Multivariate Statistics, Module #12: Structural Equation Modeling (SEM), Part 2
Dr. Broda
This week, we tackle estimating a mediation model in an SEM framework, both with observed variables and with latent factors.
Estimating A mediation model with observed variables (no latent)
Load in necessary packages
library(tidyverse)Registered S3 methods overwritten by 'dbplyr':
method from
print.tbl_lazy
print.tbl_sql
── Attaching packages ─────────────────────────────────── tidyverse 1.3.0 ──
✓ ggplot2 3.3.3 ✓ purrr 0.3.4
✓ tibble 3.0.6 ✓ dplyr 1.0.4
✓ tidyr 1.1.2 ✓ stringr 1.4.0
✓ readr 1.4.0 ✓ forcats 0.5.1
── Conflicts ────────────────────────────────────── tidyverse_conflicts() ──
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()library(psych)
Attaching package: ‘psych’
The following objects are masked from ‘package:ggplot2’:
%+%, alphalibrary(lavaan)This is lavaan 0.6-7
lavaan is BETA software! Please report any bugs.
Attaching package: ‘lavaan’
The following object is masked from ‘package:psych’:
cor2covLoad in the health data
glimpse(health_old)
Rows: 500
Columns: 4
$ id <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, …
$ consc <dbl> -0.534766, 0.522444, 1.581126, -0.458229, 0.275520, -0.8932…
$ behave <dbl> 0.099598, 0.958975, 2.484509, 0.885141, -0.840232, -1.46591…
$ health <dbl> -0.886676, 2.618775, 3.084666, 0.249537, -2.079687, -0.0254…Basic Command for a Mediation Model
Note here - we use the * convention to define specific paths a, b, and c that represent the a, b, and c paths from our proposed mediation model. Then, we use the := operator to define some nonlinear parameters that we then can estimate. These are the indirect effect ab and the total effect c + ab. We also add the missing = "ML" option to the sem call. This is the option to use full information maximum likelihood (FIML) to handle missing data.
model <- ' # direct effect
health ~ c * consc
# mediator
behave ~ a * consc
health ~ b * behave
# indirect effect (a*b)
ab := a * b
# total effect
total := c + (a*b)
'
fit <- sem(model, data = health_old, missing = "ML")lavaan WARNING: 5 cases were deleted due to missing values in
exogenous variable(s), while fixed.x = TRUE.summary(fit)lavaan 0.6-7 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 7
Used Total
Number of observations 495 500
Number of missing patterns 3
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Parameter Estimates:
Standard errors Standard
Information Observed
Observed information based on Hessian
Regressions:
Estimate Std.Err z-value P(>|z|)
health ~
consc (c) 0.268 0.043 6.219 0.000
behave ~
consc (a) 0.528 0.038 13.912 0.000
health ~
behave (b) 0.390 0.043 9.013 0.000
Intercepts:
Estimate Std.Err z-value P(>|z|)
.health 0.029 0.051 0.563 0.574
.behave 0.027 0.053 0.499 0.617
Variances:
Estimate Std.Err z-value P(>|z|)
.health 1.291 0.082 15.684 0.000
.behave 1.404 0.089 15.693 0.000
