seminR
Brandon Gavett
2022-04-13
We will explore the lavaan package and how it can be used to perform structural equation modeling in R.
Code is available at https://github.com/begavett/seminR
Required Packages
# if necessary: install.packages("pacman")
library(pacman)
p_load(tidyverse, lavaan, psych, corrgram, semPlot, blavaan)
tidyverse: a suite of data toolslavaan: the focus of today's workshoppsych: statistical tools relevant to psychological researchcorrgram: nice correlogramssemPlot: used to draw path diagramsblavaan: Bayesian lavaan
Also highly recommended
(but not used today)
semTools: package that nicely supplements lavaan
Import Data
ex5_12 <- read.table("https://www.statmodel.com/usersguide/chap5/ex5.12.dat") %>%
set_names(paste0("y", 1:12))
Describe Data
describe(ex5_12)
vars n mean sd median trimmed mad min max range skew kurtosis
y1 1 500 0.01 1.39 0.02 0.01 1.46 -4.08 3.58 7.66 -0.04 -0.27
y2 2 500 0.05 1.43 0.08 0.05 1.37 -5.19 3.94 9.13 -0.06 0.10
y3 3 500 0.00 1.38 -0.09 -0.03 1.48 -3.65 4.19 7.84 0.20 -0.43
y4 4 500 0.10 1.43 -0.01 0.11 1.41 -4.55 4.09 8.64 -0.03 0.04
y5 5 500 0.08 1.27 0.05 0.09 1.27 -3.73 4.86 8.60 -0.07 -0.01
y6 6 500 0.07 1.33 0.01 0.05 1.35 -3.20 4.27 7.48 0.24 -0.17
y7 7 500 0.05 1.52 0.08 0.07 1.57 -4.30 4.34 8.65 -0.09 -0.16
y8 8 500 0.06 1.41 0.13 0.07 1.36 -4.40 3.99 8.39 -0.08 0.02
y9 9 500 0.08 1.40 0.07 0.09 1.45 -4.20 3.43 7.63 -0.08 -0.33
y10 10 500 -0.01 1.44 0.00 -0.01 1.41 -4.17 4.11 8.29 0.02 -0.26
y11 11 500 0.04 1.23 0.04 0.03 1.16 -3.83 3.80 7.63 0.03 -0.15
y12 12 500 0.03 1.21 0.00 0.01 1.29 -3.47 3.84 7.31 0.16 -0.04
se
y1 0.06
y2 0.06
y3 0.06
y4 0.06
y5 0.06
y6 0.06
y7 0.07
y8 0.06
y9 0.06
y10 0.06
y11 0.05
y12 0.05
Visualize Data
ex5_12 %>%
pivot_longer(everything(),
names_to = "Item",
values_to = "Score") %>%
ggplot(aes(x = Item, y = Score)) +
geom_boxplot()
Visualize Data
corrgram(ex5_12, upper.panel = "panel.cor")
Guide to lavaan Syntax
Correlation/Covariance
y ~~ x
- Mplus equivalent:
y WITH x;
Regression
y ~ x
- Mplus equivalent:
y ON x;
Guide to lavaan Syntax
Reflective Factors (typical latent variables)
f =~ item1 + item2 + item3
- Mplus equivalent:
f BY item1 item2 item3;
Formative Factors
f <- item1 + item2 + item3
- Mplus equivalent:
f BY;
f ON item1 item2 item3;
f@0;
Guide to lavaan Syntax
Means/Intercepts
f ~ 1
item1 ~ 1
- Mplus equivalent:
[f];
[item1];
(Residual) Variances
f ~~ f
- Mplus equivalent:
f;
Thresholds (for categorical indicators/IRT)
item1 | t1 + t2 + t3 # Assume item1 has 4 ordered categorical responses (3 thresholds)
item2 | t1 + t2 # Assume item2 has 3 ordered categorical responses (2 thresholds)
- Mplus equivalent:
[item1$1 item1$2 item1$3];
[item2$1 item2$2];
Usually you don't need to write syntax for the thresholds (unless doing measurement invariance testing with categorical indicators)
Guide to lavaan Syntax
Fix a parameter to a specific value
Factor Loadings
f =~ 1*item1 + item2 + item3
- Mplus equivalent:
f BY item1@1 item2 item3;
Means/Intercepts
f ~ 0*1
- Mplus equivalent:
[f@0];
(Residual) Variances
f ~~ 1*f
- Mplus equivalent:
f@1;
Guide to lavaan Syntax
Freely estimate a parameter
f =~ NA*item1 + item2 + item3
- Mplus equivalent:
f BY item1* item2 item3;
Provide starting values before freely estimating a parameter
f =~ start(1.25)*item1 + item2 + item3
- Mplus equivalent:
f BY item1*1.25 item2 item3;
Guide to lavaan Syntax
Assign a label to parameter(s)
f =~ lab1*item1 + lab2*item2 + item3
- Mplus equivalent:
f BY item1 item2 (lab1-lab2)
item3;
Apply equality constraints to two or more parameters
f =~ l1*item1 + l1*item2 + item3
- Mplus equivalent:
f BY item1 item2 (l1)
item3;
Plan for This Workshop
Mplus User's Guide Example 5.12
Plan for This Workshop
https://www.statmodel.com/ugexcerpts.shtml
https://www.statmodel.com/usersguide/chapter5.shtml
Steps
- Measurement Models
- Structural Model
- Mediation
Measurement Models
- f1 & f2
- f3 & f4
Measurement Model 1: f1 & f2
mm1_f1_f2_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f1 ~~ f2
'
mm1_f1_f2_f <- cfa(mm1_f1_f2_m, data = ex5_12)
