8cqieqOJOovv6nqsUkIF6CIDs29Yv+uXJK+NXLp19dEf/auvSz9UBMlMPAZB9v74k+mXT4PiV/T1Codtil1QBMlYPAZB9z8QAXRi7fHzwysZ9lz9kXVQCyGQ9BED2bR0Q/bL2itjlZ0ZHv2wZZF2UD8hwPQRA9h39+iGiWXfHLq8tiX6psUTJBmS+HgKgDE2Z/Ol/93qNaMMf6eO+Sz6KlNxnLZUJKC/0EABl6PS0fpf+PvrvFf9A9Pr43kMXnrWWSgOUL3oIgDKl8E2LPNJDAGSfOj75pYcAyC5lfPJODwFQeqr45KMeAqDUFPHJUz0EQN1Twyd/9RAAiSnhk9d6CIC6UsEn3/UQACVSwKcA9BAAxZPPpzD0EABZSedTMHoIgOTzKSQ9BECS+RSYHip0QHL5aKEHA6b8SyofLfQQRtz5l0w+uughDNn0K4l8NNJDAORP8vjopYcAyI+k8dFODwGQ+mTx0VEPAZDqJPHRVA8BkNrk8NFXDwGQyqTw0VoPAZC63PERJkw9Gz+b5AdEK0YMuL+dNNZDAKQqt399hAlTJ62XcB+8so0eHLmr9oJfKHl68gIgFbleeYkTpqxODWugs/3+RFRdJfu5SS4NUL+BA0clrwCQlzxs+3SbMBVt7kKiV3q1d7TJfF5KSgX0+V+J1wDIfZ42nbtNmCI6PKCJaOOwBeefV9Ek87kpSABUWUsHx+27RbwVgNzmcc9LnDAV7Y7F0S9rQvMa3/vedGlPTU0CoJo5tHz15uK/G/Kr5CIAcpfnHXdxwhRR47mHo1+f6xldgb3Uq0PWk5Na8vcoAGou6hhzYu8G+qjfh4lFAOQmxus+4oQpolXXWF8PfKNZ/KukVyG788aXrymL/Xvj9sQSAHIe52XDNnHCFNHEpbGlZdMOvzbyx7Ken9xCyQRA6/uso5/Op08GfZpYAkBOY/CxXmvuNmGq5ZtbYzecmt5/yGItX0U8uzfBp9tfoKaeZ+iLO0Zfsim5BICc5Z2P7u9UpHZ27+8WTSkpmfJYp59ugGorUu8OQE7yzMcoPS0NG5dNHXXRhPlP7vg/iq/DrMUCoOqSQ6nfBEC588rHHD0pdOKFOn+TeCuDl0c+huixpRMv8YsEIE7e+JigJwud7gGQ9zzx0V6PYzrxAMhrXvjorcclnXgA5C0PfDTW44lOPADykns+uuph0IkHQO5zzUdLPWw68QDIbW756KdHEp14GK7gLpd8NNMjlU48jHdxkzs+OulRQCeYTAbkio82evKGTjxzAbnho4eePKMTz1RALvhooCcv6cQzE5BzPkHryWM68UwE5JhPoHrynk488wA55ROcngKhE880QA75BKSnoOjEMwuQMz5B6ClAOvFMAuSIj+96CpZOPHMAOeEjT48wH4gO3tB7aFXKMquW/928cubY7xQqnXimAHLAR+rfHmE+UMfwqfWbej8tLgOdZGYAys1H8ppLnA90NFRPVHFnchnoiJkAKCcf+ds93eYDXTr76I7+1clloCOmP6BcfJRsNXebD7S/Ryh0W9rMIBRLd0A5+Kja5xLnAx0fvLJx3+UPpc4MQrH0BpSdj8I9dnE+0DOjo1+2DEqZGYTi6QwoKx9lemJ7WOJ8oLUl0S81A1JmBqF4+gLKxkeNHmHnXJwP9HHfJR9FSu6j5DIkpCugLHwU6El/XUecD/T6+N5DF57tWoaE9ASUmY9sPXhJkJmOgDLykaoHdKSkH6BMfOTpAR2JqQPU/ubaBbeOGzt23K0L1r7Z7vS7MvCRpAd0pKcIUOsLlUWTqjbVH2tqOla/qWpSUeULrQ6+zZ6PDD2goyglgE4/Ujzr5W5gWl+eVfzI6RzfZsuHrQd0lKYAUNsvix+2OaNE08PFv8x2rhI7Pjw9oOND8gG9ffXcDCckaZp79duZvsuGD0MP6PiWdEDrRu3IfOOOUetsl6fz8aoHdHxOMqCOpRNOZrv95ISl6ScrSePjSQ/oBJJkQPfOaMl+h5YZ96YsSeXjXg/oBJhcQEtm5DylX9uMJeLVFD4u9YBO4EkFVD0hx98fq5YJ1cnL3fm40QM6GTJ5wNSBUY1O7tY46kD8Qjc+jvWATtYMHnHXenWW/S+xHVdbLzKKfJzpAR0HGTxkc9U8p/ect0rk40AP6DjOXECnix2twKwah/5tuC5+MZce0HGZuYBWrnB+3xX/GPsnqx7Q8ZSxgFovcXFG9aZLWrPoAR1GxgLa7OrjCncvm1V099a0nX7QYWcsoMrtbu69fUSKHtCRlKmA2oscvIbYVWtR8hhF0JGaqYDqJ6cvezi0OvbvG1+rTLttcj3oKMlUQGur0pe1XPat49F/Oq751qdpt1XdNKWk5AeLfrv3rKQnIDu7CVP3WKdGXpLtu4LPVEAPbLJZ+NrXZkW//ia0Nv2m527Slk48uwlTExfu2bPn44CfmH3J36MNoCf2JC/qC6h8r93Se/+ijk4P+n76IUC0t1zSAyvKbsIUDX854GeVucRp420AvdrjheRlfQFdf8Ru6ZkhY9r+qUeDzS1Hrpf0wIqymzDVes5N5w9Z7GpnwbdCoU5CAqDKWjo4js6M/3sTAP31Z7aLXwzN7bHI7oamYU9qnd2EqXdDSw+/OHAZBf3c7AolEgDVzKHlq2nWy3eZAGisPSCaHrq42W75Z98J+n959uwmTHVYW22rhxgDqLmoY8yJPzxARgC6znYVRtQQ+g/b5Ueuk/TAirKbMBXrlXNstuiCz24VRuVrymhiyRX9hm1OLNEX0K22G9FEh0P/abtc/n+J3OwmTG2Y1E701Mhgn1iGbDei1/eJfQjGiL9AD9TYL88EqKZM8914mwlT75274NC2wdIPCpWS7W58U88z1j9GAHoqw8EcmQCt0P6FRJsJU3uu71P8uJZrsK5EQLUVqbfqC6j+ZvvlmQDdjLcy1CQAqi45lHqrvoDaL3b1+kjLxXgzVU2mvpVBM7e5ufe2YhzOoSZjAW25y82973oIB5SpyVhArcVuDmktxiGtijIWEK20OaAjU1U4qF5V5gI6NcL5x3qG4GM9qjIXEK2a6/Sec1dRpHR24ho+WCgzgwG1XeX0o81XWTM8vhS/FR9tlpXBgOhtp8MVEoPunk+syAjDFWRl8HAFonXOxrt0jbmLlIYjXbdgvIuETB7vQrT09pwTxdtvXypejXQfWIYBU6YlecTd/Bk55om3zpiftqxpt3gNI+6MSvaU1iUTsm4HNU6w+VTMkVJhW8gKQzbNSY8xv5HS0pQDXzHm15BUDBqfl+GPUOO8zIPGG9I3njBo3IRUnOpgVXGVzSH2n1UVr8o6w/WzqZHURTjVgfYpOdnKqUeLZ23vhqVt+6ziR0/l+DacbMXAVJ3uafPMoskrNtUfaWo6Ur9pxeSimZudnO4pMukdm6U43ZPGKTzh3L6nHigfP3bs+PIHntrn+IRz0T60WYYTzumafqe8pJvDadtCVjjlpZZpCIgi4XDa0eCxcNJd/dIRUHRz+nCmW3Dab83SE5DVY7YrMpJviOwYCfOlno1/bPgDOnbLBYPmgVn39AW0K2y/LWSlwBB1YyTOlzppHQfx4JVt7SNvObCz2PE4/gJJX0DWGxz2gxliqTFEnYzE+VJWp4Y10O6vnyLa+G35j2h0OgOKleWTxMoMpcyXijZ3IdG7j1vLLlTxcAanPaAHJ9RluVWVoW7zpYgOD+j8zNKBi5ZJfyyz0x4Q7SydsDvb7UoMifOlot2xOPZPy8O97nfzkmghpD+gKKHqHHeQb0icL0XUeG7sZYUPv3uVRRk7/GImALLanW1FRtINifOliFZdY31tLbkn9gYxXjcSMwXQ/tSjFtOTakiYL0U0MXYY9+aeuxsaGmKn68TLj8lMAWTt1E/PeR95hsT5Ui3f3Gotqoq9nti36z5gRCYBim6KOLmTwn17+1oaNi6bOuqiQmVkEqBodRNzrcgoAENUwIwMA5TyUcSMBWGICpKRaYCihGZmPbI6WUCGqMAYmQfI6susEwSSBWeICoaRmYBO5t6p7yxQQ1QAjMwEFNsWOunwrkEborxmZCogonoXI8o1MER5yshcQNHaZjhckZEuhijvGBkNyFqROSekjyHKI0ZmA4oSunGnm7vrZIiUMDJ7wFRAOd2cjqWZIZLMyOgRd0E1zc2KjHQ0RNIYmTxkM7ii20L73X2HloZIAiMA8lZkT+77pKSrIWIxAiDvPevkbdZuaWyIPDICIO/tzvJRxIzpbYhcMwIgTpGwl0/daG+IXDACoEAywRBlZZT4RQIQu3/3sCIjYwxRBkadZ/0GIAlFwuFdnr7RHEOUxihx4ngAklHk37x+p1GGop3d+7tFU0pKpjwWn0EDQPJ619WbZEKWIdv5QPdY/9hM2g++s3tDnaUBartj5IgtyWsA5LxDXnbqO2uzmw9EExdGL3ws7QlKLZQsBdDG26j+L5PXAMhNkfAkr99qNx+Ihr8s5WkpKWSzDVRZSwfHvbKLmgHIax95/Ua7+UCt59x0/pDFDs6IFkTJ36MAqGYOLV9N9PPLfp1cBECue3uSlxWZ3Xygd0NLD784UPf5QAKg5qKOMSeswVijkx+EAiD32Z5AIVd284E6rIOwVw+R98yUJG5El68po+ffIRr7VmIJAHkpctvnbr/Fdj6Q1SvnZJm5p0MioPV91tFPZ7cf65ecKgBAXmt/K/d9hOzmA22Y1E701EjZz0xyIqCmnmeoedolxRuSSwDIa1+ES11tC9nMB3rv3AWHtg2WflCx5ERAtRWptwKQ9+rCpS5ew7GZD0R7ru9T/HgH6f06tQCouiTtjBEAxGm3zWnwXKf7ex14K0Nt97g7/N42rQ0BkNp2uvooYsb0NQRAqovcsFnKz9HUEAD5kpzPgepoCIB8abaUFRlpaAiA/ClSGq6X9KP0MgRAfhVx/w5ZxjQyBEB+9rykFRnpYwjDFfzsDTk79Z1pYQjjXfwtUjpf5o/TwpCvFTogIhejFh1VYIYAKNpvZa7IqLAMAZBVdKf+Vbk/sWAMAVC8yCLpP7IwDAFQV8eynpvVSwVgCIC6+oDxUcSM5bshABKLhEsVfO4rrw0BUPfeVfNj89cQAKV1bLL8FRnlrSEASs/TRxGdlI+GAMiuyCTPn6rPUd4ZAqCMvafo5+aXIQCyTZgvRQdv6D20yrqwYsSA+9ul/Pg8MgRAtgnzpTqGT63f1PtpogdH7qq94BeyHiFfDAGQXeJ8qaOheqKKO+lsvz8RVVdJfJS8MARAdnWbL3Xp7KM7+lfTK73aO5ydcNxF5hsCILu6zZfa3yMUuo1o47AF559X0ST9sQw3BEB2ifOljg9e2bjv8odoTWhe43vfm67i4Uw2BEB2ifOlnhkd/bJlED3XM7oCe6mXovlSxhoCILvE+VJrS6JfagbQgW80i1Pv5GemIQCyTZgv9XHfJR9FSu4jKpt2+LWRP1b6sAYaAiDbxPlSr4/vPXThWaJT0/sPWaz8l2uaIQBy1w4l79R3zyhDAOSufS5nLXrMHEMA5La68CxfHscQQwDkPtdTp71mgiEA8tT/3OjHiowMMARA3qoLl3o9H5nb9DYEQF6rm+PfY2lsCIA4nZb+UcSM6WoIgDh9InW+UK60NARAvCKl4VM+PlxuQxgwZVpvtvr7eDkMYcSdgTVX+Lgio+yGMGTTxCK+bgtZZTQEQGYWuVHW2GnH2RsCIIP7xO8HFA3Fz/oNQCb3AwXzhXKVMGRz3nibAEjvIuHwQf8ftWXr3UWzQp2CAMjsdh4I5GFbtoc6BQGQ+a3yf0VGoc4AKA96TcWsxRwlAIUAKB+KhB/1+RFDiV8kACFWaYCWjB7yRPIKABnUwwHs1KcD2npt6ycD/py4BkAmFd2p9+94oUQCoMpaOjhuw3qi0tcTiwDIrCKrfX9IAVDNHFpuPYFdw5NjaQDIvN7y69jpeAKg5qKOMSeo/V9L3kkuAiDzetvfnXpxG6h8TRm13vQj4RznAGRikXC5fw8mAlrfZx395nbxVgAys+P+PZQIqKnnGZrTd/DgwclteQAytj0+fRRRBFRbkXorAJlbnT9jGQRA1SWHUm8FIJOrmyb7BL824a2M/K5ln+IHAKD87nPVKzIAyvei20KfKvzxAJT/7f5C4Q8HoIKo44eqVmQAVBhFVG0LAVChVDdRyXk1Aaig+kz6T8RwhYJqpvQVGca7FFbRnfq3gn4OrAAo6OqCOHJaXgCkQ783FxEA6dAef96pVxEA6VHdhJ8E/RS8BUC6pNn0VacBkEatvcG8FRkA6VR0p/7VoJ+DywBIr+oeCfoZuAyA9OsDfz+KyAuA9OtwAPOFPAdAOhYJT1R0fnrpAZCevR/0E3AaAGnb+5NMWJEBkL7tvPlaJcecSQ2AdC5yi4+fqvcWAGnfO7nvEmAApHtflWq9Uw9A+hcJhz8M+jlkDIBMaLe+m0IAZEr/rOeKDIBMaaeeRy0CkDnVhTcG/RTSAyDD+jLoJ5ASABnWPM1WZABkWnXh0r1BPwchADKvui1BPwMhADKzbbqsyADIzPbqslMPQKZWF/5R0E/BCoDMTYs9egAyuk2Br8gAyOyiO/XdPwSEAVPIXXX3dV6I/yox4g65r3F37Mzx1kUM2UTu+3O4dHcoLgiAkJfqQgCEOIU6BQEQ8lKoMwBCnkoACgEQYgVAiBUAIVYAhFgBEGKVDujMS12XAQjlKA1Q0wLhuCEAQjkSAFXW0sFxVHk1ACHnCYBq5tDy1UT/BUDIeQKg5qKOMScACLlK3AYqX1NGAIRcJQJa32cdARBylQioqecZAiDkKhFQbUXqrQCEciQAqi45lHorAKEc4a0MxAqAECsAQqwACLECIMQKgBArAEKsAAixwnAFxArjXZBRARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVYAhFgBEGIFQIgVACFWAIRYARBiBUCIFQAhVgCEWAEQYgVAiBUAIVb/D7TUts6MqvGgAAAAAElFTkSuQmCC)
CFA model X
model.x = "
X =~ x1 + x2 + x3
"
cfa.x = cfa(model.x, data2)
summary(cfa.x, fit.measures = T, standardized = T) # just identified model
## lavaan 0.6.15 ended normally after 22 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 6
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 0.000
## Degrees of freedom 0
##
## Model Test Baseline Model:
##
## Test statistic 219.165
## Degrees of freedom 3
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 1.000
## Tucker-Lewis Index (TLI) 1.000
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -241.345
## Loglikelihood unrestricted model (H1) -241.345
##
## Akaike (AIC) 494.690
## Bayesian (BIC) 508.595
## Sample-size adjusted Bayesian (SABIC) 489.684
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.000
## 90 Percent confidence interval - lower 0.000
## 90 Percent confidence interval - upper 0.000
## P-value H_0: RMSEA <= 0.050 NA
## P-value H_0: RMSEA >= 0.080 NA
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.000
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X =~
## x1 1.000 0.667 0.917
## x2 2.193 0.142 15.403 0.000 1.464 0.976
## x3 1.824 0.153 11.883 0.000 1.217 0.872
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .x1 0.084 0.020 4.140 0.000 0.084 0.159
## .x2 0.108 0.074 1.455 0.146 0.108 0.048
## .x3 0.468 0.091 5.124 0.000 0.468 0.240
## X 0.446 0.087 5.135 0.000 1.000 1.000
semPaths(cfa.x, what = "path", whatLabels = "std", rotation = 2,
edge.color = "black", edge.label.cex = 1, residuals = F)
![](data:image/png;base64,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)
CFA model with X
& Y correlation
model.x.y = "
Y =~ y1 + y2 + y3 + y4 + y5 + y6 + y7
X =~ x1 + x2 + x3
"
cfa.x.y = cfa(model.x.y, data2)
summary(cfa.x.y, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 33 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 60.292
## Degrees of freedom 34
## P-value (Chi-square) 0.004
##
## Model Test Baseline Model:
##
## Test statistic 633.950
## Degrees of freedom 45
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.955
## Tucker-Lewis Index (TLI) 0.941
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1413.012
## Loglikelihood unrestricted model (H1) -1382.866
##
## Akaike (AIC) 2868.024
## Bayesian (BIC) 2916.691
## Sample-size adjusted Bayesian (SABIC) 2850.505
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.102
## 90 Percent confidence interval - lower 0.058
## 90 Percent confidence interval - upper 0.143
## P-value H_0: RMSEA <= 0.050 0.030
## P-value H_0: RMSEA >= 0.080 0.812
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Y =~