Defined Parameters:
Estimate Std.Err z-value P(>|z|)
ab 0.206 0.027 7.553 0.000
total 0.474 0.039 12.060 0.000Same as above, with standardized results
summary(fit, standardized=TRUE, fit.measures = TRUE)lavaan 0.6-7 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 7
Used Total
Number of observations 495 500
Number of missing patterns 3
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0
Model Test Baseline Model:
Test statistic 364.966
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) -1545.855
Loglikelihood unrestricted model (H1) -1545.855
Akaike (AIC) 3105.710
Bayesian (BIC) 3135.142
Sample-size adjusted Bayesian (BIC) 3112.924
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 RMSEA <= 0.05 NA
Standardized Root Mean Square Residual:
SRMR 0.000
Parameter Estimates:
Standard errors Standard
Information Observed
Observed information based on Hessian
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
health ~
consc (c) 0.268 0.043 6.219 0.000 0.268 0.269
behave ~
consc (a) 0.528 0.038 13.912 0.000 0.528 0.531
health ~
behave (b) 0.390 0.043 9.013 0.000 0.390 0.391
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.health 0.029 0.051 0.563 0.574 0.029 0.021
.behave 0.027 0.053 0.499 0.617 0.027 0.019
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.health 1.291 0.082 15.684 0.000 1.291 0.663
.behave 1.404 0.089 15.693 0.000 1.404 0.718
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab 0.206 0.027 7.553 0.000 0.206 0.208
total 0.474 0.039 12.060 0.000 0.474 0.477To obtain R Squared Values
lavInspect(fit, "r2")health behave
0.337 0.282 Same model, but with bootstrapped standard errors and 95% confidence intervals
fit2 <- sem(model, data = health_old, se = "bootstrap", bootstrap = 10)
summary(fit2, standardized=TRUE, ci = .95)lavaan 0.6-7 ended normally after 15 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 5
Used Total
Number of observations 491 500
Model Test User Model:
Test statistic 0.000
Degrees of freedom 0extreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpoints
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 10
Number of successful bootstrap draws 10
Regressions:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
health ~
consc (c) 0.265 0.043 6.203 0.000 0.191 0.340 0.265 0.268
behave ~
consc (a) 0.527 0.041 12.905 0.000 0.413 0.554 0.527 0.531
health ~
behave (b) 0.389 0.057 6.798 0.000 0.274 0.472 0.389 0.391
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.health 1.286 0.062 20.726 0.000 1.160 1.346 1.286 0.665
.behave 1.402 0.099 14.112 0.000 1.225 1.584 1.402 0.718
Defined Parameters:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
ab 0.205 0.037 5.575 0.000 0.146 0.249 0.205 0.207
total 0.470 0.019 25.078 0.000 0.421 0.486 0.470 0.475Visualize it with a path diagram
semPlot::semPaths(fit, whatLabels = "standardized")
Estimating A Mediation Model With Latent Vars