Other options (non-exhaustive list) to consider including in the cfa() function:
ordered- which variables, if any, are ordinal (limits your choice of estimator)estimator- probably want “ML” or “MLR” for most continuous data; WLSMV for ordinalmissing- if there is missing data, how to handle it? Prefer “fiml”mimic- do you want the results to try to match what you'd get from Mplus (mimic = "mplus") or EQS (mimic = "EQS")?std.lv- TRUE/FALSE: standardize the latent variablestd.ov- TRUE/FALSE: standardize the observed variablesorthogonal- TRUE/FALSE: make all latent variables uncorrelated with one another
Measurement Model 1: f1 & f2
mm1_f1_f2_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f1 ~~ f2
'
mm1_f1_f2_f <- cfa(mm1_f1_f2_m, data = ex5_12, estimator = "mlr", missing = "fiml")
summary(mm1_f1_f2_f)
lavaan 0.6-10 ended normally after 33 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 19
Number of observations 500
Number of missing patterns 1
Model Test User Model:
Standard Robust
Test Statistic 11.525 11.037
Degrees of freedom 8 8
P-value (Chi-square) 0.174 0.200
Scaling correction factor 1.044
Yuan-Bentler correction (Mplus variant)
Parameter Estimates:
Standard errors Sandwich
Information bread Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|)
f1 =~
y1 1.000
y2 1.279 0.119 10.774 0.000
y3 0.985 0.087 11.279 0.000
f2 =~
y4 1.000
y5 0.954 0.105 9.059 0.000
y6 0.889 0.101 8.813 0.000
Covariances:
Estimate Std.Err z-value P(>|z|)
f1 ~~
f2 -0.030 0.052 -0.586 0.558
Intercepts:
Estimate Std.Err z-value P(>|z|)
.y1 0.011 0.062 0.183 0.855
.y2 0.047 0.064 0.738 0.460
.y3 0.005 0.062 0.078 0.938
.y4 0.104 0.064 1.627 0.104
.y5 0.078 0.057 1.361 0.173
.y6 0.074 0.059 1.241 0.215
f1 0.000
f2 0.000
Variances:
Estimate Std.Err z-value P(>|z|)
.y1 1.110 0.095 11.699 0.000
.y2 0.711 0.122 5.837 0.000
.y3 1.131 0.097 11.701 0.000
.y4 1.204 0.117 10.314 0.000
.y5 0.862 0.102 8.422 0.000
.y6 1.101 0.095 11.629 0.000
f1 0.807 0.112 7.182 0.000
f2 0.835 0.134 6.242 0.000
Measurement Model 1: f1 & f2
mm1_f1_f2_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f1 ~~ f2
'
mm1_f1_f2_f <- cfa(mm1_f1_f2_m, data = ex5_12, estimator = "mlr", missing = "fiml")
summary(mm1_f1_f2_f)
Other options (non-exhaustive list) to consider including in the summary() function:
fit.measures- TRUE/FALSE: display model fit statisticsstandardized- TRUE/FALSE: display standardized parameter estimatesci- TRUE/FALSE: display confidence intervalsmodindices- TRUE/FALSE: display modification indices
Measurement Model 1: f1 & f2
mm1_f1_f2_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f1 ~~ f2
'
mm1_f1_f2_f <- cfa(mm1_f1_f2_m, data = ex5_12, estimator = "mlr", missing = "fiml")
summary(mm1_f1_f2_f, fit.measures = TRUE, standardized = TRUE)
lavaan 0.6-10 ended normally after 33 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 19
Number of observations 500
Number of missing patterns 1
Model Test User Model:
Standard Robust
Test Statistic 11.525 11.037
Degrees of freedom 8 8
P-value (Chi-square) 0.174 0.200
Scaling correction factor 1.044
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 583.437 568.645
Degrees of freedom 15 15
P-value 0.000 0.000
Scaling correction factor 1.026
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.994 0.995
Tucker-Lewis Index (TLI) 0.988 0.990
Robust Comparative Fit Index (CFI) 0.994
Robust Tucker-Lewis Index (TLI) 0.990
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4913.545 -4913.545
Scaling correction factor 0.984
for the MLR correction
Loglikelihood unrestricted model (H1) -4907.783 -4907.783
Scaling correction factor 1.002
for the MLR correction
Akaike (AIC) 9865.090 9865.090
Bayesian (BIC) 9945.168 9945.168
Sample-size adjusted Bayesian (BIC) 9884.860 9884.860
Root Mean Square Error of Approximation:
RMSEA 0.030 0.028
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.065 0.062
P-value RMSEA <= 0.05 0.801 0.831
Robust RMSEA 0.028
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.065
Standardized Root Mean Square Residual:
SRMR 0.020 0.020
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
f1 =~
y1 1.000 0.898 0.649