## y1 1.000 2.214 0.850
## y2 1.323 0.174 7.600 0.000 2.930 0.747
## y3 1.054 0.148 7.146 0.000 2.334 0.716
## y4 1.276 0.137 9.295 0.000 2.826 0.849
## y5 0.947 0.110 8.575 0.000 2.098 0.808
## y6 1.145 0.148 7.747 0.000 2.536 0.757
## y7 1.200 0.138 8.674 0.000 2.658 0.814
## X =~
## x1 1.000 0.670 0.920
## x2 2.178 0.139 15.678 0.000 1.460 0.973
## x3 1.818 0.152 11.975 0.000 1.218 0.872
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Y ~~
## X 0.735 0.209 3.513 0.000 0.496 0.496
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .y1 1.883 0.386 4.878 0.000 1.883 0.277
## .y2 6.787 1.229 5.523 0.000 6.787 0.442
## .y3 5.172 0.920 5.624 0.000 5.172 0.487
## .y4 3.081 0.631 4.884 0.000 3.081 0.278
## .y5 2.333 0.447 5.224 0.000 2.333 0.346
## .y6 4.791 0.873 5.486 0.000 4.791 0.427
## .y7 3.589 0.692 5.185 0.000 3.589 0.337
## .x1 0.081 0.020 4.130 0.000 0.081 0.153
## .x2 0.121 0.071 1.708 0.088 0.121 0.054
## .x3 0.467 0.090 5.160 0.000 0.467 0.239
## Y 4.904 1.090 4.499 0.000 1.000 1.000
## X 0.449 0.087 5.175 0.000 1.000 1.000
semPaths(cfa.x.y, what = "path", whatLabels = "std", rotation = 2,
edge.color = "black", edge.label.cex = 1, residuals = F)
![](data:image/png;base64,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)
SEM model with Y to
X path
model.y_x = "
Y =~ y1 + y2 + y3 + y4 + y5 + y6 + y7
X =~ x1 + x2 + x3
X ~ Y
"
sem.y_x = cfa(model.y_x, data2)
summary(sem.y_x, fit.measures = T, standardized = T)
## lavaan 0.6.15 ended normally after 37 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 21
##
## Number of observations 75
##
## Model Test User Model:
##
## Test statistic 60.292
## Degrees of freedom 34
## P-value (Chi-square) 0.004
##
## Model Test Baseline Model:
##
## Test statistic 633.950
## Degrees of freedom 45
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.955
## Tucker-Lewis Index (TLI) 0.941
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -1413.012
## Loglikelihood unrestricted model (H1) -1382.866
##
## Akaike (AIC) 2868.024
## Bayesian (BIC) 2916.691
## Sample-size adjusted Bayesian (SABIC) 2850.505
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.102
## 90 Percent confidence interval - lower 0.058
## 90 Percent confidence interval - upper 0.143
## P-value H_0: RMSEA <= 0.050 0.030
## P-value H_0: RMSEA >= 0.080 0.812
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.062
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## Y =~
## y1 1.000 2.214 0.850
## y2 1.323 0.174 7.600 0.000 2.930 0.747
## y3 1.054 0.148 7.146 0.000 2.334 0.716
## y4 1.276 0.137 9.295 0.000 2.826 0.849
## y5 0.947 0.110 8.575 0.000 2.098 0.808
## y6 1.145 0.148 7.747 0.000 2.536 0.757
## y7 1.200 0.138 8.674 0.000 2.658 0.814
## X =~
## x1 1.000 0.670 0.920
## x2 2.178 0.139 15.678 0.000 1.460 0.973
## x3 1.818 0.152 11.975 0.000 1.218 0.872
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## X ~
## Y 0.150 0.035 4.280 0.000 0.496 0.496
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .y1 1.883 0.386 4.878 0.000 1.883 0.277