glimpse(writing)
Rows: 1,509
Columns: 27
$ W1_FBP1 <dbl> 3, 4, 4, 3, 4, 4, 3, 4, 4, 4, 3, 4, 4, 4, 1, 4, 3, 3, 2, 4, 3, 4, 3, 4, 4,…
$ W1_FBP2 <dbl> 3, 4, 2, 3, 2, 3, 3, 2, 3, 4, 2, 4, 1, 4, 1, 4, 3, 2, 2, 4, 3, 3, 4, 2, 4,…
$ W1_FBP3 <dbl> 4, 4, 4, 3, 4, 4, 2, 1, 3, 4, 3, 4, 3, 4, 1, 4, 2, 2, 3, 4, 3, 4, 4, 3, 4,…
$ W1_FBP4 <dbl> 3, 4, 4, 3, 3, 4, 3, 2, 3, 4, 3, 4, 3, 4, 1, 4, 2, 2, 2, 4, 2, 4, 3, 4, 4,…
$ W1_FBP5 <dbl> 2, 4, 3, 3, 2, 2, 2, 2, 2, 4, 1, 4, 1, 4, 1, 3, 2, 3, 3, 4, 2, 4, 3, 2, 4,…
$ W1_SE1 <dbl> 4, 4, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 4, 3, 4, 4, 2, 4, 4, 4, 2, 4, 4, 4, 4,…
$ W1_SE2 <dbl> 4, 4, 2, 2, 4, 4, 2, 2, 4, 4, 3, 3, 3, 3, 2, 4, 2, 4, 1, 4, 3, 4, 3, 3, 4,…
$ W1_SE3 <dbl> 3, 3, 3, 2, 4, 3, 4, 4, 4, 4, 3, 4, 4, 3, 3, 3, 3, 4, 4, 4, 2, 4, 4, 4, 4,…
$ W1_SE4 <dbl> 3, 2, 2, 2, 4, 2, 3, 2, 2, 4, 2, 3, 2, 3, 2, 1, 2, 2, 2, 4, 3, 4, 2, 4, 2,…
$ W1_SE5 <dbl> 4, 2, 3, 2, 3, 4, 3, 4, 4, 4, 3, 3, 4, 2, 4, 2, 2, 3, 3, 4, 4, 3, 3, 3, 2,…
$ W1_SE6 <dbl> 2, 4, 2, 2, 4, 3, 3, 2, 4, 3, 3, 3, 3, 3, 1, 3, 2, 4, 2, 4, 1, 4, 4, 4, 4,…
$ W1_SE7 <dbl> 4, 4, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 4, 3, 1, 2, 2, 3, 3, 4, 4, 4, 4, 4, 4,…
$ W1_SE8 <dbl> 2, 3, 3, 3, 2, 3, 3, 2, 3, 3, 2, 4, 2, 3, 1, 2, 3, 2, 2, 4, 1, 3, 3, 4, 4,…
$ W1_SE9 <dbl> 3, 3, 3, 2, 4, 4, 3, 3, 2, 4, 3, 4, 4, 3, 1, 2, 3, 2, 2, 4, 4, 4, 4, 4, 4,…
$ W1_SR1 <dbl> 3, 4, 4, 2, 3, 2, 4, 3, 4, 4, 3, 3, 1, 4, 2, 3, 3, 4, 4, 4, 2, 4, 4, 4, 4,…
$ W1_SR2 <dbl> 2, 2, 3, 2, 2, 3, 2, 2, 2, 1, 3, 3, 1, 3, 1, 3, 2, 2, 1, 3, 2, 2, 4, 3, 3,…
$ W1_SR3 <dbl> 4, 4, 3, 2, 1, 2, 3, 1, 4, 2, 3, 4, 1, 3, 2, 4, 3, 2, 3, 4, 3, 3, 2, 3, 4,…
$ W1_SR4 <dbl> 4, 4, 3, 2, 2, 4, 4, 2, 3, 4, 2, 3, 2, 2, 1, 4, 3, 3, 4, 4, 2, 4, 2, 1, 4,…
$ W1_SR5 <dbl> 4, 3, 4, 2, 2, 2, 3, 2, 2, 1, 4, 2, 2, 4, 2, 3, 2, 4, 2, 2, 3, 2, 1, 2, 2,…
$ W1_SR6 <dbl> 2, 4, 1, 2, 3, 2, 2, 2, 2, 3, 3, 4, 1, 3, 2, 3, 2, 2, 1, 3, 1, 2, 4, 3, 3,…
$ W1_SR7 <dbl> 4, 3, 4, 3, 4, 3, 3, 3, 2, 4, 3, 4, 4, 2, 2, 4, 2, 2, 4, 3, 2, 4, 3, 4, 4,…
$ W1_SR8 <dbl> 2, 2, 3, 2, 3, 2, 3, 3, 3, 1, 3, 3, 2, 3, 1, 2, 3, 2, 2, 4, 4, 3, 3, 4, 4,…
$ W1_SR9 <dbl> 3, 3, 4, 3, 4, 2, 3, 3, 2, 4, 2, 3, 1, 3, 1, 3, 1, 4, 3, 4, 3, 2, 4, 4, 2,…
$ W1_SR10 <dbl> 4, 4, 4, 2, 3, 2, 2, 1, 3, 1, 3, 4, 1, 4, 1, 3, 2, 3, 2, 4, 2, 2, 3, 3, 4,…
$ W1_SR11 <dbl> 4, 3, 4, 4, 3, 2, 4, 4, 4, 3, 2, 3, 2, 3, 3, 4, 3, 2, 4, 3, 3, 2, 1, 4, 4,…
$ W1_SR12 <dbl> 4, 4, 4, 2, 4, 3, 3, 2, 3, 4, 4, 4, 1, 3, 1, 2, 2, 4, 2, 4, 2, 4, 2, 4, 3,…
$ W1_TNum <dbl> 71, 34, 63, 52, 81, 71, 71, 71, 83, 70, 84, 83, 76, 60, 85, 80, 39, 8, 9, …Start with CFAs for all three latent measures
cfa.model <- ' FBP =~ W1_FBP1 + W1_FBP2 + W1_FBP3 + W1_FBP4 + W1_FBP5
SE =~ W1_SE1 + W1_SE2 + W1_SE3 + W1_SE4 + W1_SE5 + W1_SE6 + W1_SE7 + W1_SE8 + W1_SE9
SR =~ W1_SR1 + W1_SR2 + W1_SR3 + W1_SR4 + W1_SR5 + W1_SR6 + W1_SR7 + W1_SR8 + W1_SR9 + W1_SR10 + W1_SR11 + W1_SR12'