y2 1.279 0.119 10.774 0.000 1.149 0.806
y3 0.985 0.087 11.279 0.000 0.885 0.640
f2 =~
y4 1.000 0.914 0.640
y5 0.954 0.105 9.059 0.000 0.872 0.685
y6 0.889 0.101 8.813 0.000 0.813 0.612
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 ~~
f2 -0.030 0.052 -0.586 0.558 -0.037 -0.037
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 0.011 0.062 0.183 0.855 0.011 0.008
.y2 0.047 0.064 0.738 0.460 0.047 0.033
.y3 0.005 0.062 0.078 0.938 0.005 0.003
.y4 0.104 0.064 1.627 0.104 0.104 0.073
.y5 0.078 0.057 1.361 0.173 0.078 0.061
.y6 0.074 0.059 1.241 0.215 0.074 0.055
f1 0.000 0.000 0.000
f2 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 1.110 0.095 11.699 0.000 1.110 0.579
.y2 0.711 0.122 5.837 0.000 0.711 0.350
.y3 1.131 0.097 11.701 0.000 1.131 0.591
.y4 1.204 0.117 10.314 0.000 1.204 0.590
.y5 0.862 0.102 8.422 0.000 0.862 0.531
.y6 1.101 0.095 11.629 0.000 1.101 0.625
f1 0.807 0.112 7.182 0.000 1.000 1.000
f2 0.835 0.134 6.242 0.000 1.000 1.000
Measurement Model 1: f1 & f2
Fit Statistics
fitMeasures(mm1_f1_f2_f, c("chisq", "df", "pvalue", "cfi", "tli",
"rmsea", "rmsea.ci.lower", "rmsea.ci.upper",
"srmr"),
output = "matrix")
chisq 11.525
df 8.000
pvalue 0.174
cfi 0.994
tli 0.988
rmsea 0.030
rmsea.ci.lower 0.000
rmsea.ci.upper 0.065
srmr 0.020
Measurement Model 1: f1 & f2
Parameter Estimates
parameterEstimates(mm1_f1_f2_f, standardized = TRUE)
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all
1 f1 =~ y1 1.000 0.000 NA NA 1.000 1.000 0.898 0.649
2 f1 =~ y2 1.279 0.119 10.774 0.000 1.046 1.511 1.149 0.806
3 f1 =~ y3 0.985 0.087 11.279 0.000 0.814 1.156 0.885 0.640
4 f2 =~ y4 1.000 0.000 NA NA 1.000 1.000 0.914 0.640
5 f2 =~ y5 0.954 0.105 9.059 0.000 0.748 1.161 0.872 0.685
6 f2 =~ y6 0.889 0.101 8.813 0.000 0.691 1.087 0.813 0.612
7 f1 ~~ f2 -0.030 0.052 -0.586 0.558 -0.132 0.071 -0.037 -0.037
8 y1 ~~ y1 1.110 0.095 11.699 0.000 0.924 1.296 1.110 0.579
9 y2 ~~ y2 0.711 0.122 5.837 0.000 0.472 0.950 0.711 0.350
10 y3 ~~ y3 1.131 0.097 11.701 0.000 0.941 1.320 1.131 0.591
11 y4 ~~ y4 1.204 0.117 10.314 0.000 0.975 1.433 1.204 0.590
12 y5 ~~ y5 0.862 0.102 8.422 0.000 0.661 1.062 0.862 0.531
13 y6 ~~ y6 1.101 0.095 11.629 0.000 0.915 1.286 1.101 0.625
14 f1 ~~ f1 0.807 0.112 7.182 0.000 0.587 1.028 1.000 1.000
15 f2 ~~ f2 0.835 0.134 6.242 0.000 0.573 1.098 1.000 1.000
16 y1 ~1 0.011 0.062 0.183 0.855 -0.110 0.133 0.011 0.008
17 y2 ~1 0.047 0.064 0.738 0.460 -0.078 0.172 0.047 0.033
18 y3 ~1 0.005 0.062 0.078 0.938 -0.116 0.126 0.005 0.003
19 y4 ~1 0.104 0.064 1.627 0.104 -0.021 0.229 0.104 0.073
20 y5 ~1 0.078 0.057 1.361 0.173 -0.034 0.189 0.078 0.061
21 y6 ~1 0.074 0.059 1.241 0.215 -0.043 0.190 0.074 0.055
22 f1 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
23 f2 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
std.nox
1 0.649
2 0.806
3 0.640
4 0.640
5 0.685
6 0.612
7 -0.037
8 0.579
9 0.350
10 0.591
11 0.590
12 0.531
13 0.625
14 1.000
15 1.000
16 0.008
17 0.033
18 0.003
19 0.073
20 0.061
21 0.055
22 0.000
23 0.000
Measurement Models
- f1 & f2
- f3 & f4
Measurement Model 2: f3 & f4
mm2_f3_f4_m <- '
f3 =~ y7 + y8 + y9
f4 =~ y10 + y11 + y12
f3 ~~ f4
'
mm2_f3_f4_f <- cfa(mm2_f3_f4_m, data = ex5_12, estimator = "mlr", missing = "fiml")
Measurement Model 2: f3 & f4
summary(mm2_f3_f4_f, fit.measures = TRUE, standardized = TRUE)
lavaan 0.6-10 ended normally after 31 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 19
Number of observations 500
Number of missing patterns 1
Model Test User Model:
Standard Robust
Test Statistic 7.163 7.686
Degrees of freedom 8 8
P-value (Chi-square) 0.519 0.465
Scaling correction factor 0.932
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 706.165 713.248
Degrees of freedom 15 15
P-value 0.000 0.000
Scaling correction factor 0.990
User Model versus Baseline Model:
Comparative Fit Index (CFI) 1.000 1.000
Tucker-Lewis Index (TLI) 1.002 1.001
Robust Comparative Fit Index (CFI) 1.000
Robust Tucker-Lewis Index (TLI) 1.001
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -4833.308 -4833.308
Scaling correction factor 0.998
for the MLR correction