## .y2 6.787 1.229 5.523 0.000 6.787 0.442
## .y3 5.172 0.920 5.624 0.000 5.172 0.487
## .y4 3.081 0.631 4.884 0.000 3.081 0.278
## .y5 2.333 0.447 5.224 0.000 2.333 0.346
## .y6 4.791 0.873 5.486 0.000 4.791 0.427
## .y7 3.589 0.692 5.185 0.000 3.589 0.337
## .x1 0.081 0.020 4.130 0.000 0.081 0.153
## .x2 0.121 0.071 1.708 0.088 0.121 0.054
## .x3 0.467 0.090 5.160 0.000 0.467 0.239
## Y 4.904 1.090 4.499 0.000 1.000 1.000
## .X 0.339 0.067 5.043 0.000 0.754 0.754
semPaths(sem.y_x, what = "path", whatLabels = "par", rotation = 2,
edge.color = "black", edge.label.cex = 1, residuals = F,
sizeMan = 8, sizeLat = 8)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAkAAAAJACAMAAABSRCkEAAAC7lBMVEUAAAABAQECAgIDAwMEBAQFBQUGBgYHBwcICAgJCQkKCgoLCwsMDAwNDQ0ODg4PDw8QEBARERESEhITExMUFBQVFRUWFhYXFxcYGBgZGRkbGxscHBwdHR0eHh4fHx8gICAhISEiIiIjIyMkJCQlJSUmJiYnJycoKCgpKSkqKiorKyssLCwtLS0uLi4vLy8wMDAxMTEyMjIzMzM0NDQ1NTU2NjY3Nzc4ODg5OTk6Ojo7Ozs8PDw9PT0+Pj4/Pz9AQEBBQUFCQkJERERFRUVGRkZHR0dISEhJSUlKSkpLS0tMTExNTU1OTk5QUFBRUVFSUlJTU1NUVFRVVVVWVlZXV1dYWFhZWVlaWlpbW1tcXFxdXV1eXl5fX19gYGBhYWFiYmJjY2NkZGRlZWVmZmZoaGhpaWlqampra2tsbGxtbW1ubm5vb29wcHBxcXFycnJzc3N0dHR1dXV2dnZ3d3d4eHh5eXl6enp7e3t8fHx9fX1+fn5/f3+AgICBgYGCgoKDg4OEhISFhYWGhoaHh4eIiIiJiYmKioqLi4uMjIyNjY2Ojo6Pj4+QkJCRkZGSkpKTk5OUlJSVlZWWlpaXl5eYmJiZmZmampqbm5ucnJydnZ2enp6fn5+goKChoaGioqKjo6OkpKSlpaWmpqanp6eoqKipqamqqqqrq6usrKytra2urq6vr6+wsLCysrKzs7O0tLS1tbW2tra3t7e5ubm6urq7u7u8vLy9vb2+vr6/v7/AwMDBwcHCwsLDw8PExMTFxcXGxsbHx8fIyMjJycnKysrLy8vMzMzNzc3Ozs7Pz8/Q0NDR0dHS0tLT09PU1NTV1dXW1tbX19fY2NjZ2dna2trb29vc3Nzd3d3e3t7f39/g4ODh4eHi4uLj4+Pk5OTl5eXm5ubn5+fo6Ojp6enq6urr6+vs7Ozt7e3u7u7v7+/w8PDx8fHy8vLz8/P09PT19fX29vb39/f4+Pj5+fn6+vr7+/v8/Pz9/f3+/v7///+VdLTTAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAgAElEQVR4nO2de2AU1aHGTwBTgQBRw0NTiURDUCokqHgtIBVKuVWoj9YLIgWx92J8e80VSWhrKFBta70URcRHTVtEi0XbWIjX+hYDhLA8FNsqDeGikhQMXjbJ5vx3Z3Yzm9l57c6emT3nzH6/P3YnM0POzOGX/ebsnDmHUAAYILwPAMgNBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTHgl0KIJLrnZo4JBFG7175VA4//R6oqDZR4VDKJwq3/PBPrC3f7HIZCncKt/CBQMIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYCK4Ar1GYixKXA2BvMVeoJPVoweMebDTsFYegf7xkEp1zprE1RDIW+wFquhX+fw9faoMa+URKMYtk7sTV0Agb7Gt/y/7rlBe55xlWC2+QNX5HcrrlBnRH97K+8iwGQJ5i6n+/5KzkdJ9uWv+NqlB+eneIX79Afsm0G5SR+nBnFp1OfK1Jcb9IZC3mD+BKoa3dk++IubNnnPmG7aKLxAtVS6bV+WdUBefzW81boVA3mKu/y+KFj6W97G69GIeuSxs2CqBQFUFXXRcVPzOUctM+0Mgb7G4BtqSM2BtdOHw5pUFMw0bJRCoidSHSL269IecT0z7QyBvsbqIHjswvvIFYrgIlUAgWrp4SWFEXbjqCvP+EMhbLOr/yQEFtyvqTFKvIvaTTYkbZRCoakRRpfre1m+1eX8I5C3m+m8e8vNn+7xDXyWblR8eJ/sTt8ogUBMhIfV9E2k07w+BvMVc/zMv6qLTzw9HZhY8uGnZwDmGrTIIRIvLo2+LB0XM2yCQt5jqf32/XZT+tf8yevLO8QMvWHHSsFkGgdr6P2y/PwTyluDdTI20V+Yesd8fAnlL8ARqJqTaYX8I5C3BE6iz7oDT/hDIW4InUBIgkLdAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkzILxCme+KK9NM9YcI5vkg/4VzqBWKSTR/JfO1m/r8TBvkHh7rlIRAU8gcuNctHIBjkA3wqlpNAUMhreFUrL4EyXmzgyRqB1DN9MPOlBp8HufxdchGo45JtmS826OyYEM4SgRR2Xvh/XMoNMOGy97mUy+lipOp+PuUGlyVOzwH7CCeBEGIeowQYn4J5NYcQYp7CK8D4CYQQ8xReAcZRIISYh3ALMJ7dORBinsEvwLh2KEOIeQW/AOPapRUh5hEcA4xvn2iEmCfwDDDOneoRYl7AM8A4C4QQ8wCuAcb7sR6EGDN8A4y3QAgxZvgGGHeBEGKMcA4w7gIhxNjgHWD8BUKIMcE7wAQQCCHGAPcAE0AghFj68A8wEQRCiKUN/wATQiCEWJoIEGBCCIQQSw8RAkwMgRBiaSFCgAkiEEIsDYQIMEEEQoi5R4wAy4hALfPOOuvOLw0rDWP0IcTcIkaAZUKgQ8Xla28/9SbDWoNACDGXCBJgmRCo8syjlN7Zry1xrXGUUISYK0QJMB8Fqs7vUF6nzOgacbfy/kXjicTNpmFmEWJuECXAfBRoN6mj9GBO7T/Ixo7te7uM+5sEQoi5