cfa_fit <- cfa(cfa.model, data=writing, missing = "ML")
summary(cfa_fit, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 96 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 81
Number of observations 1509
Number of missing patterns 27
Model Test User Model:
Test statistic 1988.299
Degrees of freedom 296
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 13338.258
Degrees of freedom 325
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.870
Tucker-Lewis Index (TLI) 0.857
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -48264.380
Loglikelihood unrestricted model (H1) -47270.231
Akaike (AIC) 96690.761
Bayesian (BIC) 97121.616
Sample-size adjusted Bayesian (BIC) 96864.301
Root Mean Square Error of Approximation:
RMSEA 0.062
90 Percent confidence interval - lower 0.059
90 Percent confidence interval - upper 0.064
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.050
Parameter Estimates:
Standard errors Standard
Information Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FBP =~
W1_FBP1 1.000 0.633 0.707
W1_FBP2 1.276 0.047 27.173 0.000 0.807 0.779
W1_FBP3 1.117 0.044 25.105 0.000 0.707 0.705
W1_FBP4 1.194 0.040 29.778 0.000 0.755 0.814
W1_FBP5 1.416 0.050 28.118 0.000 0.896 0.811
SE =~
W1_SE1 1.000 0.243 0.343
W1_SE2 2.274 0.190 11.941 0.000 0.552 0.625
W1_SE3 1.293 0.126 10.291 0.000 0.314 0.396
W1_SE4 2.873 0.236 12.166 0.000 0.697 0.695
W1_SE5 0.852 0.111 7.679 0.000 0.207 0.247
W1_SE6 2.654 0.214 12.390 0.000 0.644 0.729
W1_SE7 2.552 0.207 12.308 0.000 0.619 0.718
W1_SE8 2.559 0.217 11.767 0.000 0.621 0.609
W1_SE9 2.657 0.220 12.106 0.000 0.645 0.670
SR =~
W1_SR1 1.000 0.490 0.550
W1_SR2 1.201 0.070 17.251 0.000 0.588 0.588
W1_SR3 1.026 0.070 14.625 0.000 0.503 0.471
W1_SR4 0.738 0.065 11.329 0.000 0.361 0.342
W1_SR5 0.729 0.066 11.120 0.000 0.357 0.335
W1_SR6 1.344 0.074 18.180 0.000 0.658 0.643
W1_SR7 0.931 0.062 15.106 0.000 0.456 0.489
W1_SR8 1.068 0.068 15.638 0.000 0.523 0.511
W1_SR9 1.036 0.070 14.878 0.000 0.507 0.480
W1_SR10 1.228 0.073 16.846 0.000 0.601 0.570
W1_SR11 0.842 0.057 14.847 0.000 0.412 0.471
W1_SR12 1.320 0.077 17.073 0.000 0.646 0.586
Covariances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FBP ~~
SE 0.096 0.009 10.467 0.000 0.627 0.627
SR 0.210 0.015 14.127 0.000 0.679 0.679
SE ~~
SR 0.091 0.009 10.191 0.000 0.764 0.764
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.W1_FBP1 3.394 0.023 147.261 0.000 3.394 3.792
.W1_FBP2 2.941 0.027 110.275 0.000 2.941 2.840
.W1_FBP3 3.232 0.026 125.156 0.000 3.232 3.224
.W1_FBP4 3.245 0.024 135.924 0.000 3.245 3.500
.W1_FBP5 2.800 0.028 98.440 0.000 2.800 2.534
.W1_SE1 3.552 0.018 194.684 0.000 3.552 5.018
.W1_SE2 2.963 0.023 130.449 0.000 2.963 3.359
.W1_SE3 3.355 0.020 164.465 0.000 3.355 4.234
.W1_SE4 2.862 0.026 110.737 0.000 2.862 2.853
.W1_SE5 3.133 0.022 145.393 0.000 3.133 3.744
.W1_SE6 3.084 0.023 135.652 0.000 3.084 3.493
.W1_SE7 3.166 0.022 142.529 0.000 3.166 3.670