Loglikelihood unrestricted model (H1) -4829.726 -4829.726
Scaling correction factor 0.979
for the MLR correction
Akaike (AIC) 9704.616 9704.616
Bayesian (BIC) 9784.693 9784.693
Sample-size adjusted Bayesian (BIC) 9724.386 9724.386
Root Mean Square Error of Approximation:
RMSEA 0.000 0.000
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.049 0.052
P-value RMSEA <= 0.05 0.956 0.936
Robust RMSEA 0.000
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.049
Standardized Root Mean Square Residual:
SRMR 0.017 0.017
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
f3 =~
y7 1.000 1.179 0.776
y8 0.864 0.065 13.294 0.000 1.019 0.725
y9 0.855 0.067 12.784 0.000 1.008 0.721
f4 =~
y10 1.000 0.928 0.647
y11 0.823 0.090 9.196 0.000 0.764 0.624
y12 0.680 0.091 7.439 0.000 0.631 0.521
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f3 ~~
f4 0.659 0.088 7.486 0.000 0.602 0.602
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y7 0.051 0.068 0.754 0.451 0.051 0.034
.y8 0.063 0.063 1.000 0.317 0.063 0.045
.y9 0.078 0.063 1.248 0.212 0.078 0.056
.y10 -0.008 0.064 -0.128 0.898 -0.008 -0.006
.y11 0.039 0.055 0.716 0.474 0.039 0.032
.y12 0.031 0.054 0.563 0.574 0.031 0.025
f3 0.000 0.000 0.000
f4 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y7 0.921 0.105 8.789 0.000 0.921 0.399
.y8 0.938 0.090 10.404 0.000 0.938 0.475
.y9 0.938 0.080 11.657 0.000 0.938 0.480
.y10 1.200 0.123 9.719 0.000 1.200 0.582
.y11 0.917 0.088 10.460 0.000 0.917 0.611
.y12 1.071 0.080 13.366 0.000 1.071 0.729
f3 1.391 0.155 8.991 0.000 1.000 1.000
f4 0.861 0.132 6.504 0.000 1.000 1.000
Measurement Model 2: f3 & f4
Fit Statistics
fitMeasures(mm2_f3_f4_f, c("chisq", "df", "pvalue", "cfi", "tli",
"rmsea", "rmsea.ci.lower", "rmsea.ci.upper",
"srmr"),
output = "matrix")
chisq 7.163
df 8.000
pvalue 0.519
cfi 1.000
tli 1.002
rmsea 0.000
rmsea.ci.lower 0.000
rmsea.ci.upper 0.049
srmr 0.017
Measurement Model 2: f3 & f4
Parameter Estimates
parameterEstimates(mm2_f3_f4_f, standardized = TRUE)
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all
1 f3 =~ y7 1.000 0.000 NA NA 1.000 1.000 1.179 0.776
2 f3 =~ y8 0.864 0.065 13.294 0.000 0.737 0.992 1.019 0.725
3 f3 =~ y9 0.855 0.067 12.784 0.000 0.724 0.986 1.008 0.721
4 f4 =~ y10 1.000 0.000 NA NA 1.000 1.000 0.928 0.647
5 f4 =~ y11 0.823 0.090 9.196 0.000 0.648 0.999 0.764 0.624
6 f4 =~ y12 0.680 0.091 7.439 0.000 0.501 0.860 0.631 0.521
7 f3 ~~ f4 0.659 0.088 7.486 0.000 0.486 0.831 0.602 0.602
8 y7 ~~ y7 0.921 0.105 8.789 0.000 0.716 1.127 0.921 0.399
9 y8 ~~ y8 0.938 0.090 10.404 0.000 0.761 1.115 0.938 0.475
10 y9 ~~ y9 0.938 0.080 11.657 0.000 0.780 1.096 0.938 0.480
11 y10 ~~ y10 1.200 0.123 9.719 0.000 0.958 1.441 1.200 0.582
12 y11 ~~ y11 0.917 0.088 10.460 0.000 0.745 1.089 0.917 0.611
13 y12 ~~ y12 1.071 0.080 13.366 0.000 0.914 1.229 1.071 0.729
14 f3 ~~ f3 1.391 0.155 8.991 0.000 1.088 1.694 1.000 1.000
15 f4 ~~ f4 0.861 0.132 6.504 0.000 0.602 1.121 1.000 1.000
16 y7 ~1 0.051 0.068 0.754 0.451 -0.082 0.185 0.051 0.034
17 y8 ~1 0.063 0.063 1.000 0.317 -0.060 0.186 0.063 0.045
18 y9 ~1 0.078 0.063 1.248 0.212 -0.044 0.201 0.078 0.056
19 y10 ~1 -0.008 0.064 -0.128 0.898 -0.134 0.118 -0.008 -0.006
20 y11 ~1 0.039 0.055 0.716 0.474 -0.068 0.147 0.039 0.032
21 y12 ~1 0.031 0.054 0.563 0.574 -0.076 0.137 0.031 0.025
22 f3 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
23 f4 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
std.nox
1 0.776
2 0.725
3 0.721
4 0.647
5 0.624
6 0.521
7 0.602
8 0.399
9 0.475
10 0.480
11 0.582
12 0.611
13 0.729
14 1.000
15 1.000
16 0.034
17 0.045
18 0.056
19 -0.006
20 0.032
21 0.025
22 0.000
23 0.000
Structural Model
Exericse: Write the syntax for this model on your own
Structural Model
sm1_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f3 =~ y7 + y8 + y9
f4 =~ y10 + y11 + y12
f1 ~~ f2
f4 ~ f3
f3 ~ f1 + f2
'
sm1_f <- sem(sm1_m, data = ex5_12, estimator = "mlr", missing = "fiml")
summary(sm1_f, fit.measures = TRUE, standardized = TRUE)
lavaan 0.6-10 ended normally after 35 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 40
Number of observations 500