QJgA8zPCShdRuirvRAOpPo2QUW8ZtpoHukaIpYw4AeanQFUFXXTcfPoKGfL743suG/Z54laLkdIRYqkiToD5KVATqQ+Revo+WUXVQPtN4lYLgRBiKSJQgPnaCitdvKQwQg+RjcrycfKLxI1WczUgxFJCpADzVaCqEUWVytul85SX58nriRstJ/tYutSjowk091fxPgI9PgrUREhIeduae+PG5YNmGTZaCoQQSwGhAszfLxKLy6NvWy4fPLrqpGGb9XRDCLGkiBVgvgrU1v9h+/1t5qtCiCVDrADzUaBIe2XuEfv9bQRCiCVBsADzUaBmQpy+rbCbMQ8h5ohoAeajQJ11B5z2t51yESHmhGgBJkqHMh0IMQeECzABBUKI2SNegIkoEELMFvECTEiBEGI2CBhgQgqEELNGxAATUyCEmCUiBpigAiHELBAywAQVCCFmRswAE1UghJgJMQNMWIEQYgYEDTBhBUKIJSJqgIkrEEIsAVEDTGCBEGI6hA0wrtM9JQEhFkfcAOM44VzyghFiGuIGGMcpLylJVjRCrAeBA4yvQMkUQohFETnAeAoUNcjZIYSYisgBJoBATgeAEKOCB5gAAllv23m1tnR49tAzK04o7f4bz7jg+UwdGmd6z37/jEEja2hvLYgHR4GiBjVabejeM2Vqz2KkdPbet0sqKJ0zNVSbuyuDR8cN3dl3n3td46ZB63trQTw4C9R4ntUF4h35p2pVuK3vMUo3DqMt/UKUzr05k4fHC93Zt6h/YN+bH68FAeEpkFq4tUH0Ia0KDzyivKwdTrecrr5fnLFD40r87OnYH7S8ccaz8VoQEK4CqVgb1FuFCnu/uow+M1pZ2FSYoYPiTO/Z7zmFkO/GFtVaEBDuAlkbpBOoY3nenRH6VFQgIf8GvSd+9p8Wrjy668IfUq0WBIS/QJYG9Qr0SdlEtS1fV6C8rBufwcPiSPzsn7pAeXnpzHgtCIgAAlkZFK/CzjG3Rkd4ben7IaULFmb0uLgRP/t1Y5SXFwvitSAgIghkYVCsCje8SjcP2BYKhfZSevWsI6/kvcfh4DgQP/tD+UsPvjXmjt5aEA8hBDIbFKvC8YtoTfTbxnxKj19/+tjneBwbB+JnT9+fOmjkfSd7a0E8uHXnSPxKx6Y130N23hMT+x6YhigdyhwNCpcLegXpJzvGGYcFFBJhurQ6GpSFHTvE7sTRizACORuUfSEmR4CJJJCjQVkXYpIEmFACORqUZSEmS4CJJZCjQdkVYrIEmGACORmUVSEmTYCJJpCTQVkUYvIEmHACORmUPSEmT4CJJ5CDQVkTYhIFmIACORiUJSEmU4CJKJCDQdkRYjIFmJAC2RuUFSEmVYCJKZC9QVkQYnIFmKAC2RsU/BCTK8BEFcjWoMCHmGQBJqxAtgYFPMRkCzBxBbI1KNghJluAZUKg+mh/3iLD2qQC2RkU6BCTLsAyIdDjX3lI4XHD2uQC2RkU4BCTL8AyIVDlGKu1KQhkZ1BwQ0y+APNRoOr8DuV1ygx67VVW+6cikI1BgQ0xCQPMR4F2kzpKD+bU0rIpk/NK/ssYOykJZGNQQENMxgDzM8JKF1G6Ku8EHXzq0t/dfcq/GrYmF6h3mC5t+Vb1alzNr2CGmIwB5qdAVQVddNx82vX0TuWH1eSNxK3JBNIN0xVf/tZ9DQ0Nh2hAQ0zKAPNToCZSHyL1PT8cIb9M3JpMIN0wXfHlc7XfFsQQkzPAfG2FlS5eUhihR95VL6aPkvWJG5NHmH6MqehyZ79vDzn7/o7oiuCFmJwB5qtAVSOKKil9k/xMWV6fsydxYxoCHSBVH/1xRGyYrsCFmKQB5qtATYSElAuYGXm3Pbek/y2GjWkI1K1W8aNnx9YELMRkDTB/v0gsLldfO5eNzxv/SLdhWxoCRXm9X89vClaIyRpgvgrU1v9h+/3TEGjDVRFKnyjtWRWoEJM2wHwUKNJemXvEfv9UBdrwanz5b6fe/eGWwrXa9gCFmLwB5qNAzYRUO+yfqkDqMF3acsPlg0t0WRicEJM3wHwUqLPugNP+qd3K0GG+qxEuC0iISRxgAncoM2E2KCAhJnOAySSQhUHBCDGZA4ynQMlnLDRiMigQISZ1gHH9BEo+4ZwRk0EBCDG5A0wygcwGyR9icgcY32ugqD/uQshokPQhJnmAcb6IVgX65vQ33fw7o0GSh5jsAca7FaYG2NtXTnrVxT80GiR3iMkeYLwFihXvTiGDQVKHmPQBxl2gHlwpZDBI4hCTP8BEEcidQgaD5A0x+QNMHIFcKZRokLQhFoAAE0kgNwolGiRpiAUhwMSZ7ilGygolGiRniAUhwISZcC5OqgolGCRliAUiwESZ8lJPigolGCRhiAUjwEQUKFWFEgySL8SCEWBiCpSiQnqDpAuxgASYoAIdv/GMC57vWd49bfCFv6O6kRV60RskWYgFJcAEFWjO1FBt7q7o4ufD7vvk5YKtupEVdOgNkivEghJgYgrU0i9E6dxYM+3XxcrL8iv1Iyvo0BkkVYgFJsDEFGjL6crL2oujy2vGKi+PFCeMrKBDZ5BEIRacABNToGdGKy+bCqPLB76ytn3byMEJIyvo0RkkT4gFJ8DEFOipqEDDYz/8oYiM/s+RiSMr6Ok1SJoQC1CAiSlQXYHysm689uNJ+t8TY0vxkRX09BokSYgFKcDEFKil74eULlgYXf543jFKv73MMLJCAr0GyRFiQQowMQWiV8868kree9GRFTrPXvDBL/I/No6skEDcIClCLFABJqhAx68/fexzNDaywo6LB03dQU0jKyQQN0iCEAtWgAkqkA32NzjiBokfYsEKMPG6czhjq5BmkC7EIk3r7r528oQJk6+9e11TJJ3S2LAu368Ay0z9WyBWh7Lk2CmkGdQTYp0v31B8Vc2mxsOtrYcbN9VcVXzDy51pnlla2JXvW4Blqv5NiNSlNTVsFNIMUkPs+IqSBfUJwnTWLyhZcTzdIt1iX75vAZa5+jcgn0B2CvUYFC5791cly1vN21uXl/yqK/1CU6fLvvwG31pgEMgVlgr1GPTC4Fss/vtUWm+5dB9Lqamx71L78ge/4FepEMglVgpFDao9/w2r/WO8cX4tW7HJ4VQ+BHKNhUKN522rmva50z/6fFqVzXdJ3tDNq3wIlAZmhRpPm2vq8ZFIx9zb2Qu253Ze5UOgtDAqtHRu0svkrrk+ftfIr3wIlCYJCj07Lcnfv0rHtGe9KdoMx/IhUNr0KrT3/KOp/IOj5+/1quxEeJYPgRjoUajzUof2j543LvXlW2mu5UMgJqIKra5IdfeK1V4WrsG1fAjEyJvTryhJKUBUjpb4cFfjONfyIRAz//FA6vs+sNLr0ildybV8CMRK52ibGwhWtI72/CqEc/kQiJXNC93svXCzx8XzLh8CsXLDVjd7b73B4+J5lx9wgTpNH+9eCxQpTuE7vF46iz3uo8i7/IALtLDIuMZrgRpnmdctJ49G33f0ucG0bVaj/+UfOq0seqkzv997vpfvUP+1lw8+57Z/GlbKJdDviUuBdl6tLR2ePfTMihOU7p8xaGSNw79YZ7Gx42unfaq8dV92mnny1pp19r9LP7qMdiwWo8skLZ/+hixXXv9Efmje5FS+ds768pOdv339ryHX/bZm0DcMnQCkEujQGSNdCdS9Z4o2Y3OkdPbet0sqaPe51zVuGrTe/t/ctcli5Xt9FiivvyYW/1m/v9v+d+lGl4kfi9XoMknLp9d+ZQ89VniJRZPLoXztnPXlJz1/2/qPDP2O8rqBvJa4WnyBqvPVi4IpM5STnz7n3+0Espzu6Y78UzWBtvU9RunGYbSFKB/535tvX/41O63W3p7zJj1+5tctuuDsvMb2V+lHl4kfi+XoMroTsC7/s+ETIzcP+MBii0P52jnry7c9f618U/3/JWcjpfty17QQtQ/b4Z40jyO+QLtJHaUHc5Sj/1lhm41AtvOFxeeMP/CI8rJ2OKVjf9DyxhkOt7Evb7Za+8XZ47ruOSVksaX5cttfpR9dRjsWm9Flek/Buny6mXyXrLHa4FB+/Jx15duev1a++ROoYnhr9+QrusP725UfXiCvJG4VXyBauojSVXkn6K5Tt1BLgXomnFtrhOoEUtn71WWU7jmFkO8q9WpHUZvlYf2R3HLKEqsNrefY/ir96DLasWijy5h21mbNu8i6fDqPTLdc71B+/Jx15duev1a+uf6/KFr4WN7HseV3h15saPVJIFBVQRcdN5/+39jbKYtAHcvz7ozQTwtXHt114Q9dC0T/jYz60mp9W5Htr0oYXabnWLTRZWz/AydYl98xgYyyvDpxKF87Z335tudvLxDdkjMgNpZA+72nTDI2IyQQqInUh0g9XTHo+Zdfnjns5V2JW1OMMPpJ2UT1WdOnLlBeXjrTvvwp1hFCQ+SXluubp9j+KsPoMr3HYjW6jHYKNuUv7fPkqTe5LF87Z335tudvH2FK7A2Mrnx91NBHTd86SSAQLV28pDBC7+n5G1mUuNHpIlr3n9Y55tZoJ9F1Y5SXFwvsy7/W8iKW0o/IY5brd1xn+6v0o8tox2I7uox2Atblv933brqS/MFd+do568u3PX/bi2hKnxxQoPa/3po7x+LTUQaBqkYUVfYs2rbCbIgJtOFVunnAtlAotJceyl968K0xd9j/i7tetF5vJ9CLd9n/Lt3oMtqxOI0uY19++7nnfUm7Lh76v67K185ZX37S8zfXf/OQnz/b5x0aKbrKan8ZBGoiRGv/pCfQ+EW0JvrplU/p+1MHjbzP4bHOJ2w6U9gJ9MAT9r9LP7qMdixOo8vYlv+DPmofxd25V7oqP37O+vKTnb+5/mde1EWnnx9+i9y0WsXwSKUMAtHicm3JrUDuabT4T1KxE+hKr29lWJT/Mok9wvMAMX90eV2+qf7X91OuOv/af9nTPZcQTydulkGgtv4P2+/v+c3UUa5uZnaM8vpmKufyg3czNdJemWu+BRXH8+4c87a42XvLPI+L511+8ARqJqTaYX/PBXrp+272/v5LHhfPu/zgCdRZd8Bpf++7tJa46VJa4n2XVr7lB0+gJPjQqd6pt4OBGj861XMtHwIx8ub0K85O/bGa8455W7rKsfN4lg+BmIg9WHhLqrvf4s+DhTzLh0AM9Dza3DUx1UeLJ/oy1B3X8iFQ2vQOrrAv1cENfBrojmf5EChNEoZ3qU1teBXfhrnjWD4ESgvjAFNVc5J+wRuZU+VFydbwKx8CpYHlEHdJvmDpnHsbe8H23MarfAjkGqtBNs9tWDrN8Trk6DSfJ9PgVT4EconlML/nNmCY3xTJcoGsBxpX/VEHGq+w+RA4WpGZgcbty8dA47YIMNVBzJ9w2XurS2osOnG21ZSszsxUB/blb/dtPjMIlDJ2k63E/IlOZ3JsVcmCrQmydG1dULLKh/sX1tiX79t8ZvILxHu6px5/Pr8orL51bp5XPOuBTY3Nra3NjZsemFU8b3Nmp3uyKT98keNA9ukj/XRPvCec6/FHR2TXE3ddM3XChKnX3PXELh4TzmW0fOknnMsEDlNemv0BmUFQgXrHd9HGWnEaXyXuz76mDBwbI00ZaAlmECEF0o3vEh9rxWF8lbg/4fIdGTk+JnaUh3kfgpcIKZBufJf4WCt246vo80uOGZHFn1naDUIKpHu2WRtrxXZ8FZ0/fs2I7DG6maUDgOgCaWOtaOOrmNBdP9faPB8vGjt9v5+SQUQXSBtrRRtfxQjaX5wRXaCEsVbM46vAH96ILpA21or1+Co6f8LX+zoZqrd0Xx+YlpjQAqnjm/SMtWI5vor+80eOFphGcFpiQgukjm+ijbViMb6K3h9JWmAawWmJiSmQ/U0LHXp/IuWSXQs1lHO4PecHIgqUkj6G62fzZAKCI90B2yCeQKnpg/aXIIjWnSNFfRL96cpYVzEvOZaR/pF+I1aHslT1MXz+LH3Ii1PINA8FoiUmUpfWlPUx+CNZC0wjGC0xcQRKXR+DP+Gy992VLQo7fetin0FEEciFPsbr52csbrHKwbJneB8BO2II5EYftL+EgrNA0eJd6QN/xIKvQOpED+70MfnzYru7gsWi3WaGBnngKpDaT/6b09908++M/jSUuxrgWzQ6ZLsFY4KnQNEh+N01ZY3+SNsC05C+JcZRIG2uNBeYrn/k6sRhhewdO6QSyHz9/CPpO2aFf8T7CNjgJ5DbTx+0v4REjO+BUgL+iIg8Apn92X6f298hJvdt530EDEgjkNkf6VtgGlK3xMQVqHd8hXf+ZWDRCuX98OyhZ1aciO8gfwtMQ+aWmKgC6cZXOD6s8qPf5m6gkdLZe98uqdD22B2cQQrC5bt5H0LaiCqQbnyF+mHKy5WL6ba+xyjdOEzb4+jH7koUmY9TnuhHOPwX6GT16AFjHjQOMJc8wuLPFn7xCaUnvraGHnhE+WHtcIaDBN7jv0AV/Sqfv6dPlWGtC4EULi+4PtaBeO9Xezr/fCb1LTAzHZ/xPoI08V2gL/uq179zzjKsdifQ6z8ZuV5561ied2fscapw+YfpHKW4fCjrFZ1vAlXnq58RU2b8bZLa/L53iOHJdRcCtap/nI8r+39SNlG79RqcFpiGrC0x3wTaTeooPZgTGwpnzznzDZtdCLRisvKybgztHHOr9iCMpN3onZC1i71/EVa6iNJVeerXNi/mkcuMH9CpCrThVbpv4KOH3hj1I7p5wLZQKLRXXXtjAG9qNNzI+wjSwj+Bqgq66LjoB8/hzSsLZhq2piqQOr7C/3x90Kgfd9Ka6M37fE8OF3iFfwI1kfoQ0UbGfIF8lLg1tVsZuH8qPD62wkoXLymM0BcmqSm2n2xK3JiSQNb+hJ9O5wBl4GkJW2I+ClQ1oqiS0lfJZmX5cbI/cWMqAtl8/sjaXkmOjGfmo0BNhIQojcwseHDTsoFzDBtTEMjGnwC2wDRkbIn5+UVicbn6evLO8QMvWGH8T08ukI0/genEYYWEHTt8FKit/8P2+ycVyO76ueVJF0clHU+28D4Ct/gmUKS9MveI/f7JBEL7SxJ8E6iZkGqH/ZMIBH9kwTeBOusOOO3vLJCtPz/5s6ujkpA//4T3EbhDyA5ltv4EuAWmIVtLTESBbP0JdAtMQ7KWmIAC2V//1Ej4RZt7ltbwPgI3iCeQw/XzgYB1Q7Smw/HiUTSEEwjtL7kQTSAHfw66K0FmJDpVwQRy8Gf7RHclyMxEeR52FksgB3+yogWmsXOcNC0xoQRyuv5ZWuWuALmR52xFEsjJny+nStjZKn3CU7/kfQgpIpBAaH/JiDgCwR8pEUYgR392v+b6gKTnNTlG7BBluidHf8LSj6acBg1yPOwsyIRzzvklY2dzduR4fFuMKS9N/vQOT3b8xjMueF73ng3IdPZCCGT0Rzc8GZ0zNVSbu6v3PfjIdfYiCGT6/NENT9bSL0Tp3Jvj71mAXGcvgEBW1z/xoTm2nK68rL04/p4VyHT2/AWyvH6OV+Ezo5WXTYXx96xAprPnLpB1+ytehU9Fq254/D0rkOnsuQpEbNvv8SqsK1Be1o2Pv2cFMp09T4EIIXbf/8SrsKXvh5QuWBh/zwpkOnvOApFG603x4cno1bOOvJL3Xu97NiDT2XMUyGm6sN7hyY5ff/rY52jvezYg09lzF8jpADr/nqljEZm/GwdpFwruAjntUbU8U8ciMsureB+BE/wESj7fpUQ9g/1E7N7gPAVKsoPYFZdBhP5D4tadI3nBf5LqEV8/qfkT7yOwR5QOZUBShOnSCuREWIGedhgfL/s4IuzY2KIKtL1Mih7BmSJcJurDzoIKhBaYAWFbYoIKVHU/w7EEElG72Asq0DoEmIHwOt5HYI2gAgFZgECACREF2n4T27EElZtEbIkJKBBaYDYI2RITUKDsfJA5FURsiYkn0Af4CtGOcNkHvA/BhHgCnfyU9ViCy6fizfQgnkBAKkQTqPkY+7EEmWPNvI/AgGAChctDHhxMgAmJNuyUYAKhBZYM0VpiGRCo9vLB59z2T8NKa4GE/KZDLET7lsx/gdaQ635bM+gb3YlrrQW6JwvHQnRLwz28jyAB3wWKDP2O8rqBGMZZRSssIPgmUHW+OrnXlBktpFZ5P0weTdwMgQKCbwLtJnWUHsypDe9vV356gbySuNlCoPBPPTqWwPNTgVpi/kVY6SJKV+WdiC6/O/TiSOJWC4HQAksVkVpi/glUVdBFx81Xl9rvPWWS8RkLs0BogaWMSC0x/wRqIvUhUq8svD5q6KMR41aTQB3ZOBp9ujSUCzN7rI+tsNLFSwoVcbbmzmkz728S6NgGj44kK9ggzB0fHwWqGlFUqTTji66y2h+tsIDgo0BNhIQofYvctFplX+JGCBQQ/PwisbhceXm6ZyAyw7O5BoF+jABzyYYf8z6CGD4K1Nb/Yfv9EwVCC8w1orTEfBMo0l6Z6zA+QoJAolSGVAjyR+ebQM2EVDvsnyDQT/EgcxrcL8Q3974J1Fl3wGn/BIE+FXocUlHpFKLzuGAdyoBsCCCQiM9bSoIAVcdfoO3l3U47Anu6y/kbxF0gtMAYEKAlxl0gdOJggX/HDt4CRWYL1DlKPsKzTf0cMgxvgYDkQCDABF+BduEeKjMb+E4nz1UgtMA8gHNLjKtAaIF5Ad+WGE+BdmAoKS8Il+3gWDpXgfZ6VHiWszcQAmG6p+yE24RzN3tUMOALtykvw5dYPOwD0qPtEm5Xk9wEQgvMS/i1xHgJJMB95CDB7xs1XgJNwoPMntIwiVPBvARq5VRuYOFVofzmjQeBgINAhIR5fvMVWHaECY//TQ5FEuLwyCpIl4dJdggUe1Q+48UGHk71yksgGOQxvKqVk0AZLzULyCaBMl5oVpA1AmW8yKwhGwSCP36S+dpFd45gwK3+0aEsGHCrfzwXFgy41T8ECgYQCDABgQATEAgwAYEAExAIMAGBABMQCDABgQATEAgwAYEAExAIMAGBABMQCDABgQATEAgwEWyBnvqmaRUE8hZu9Z8JgT4bPdW0DgJ5C7f691+gHdMGEAjkN9zq3zeBqvM7lNcpM+iHK1eWQCC/MdX/X/Rxk+gAAAI3SURBVHI2Urovd43f9e+bQLtJHaUHc2rV5W9BIL8xfwJVDG/tnnxFdDZIP+vfvwgrXUTpqrwT6iIE8h1z/X9RtPCxvI+ji3IKVFXQRcfNjy5CIN+xuAbakjNgbWxJToGaSH2I1EcXIZDvWF1Ejx3Ys1JOgWjp4iWFsQkZIZDvWNT/kwMKbo8tSSpQ1YiiytgSBPIdc/03D/n5s33eiS5KKlATIaHYEgTyHXP9z7yoi04/PzoFgqQC0eLyngUI5Dum+l/fbxelf+2/TF2WVKC2/g6DsUIgbwnezdRIe2XuEfv9IZC3BE+gZkKqHfaHQN4SPIE66w447Q+BvCV4AiUBAnkLBAJMQCDABAQCTEAgwAQEAkxAIMAEBAJMQCDABAQCTEAgwAQEAkxAIMCE/AJhuieuSD/dEyac44v0E86BLAUCASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBgAgIBJiAQYAICASYgEGACAgEmIBBg4v8BwPR/p5uCOuAAAAAASUVORK5CYII=)