Number of missing patterns 1
Model Test User Model:
Standard Robust
Test Statistic 53.704 54.949
Degrees of freedom 50 50
P-value (Chi-square) 0.334 0.293
Scaling correction factor 0.977
Yuan-Bentler correction (Mplus variant)
Model Test Baseline Model:
Test statistic 1524.403 1533.872
Degrees of freedom 66 66
P-value 0.000 0.000
Scaling correction factor 0.994
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.997 0.997
Tucker-Lewis Index (TLI) 0.997 0.996
Robust Comparative Fit Index (CFI) 0.997
Robust Tucker-Lewis Index (TLI) 0.996
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9646.960 -9646.960
Scaling correction factor 0.999
for the MLR correction
Loglikelihood unrestricted model (H1) -9620.108 -9620.108
Scaling correction factor 0.987
for the MLR correction
Akaike (AIC) 19373.920 19373.920
Bayesian (BIC) 19542.505 19542.505
Sample-size adjusted Bayesian (BIC) 19415.542 19415.542
Root Mean Square Error of Approximation:
RMSEA 0.012 0.014
90 Percent confidence interval - lower 0.000 0.000
90 Percent confidence interval - upper 0.032 0.033
P-value RMSEA <= 0.05 1.000 1.000
Robust RMSEA 0.014
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.033
Standardized Root Mean Square Residual:
SRMR 0.027 0.027
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
f1 =~
y1 1.000 0.940 0.679
y2 1.183 0.105 11.215 0.000 1.112 0.780
y3 0.938 0.085 10.996 0.000 0.881 0.637
f2 =~
y4 1.000 0.942 0.660
y5 0.870 0.083 10.423 0.000 0.820 0.644
y6 0.891 0.101 8.850 0.000 0.839 0.633
f3 =~
y7 1.000 1.165 0.766
y8 0.872 0.061 14.270 0.000 1.016 0.723
y9 0.882 0.064 13.761 0.000 1.028 0.736
f4 =~
y10 1.000 0.927 0.645
y11 0.826 0.090 9.226 0.000 0.765 0.625
y12 0.682 0.091 7.503 0.000 0.632 0.521
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f4 ~
f3 0.473 0.054 8.715 0.000 0.595 0.595
f3 ~
f1 0.563 0.066 8.582 0.000 0.454 0.454
f2 0.790 0.088 8.968 0.000 0.639 0.639
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 ~~
f2 -0.030 0.056 -0.534 0.593 -0.034 -0.034
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 0.011 0.062 0.183 0.855 0.011 0.008
.y2 0.047 0.064 0.738 0.460 0.047 0.033
.y3 0.005 0.062 0.078 0.938 0.005 0.003
.y4 0.104 0.064 1.627 0.104 0.104 0.073
.y5 0.078 0.057 1.361 0.173 0.078 0.061
.y6 0.074 0.059 1.241 0.215 0.074 0.055
.y7 0.051 0.068 0.754 0.451 0.051 0.034
.y8 0.063 0.063 1.000 0.317 0.063 0.045
.y9 0.078 0.063 1.248 0.212 0.078 0.056
.y10 -0.008 0.064 -0.128 0.898 -0.008 -0.006
.y11 0.039 0.055 0.716 0.474 0.039 0.032
.y12 0.031 0.054 0.563 0.574 0.031 0.025
f1 0.000 0.000 0.000
f2 0.000 0.000 0.000
.f3 0.000 0.000 0.000
.f4 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 1.033 0.093 11.067 0.000 1.033 0.539
.y2 0.795 0.109 7.269 0.000 0.795 0.392
.y3 1.137 0.090 12.660 0.000 1.137 0.594
.y4 1.151 0.103 11.125 0.000 1.151 0.564
.y5 0.950 0.088 10.755 0.000 0.950 0.586
.y6 1.056 0.090 11.709 0.000 1.056 0.600
.y7 0.954 0.098 9.724 0.000 0.954 0.413
.y8 0.945 0.083 11.334 0.000 0.945 0.478
.y9 0.896 0.073 12.237 0.000 0.896 0.459
.y10 1.202 0.123 9.780 0.000 1.202 0.583
.y11 0.916 0.088 10.408 0.000 0.916 0.610
.y12 1.071 0.080 13.346 0.000 1.071 0.728
f1 0.884 0.116 7.623 0.000 1.000 1.000
f2 0.888 0.134 6.612 0.000 1.000 1.000
.f3 0.550 0.091 6.040 0.000 0.405 0.405
.f4 0.555 0.101 5.502 0.000 0.646 0.646
Structural Model
Fit Statistics
fitMeasures(sm1_f, c("chisq", "df", "pvalue", "cfi", "tli",
"rmsea", "rmsea.ci.lower", "rmsea.ci.upper",
"srmr"),
output = "matrix")
chisq 53.704
df 50.000
pvalue 0.334
cfi 0.997
tli 0.997
rmsea 0.012
rmsea.ci.lower 0.000
rmsea.ci.upper 0.032
srmr 0.027
Structural Model
Parameter Estimates
parameterEstimates(sm1_f, standardized = TRUE)
lhs op rhs est se z pvalue ci.lower ci.upper std.lv std.all
1 f1 =~ y1 1.000 0.000 NA NA 1.000 1.000 0.940 0.679
2 f1 =~ y2 1.183 0.105 11.215 0.000 0.976 1.389 1.112 0.780
3 f1 =~ y3 0.938 0.085 10.996 0.000 0.770 1.105 0.881 0.637
4 f2 =~ y4 1.000 0.000 NA NA 1.000 1.000 0.942 0.660
5 f2 =~ y5 0.870 0.083 10.423 0.000 0.706 1.033 0.820 0.644
6 f2 =~ y6 0.891 0.101 8.850 0.000 0.694 1.088 0.839 0.633
7 f3 =~ y7 1.000 0.000 NA NA 1.000 1.000 1.165 0.766
8 f3 =~ y8 0.872 0.061 14.270 0.000 0.752 0.991 1.016 0.723
9 f3 =~ y9 0.882 0.064 13.761 0.000 0.757 1.008 1.028 0.736
10 f4 =~ y10 1.000 0.000 NA NA 1.000 1.000 0.927 0.645
11 f4 =~ y11 0.826 0.090 9.226 0.000 0.650 1.001 0.765 0.625
12 f4 =~ y12 0.682 0.091 7.503 0.000 0.504 0.860 0.632 0.521
13 f1 ~~ f2 -0.030 0.056 -0.534 0.593 -0.141 0.080 -0.034 -0.034
14 f4 ~ f3 0.473 0.054 8.715 0.000 0.367 0.579 0.595 0.595
15 f3 ~ f1 0.563 0.066 8.582 0.000 0.434 0.692 0.454 0.454
16 f3 ~ f2 0.790 0.088 8.968 0.000 0.617 0.963 0.639 0.639
17 y1 ~~ y1 1.033 0.093 11.067 0.000 0.850 1.216 1.033 0.539
18 y2 ~~ y2 0.795 0.109 7.269 0.000 0.581 1.010 0.795 0.392
19 y3 ~~ y3 1.137 0.090 12.660 0.000 0.961 1.313 1.137 0.594
20 y4 ~~ y4 1.151 0.103 11.125 0.000 0.948 1.354 1.151 0.564
21 y5 ~~ y5 0.950 0.088 10.755 0.000 0.777 1.123 0.950 0.586
22 y6 ~~ y6 1.056 0.090 11.709 0.000 0.879 1.233 1.056 0.600
23 y7 ~~ y7 0.954 0.098 9.724 0.000 0.762 1.147 0.954 0.413
24 y8 ~~ y8 0.945 0.083 11.334 0.000 0.781 1.108 0.945 0.478
25 y9 ~~ y9 0.896 0.073 12.237 0.000 0.753 1.040 0.896 0.459
26 y10 ~~ y10 1.202 0.123 9.780 0.000 0.961 1.443 1.202 0.583
27 y11 ~~ y11 0.916 0.088 10.408 0.000 0.743 1.088 0.916 0.610
28 y12 ~~ y12 1.071 0.080 13.346 0.000 0.914 1.228 1.071 0.728
29 f1 ~~ f1 0.884 0.116 7.623 0.000 0.657 1.111 1.000 1.000
30 f2 ~~ f2 0.888 0.134 6.612 0.000 0.625 1.151 1.000 1.000
31 f3 ~~ f3 0.550 0.091 6.040 0.000 0.372 0.729 0.405 0.405
32 f4 ~~ f4 0.555 0.101 5.502 0.000 0.357 0.752 0.646 0.646
33 y1 ~1 0.011 0.062 0.183 0.855 -0.110 0.133 0.011 0.008
34 y2 ~1 0.047 0.064 0.738 0.460 -0.078 0.172 0.047 0.033
35 y3 ~1 0.005 0.062 0.078 0.938 -0.116 0.126 0.005 0.003
36 y4 ~1 0.104 0.064 1.627 0.104 -0.021 0.229 0.104 0.073
37 y5 ~1 0.078 0.057 1.361 0.173 -0.034 0.189 0.078 0.061
38 y6 ~1 0.074 0.059 1.241 0.215 -0.043 0.190 0.074 0.055
39 y7 ~1 0.051 0.068 0.754 0.451 -0.082 0.185 0.051 0.034
40 y8 ~1 0.063 0.063 1.000 0.317 -0.060 0.186 0.063 0.045
41 y9 ~1 0.078 0.063 1.248 0.212 -0.044 0.201 0.078 0.056
42 y10 ~1 -0.008 0.064 -0.128 0.898 -0.134 0.118 -0.008 -0.006
43 y11 ~1 0.039 0.055 0.716 0.474 -0.068 0.147 0.039 0.032
44 y12 ~1 0.031 0.054 0.563 0.574 -0.076 0.137 0.031 0.025
45 f1 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
46 f2 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
47 f3 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
48 f4 ~1 0.000 0.000 NA NA 0.000 0.000 0.000 0.000
std.nox
1 0.679
2 0.780
3 0.637
4 0.660
5 0.644
6 0.633
7 0.766
8 0.723
9 0.736
10 0.645
11 0.625
12 0.521
13 -0.034
14 0.595
15 0.454
16 0.639
17 0.539
18 0.392
19 0.594
20 0.564
21 0.586
22 0.600
23 0.413
24 0.478
25 0.459
26 0.583
27 0.610
28 0.728
29 1.000
30 1.000
31 0.405
32 0.646
33 0.008
34 0.033
35 0.003
36 0.073
37 0.061
38 0.055
39 0.034
40 0.045
41 0.056
42 -0.006
43 0.032
44 0.025
45 0.000
46 0.000
47 0.000
48 0.000
Structural Model Results
semPaths(sm1_f, layout = "tree2", what = "path", whatLabels = "std",
style = "lisrel", intercepts = FALSE, rotation = 2)
Saving semPaths Figures for Editing
Not recommended
svg("Path Diagram.svg")
semPaths(sm1_f, layout = "tree2", what = "path", whatLabels = "std",
style = "lisrel", intercepts = FALSE, rotation = 2)
dev.off()
quartz_off_screen
2
Recommended
Download draw.io (https://www.diagrams.net/) and create your own.
Mediation Model
Exericse: Write the syntax for this model on your own
Mediation Model
mm1_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f3 =~ y7 + y8 + y9
f4 =~ y10 + y11 + y12
f1 ~~ f2
f4 ~ f3
f3 ~ f1 + f2
# New (c` path)
f4 ~ f1
'
Mediation Model
How to estimate the indirect effects?
mm1_m <- '
f1 =~ y1 + y2 + y3
f2 =~ y4 + y5 + y6
f3 =~ y7 + y8 + y9
f4 =~ y10 + y11 + y12
f1 ~~ f2
f4 ~ b*f3
f3 ~ a*f1 + f2
# New (c` path)
f4 ~ cprime*f1
# Indirect (Mediation) Effects
# Create a new variable representing the product of a times b
ind := a * b
# Total Effect
# Create a new variable representing the product of ind times cprime
tot := ind * cprime
'
Mediation Model
How to get bootstrap standard errors for the indirect effect?
set.seed(90210)
mm1_f <- sem(mm1_m, data = ex5_12, estimator = "ml", missing = "fiml", se = "bootstrap", bootstrap = 2000)
summary(mm1_f, fit.measures = TRUE, standardized = TRUE)
lavaan 0.6-10 ended normally after 36 iterations
Estimator ML
Optimization method NLMINB
Number of model parameters 41
Number of observations 500
Number of missing patterns 1
Model Test User Model:
Test statistic 52.524
Degrees of freedom 49
P-value (Chi-square) 0.339
Model Test Baseline Model:
Test statistic 1524.403
Degrees of freedom 66
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.998
Tucker-Lewis Index (TLI) 0.997
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -9646.370
Loglikelihood unrestricted model (H1) -9620.108
Akaike (AIC) 19374.741
Bayesian (BIC) 19547.539
Sample-size adjusted Bayesian (BIC) 19417.403
Root Mean Square Error of Approximation:
RMSEA 0.012
90 Percent confidence interval - lower 0.000
90 Percent confidence interval - upper 0.032
P-value RMSEA <= 0.05 1.000
Standardized Root Mean Square Residual:
SRMR 0.026
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 2000
Number of successful bootstrap draws 2000
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 =~
y1 1.000 0.938 0.677
y2 1.189 0.109 10.922 0.000 1.115 0.782
y3 0.939 0.089 10.556 0.000 0.881 0.637
f2 =~
y4 1.000 0.943 0.660
y5 0.869 0.082 10.563 0.000 0.819 0.643
y6 0.891 0.103 8.677 0.000 0.840 0.633
f3 =~
y7 1.000 1.166 0.767
y8 0.872 0.062 14.059 0.000 1.017 0.724
y9 0.881 0.065 13.573 0.000 1.028 0.736
f4 =~
y10 1.000 0.922 0.643
y11 0.830 0.093 8.915 0.000 0.766 0.625
y12 0.688 0.095 7.263 0.000 0.635 0.524
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f4 ~
f3 (b) 0.443 0.062 7.191 0.000 0.560 0.560
f3 ~
f1 (a) 0.556 0.068 8.164 0.000 0.447 0.447
f2 0.795 0.088 8.992 0.000 0.642 0.642
f4 ~
f1 (c) 0.072 0.071 1.021 0.307 0.074 0.074
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
f1 ~~
f2 -0.031 0.058 -0.532 0.595 -0.035 -0.035
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 0.011 0.062 0.182 0.855 0.011 0.008
.y2 0.047 0.063 0.743 0.458 0.047 0.033
.y3 0.005 0.061 0.079 0.937 0.005 0.003
.y4 0.104 0.063 1.656 0.098 0.104 0.073
.y5 0.078 0.057 1.363 0.173 0.078 0.061
.y6 0.074 0.059 1.251 0.211 0.074 0.055
.y7 0.051 0.071 0.726 0.468 0.051 0.034
.y8 0.063 0.063 1.000 0.317 0.063 0.045
.y9 0.078 0.063 1.236 0.217 0.078 0.056
.y10 -0.008 0.063 -0.130 0.896 -0.008 -0.006
.y11 0.039 0.056 0.698 0.485 0.039 0.032
.y12 0.031 0.055 0.557 0.577 0.031 0.025
f1 0.000 0.000 0.000
f2 0.000 0.000 0.000
.f3 0.000 0.000 0.000
.f4 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.y1 1.038 0.093 11.103 0.000 1.038 0.541
.y2 0.789 0.110 7.144 0.000 0.789 0.388
.y3 1.138 0.091 12.540 0.000 1.138 0.595
.y4 1.151 0.104 11.023 0.000 1.151 0.564
.y5 0.951 0.091 10.478 0.000 0.951 0.586
.y6 1.056 0.089 11.819 0.000 1.056 0.600
.y7 0.952 0.099 9.574 0.000 0.952 0.412
.y8 0.942 0.084 11.258 0.000 0.942 0.477
.y9 0.897 0.073 12.314 0.000 0.897 0.459
.y10 1.210 0.126 9.578 0.000 1.210 0.587
.y11 0.914 0.089 10.268 0.000 0.914 0.609
.y12 1.067 0.083 12.916 0.000 1.067 0.726
f1 0.879 0.118 7.439 0.000 1.000 1.000
f2 0.888 0.134 6.617 0.000 1.000 1.000
.f3 0.555 0.092 6.026 0.000 0.408 0.408
.f4 0.550 0.101 5.467 0.000 0.646 0.646
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ind 0.246 0.043 5.758 0.000 0.250 0.250
tot 0.018 0.017 1.022 0.307 0.018 0.018
Mediation Model
Fit Statistics
fitMeasures(mm1_f, c("chisq", "df", "pvalue", "cfi", "tli",
"rmsea", "rmsea.ci.lower", "rmsea.ci.upper",
"srmr"),
output = "matrix")
chisq 52.524
df 49.000
pvalue 0.339
cfi 0.998
tli 0.997
rmsea 0.012
rmsea.ci.lower 0.000
rmsea.ci.upper 0.032
srmr 0.026
Mediation Model
Parameter Estimates (part 1)
parameterEstimates(mm1_f, boot.ci.type = "bca.simple", standardized = TRUE) %>%
slice_head(prop = .5)
lhs op rhs label est se z pvalue ci.lower ci.upper std.lv std.all
1 f1 =~ y1 1.000 0.000 NA NA 1.000 1.000 0.938 0.677
2 f1 =~ y2 1.189 0.109 10.922 0.000 0.993 1.420 1.115 0.782
3 f1 =~ y3 0.939 0.089 10.556 0.000 0.779 1.132 0.881 0.637
4 f2 =~ y4 1.000 0.000 NA NA 1.000 1.000 0.943 0.660
5 f2 =~ y5 0.869 0.082 10.563 0.000 0.720 1.048 0.819 0.643
6 f2 =~ y6 0.891 0.103 8.677 0.000 0.708 1.117 0.840 0.633
7 f3 =~ y7 1.000 0.000 NA NA 1.000 1.000 1.166 0.767
8 f3 =~ y8 0.872 0.062 14.059 0.000 0.758 1.003 1.017 0.724
9 f3 =~ y9 0.881 0.065 13.573 0.000 0.761 1.019 1.028 0.736
10 f4 =~ y10 1.000 0.000 NA NA 1.000 1.000 0.922 0.643
11 f4 =~ y11 0.830 0.093 8.915 0.000 0.667 1.027 0.766 0.625
12 f4 =~ y12 0.688 0.095 7.263 0.000 0.522 0.896 0.635 0.524
13 f1 ~~ f2 -0.031 0.058 -0.532 0.595 -0.152 0.079 -0.035 -0.035
14 f4 ~ f3 b 0.443 0.062 7.191 0.000 0.333 0.570 0.560 0.560
15 f3 ~ f1 a 0.556 0.068 8.164 0.000 0.431 0.689 0.447 0.447
16 f3 ~ f2 0.795 0.088 8.992 0.000 0.641 0.995 0.642 0.642
17 f4 ~ f1 c 0.072 0.071 1.021 0.307 -0.060 0.218 0.074 0.074
18 y1 ~~ y1 1.038 0.093 11.103 0.000 0.858 1.231 1.038 0.541
19 y2 ~~ y2 0.789 0.110 7.144 0.000 0.581 1.028 0.789 0.388
20 y3 ~~ y3 1.138 0.091 12.540 0.000 0.970 1.330 1.138 0.595
21 y4 ~~ y4 1.151 0.104 11.023 0.000 0.935 1.358 1.151 0.564
22 y5 ~~ y5 0.951 0.091 10.478 0.000 0.787 1.141 0.951 0.586
23 y6 ~~ y6 1.056 0.089 11.819 0.000 0.890 1.246 1.056 0.600
24 y7 ~~ y7 0.952 0.099 9.574 0.000 0.770 1.158 0.952 0.412
25 y8 ~~ y8 0.942 0.084 11.258 0.000 0.792 1.119 0.942 0.477
std.nox
1 0.677
2 0.782
3 0.637
4 0.660
5 0.643
6 0.633
7 0.767
8 0.724
9 0.736
10 0.643
11 0.625
12 0.524
13 -0.035
14 0.560
15 0.447
16 0.642
17 0.074
18 0.541
19 0.388
20 0.595
21 0.564
22 0.586
23 0.600
24 0.412
25 0.477
Mediation Model
Parameter Estimates (part 2)
parameterEstimates(mm1_f, boot.ci.type = "bca.simple", standardized = TRUE) %>%
slice_tail(prop = .5)
lhs op rhs label est se z pvalue ci.lower ci.upper std.lv
1 y10 ~~ y10 1.210 0.126 9.578 0.000 0.972 1.483 1.210
2 y11 ~~ y11 0.914 0.089 10.268 0.000 0.746 1.086 0.914
3 y12 ~~ y12 1.067 0.083 12.916 0.000 0.919 1.247 1.067
4 f1 ~~ f1 0.879 0.118 7.439 0.000 0.672 1.138 1.000
5 f2 ~~ f2 0.888 0.134 6.617 0.000 0.649 1.175 1.000
6 f3 ~~ f3 0.555 0.092 6.026 0.000 0.397 0.780 0.408
7 f4 ~~ f4 0.550 0.101 5.467 0.000 0.373 0.765 0.646
8 y1 ~1 0.011 0.062 0.182 0.855 -0.108 0.140 0.011
9 y2 ~1 0.047 0.063 0.743 0.458 -0.080 0.169 0.047
10 y3 ~1 0.005 0.061 0.079 0.937 -0.109 0.131 0.005
11 y4 ~1 0.104 0.063 1.656 0.098 -0.017 0.229 0.104
12 y5 ~1 0.078 0.057 1.363 0.173 -0.032 0.192 0.078
13 y6 ~1 0.074 0.059 1.251 0.211 -0.044 0.188 0.074
14 y7 ~1 0.051 0.071 0.726 0.468 -0.082 0.194 0.051
15 y8 ~1 0.063 0.063 1.000 0.317 -0.067 0.183 0.063
16 y9 ~1 0.078 0.063 1.236 0.217 -0.043 0.206 0.078
17 y10 ~1 -0.008 0.063 -0.130 0.896 -0.134 0.109 -0.008
18 y11 ~1 0.039 0.056 0.698 0.485 -0.075 0.147 0.039
19 y12 ~1 0.031 0.055 0.557 0.577 -0.076 0.140 0.031
20 f1 ~1 0.000 0.000 NA NA 0.000 0.000 0.000
21 f2 ~1 0.000 0.000 NA NA 0.000 0.000 0.000
22 f3 ~1 0.000 0.000 NA NA 0.000 0.000 0.000
23 f4 ~1 0.000 0.000 NA NA 0.000 0.000 0.000
24 ind := a*b ind 0.246 0.043 5.758 0.000 0.172 0.346 0.250
25 tot := ind*c tot 0.018 0.017 1.022 0.307 -0.016 0.054 0.018
std.all std.nox
1 0.587 0.587
2 0.609 0.609
3 0.726 0.726
4 1.000 1.000
5 1.000 1.000
6 0.408 0.408
7 0.646 0.646
8 0.008 0.008
9 0.033 0.033
10 0.003 0.003
11 0.073 0.073
12 0.061 0.061
13 0.055 0.055
14 0.034 0.034
15 0.045 0.045
16 0.056 0.056
17 -0.006 -0.006
18 0.032 0.032
19 0.025 0.025
20 0.000 0.000
21 0.000 0.000
22 0.000 0.000
23 0.000 0.000
24 0.250 0.250
25 0.018 0.018
Mediation Model Results
semPaths(mm1_f, layout = "tree2", what = "path", whatLabels = "std",
style = "lisrel", intercepts = FALSE, rotation = 2)
Mediation Model: Bayesian Alternative
blavaan package
bmm1_f <- bsem(mm1_m, data = ex5_12,
n.chains = 4, burnin = 1000, sample = 4000, inits = "Mplus", seed = 90210)
summary(bmm1_f, fit.measures = TRUE, standardized = TRUE)