.W1_SE8 2.751 0.026 104.818 0.000 2.751 2.698
.W1_SE9 2.903 0.025 117.137 0.000 2.903 3.016
.W1_SR1 3.206 0.023 139.602 0.000 3.206 3.601
.W1_SR2 2.576 0.026 99.917 0.000 2.576 2.574
.W1_SR3 2.710 0.027 98.553 0.000 2.710 2.539
.W1_SR4 2.815 0.027 103.474 0.000 2.815 2.665
.W1_SR5 2.631 0.027 95.762 0.000 2.631 2.466
.W1_SR6 2.542 0.026 96.493 0.000 2.542 2.485
.W1_SR7 3.109 0.024 129.462 0.000 3.109 3.336
.W1_SR8 2.789 0.026 105.833 0.000 2.789 2.725
.W1_SR9 2.845 0.027 104.595 0.000 2.845 2.695
.W1_SR10 2.721 0.027 100.079 0.000 2.721 2.577
.W1_SR11 3.179 0.023 141.229 0.000 3.179 3.636
.W1_SR12 2.981 0.028 105.010 0.000 2.981 2.704
FBP 0.000 0.000 0.000
SE 0.000 0.000 0.000
SR 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.W1_FBP1 0.401 0.017 23.683 0.000 0.401 0.500
.W1_FBP2 0.422 0.019 21.667 0.000 0.422 0.393
.W1_FBP3 0.506 0.021 24.067 0.000 0.506 0.503
.W1_FBP4 0.290 0.015 19.961 0.000 0.290 0.337
.W1_FBP5 0.418 0.021 20.310 0.000 0.418 0.342
.W1_SE1 0.442 0.016 26.851 0.000 0.442 0.883
.W1_SE2 0.474 0.019 24.727 0.000 0.474 0.609
.W1_SE3 0.529 0.020 26.663 0.000 0.529 0.843
.W1_SE4 0.520 0.022 23.367 0.000 0.520 0.517
.W1_SE5 0.658 0.024 27.179 0.000 0.658 0.939
.W1_SE6 0.365 0.016 22.449 0.000 0.365 0.468
.W1_SE7 0.361 0.016 22.862 0.000 0.361 0.485
.W1_SE8 0.654 0.026 24.813 0.000 0.654 0.629
.W1_SE9 0.511 0.021 24.013 0.000 0.511 0.551
.W1_SR1 0.553 0.022 25.348 0.000 0.553 0.698
.W1_SR2 0.656 0.027 24.700 0.000 0.656 0.655
.W1_SR3 0.887 0.034 26.074 0.000 0.887 0.778
.W1_SR4 0.986 0.037 26.824 0.000 0.986 0.883
.W1_SR5 1.011 0.038 26.842 0.000 1.011 0.888
.W1_SR6 0.613 0.026 23.809 0.000 0.613 0.586
.W1_SR7 0.660 0.026 25.844 0.000 0.660 0.761
.W1_SR8 0.774 0.030 25.707 0.000 0.774 0.739
.W1_SR9 0.857 0.033 26.025 0.000 0.857 0.769
.W1_SR10 0.753 0.030 25.126 0.000 0.753 0.676
.W1_SR11 0.595 0.023 26.089 0.000 0.595 0.778
.W1_SR12 0.798 0.032 24.925 0.000 0.798 0.656
FBP 0.400 0.027 15.012 0.000 1.000 1.000
SE 0.059 0.009 6.378 0.000 1.000 1.000
SR 0.240 0.022 10.737 0.000 1.000 1.000Visualize it with a path diagram
To make the diagram a little less full, I removed the residual estimates for items using residuals = FALSE.
semPlot::semPaths(cfa_fit, whatLabels = "standardized", residuals = FALSE)
Now, specify the SEM model
Notice, with a latent mediation model, we have two steps. Step 1 is specifying the measurement model. This is identical to the code for the CFA model above. Step 2 is the structural model. This is where we actually define the mediation portion. The code here is very similar to what we did for the health data above.
sem.model <- '
#Measurement Model
FBP =~ W1_FBP1 + W1_FBP2 + W1_FBP3 + W1_FBP4 + W1_FBP5
SE =~ W1_SE1 + W1_SE2 + W1_SE3 + W1_SE4 + W1_SE5 + W1_SE6 + W1_SE7 + W1_SE8 + W1_SE9
SR =~ W1_SR1 + W1_SR2 + W1_SR3 + W1_SR4 + W1_SR5 + W1_SR6 + W1_SR7 + W1_SR8 + W1_SR9 + W1_SR10 + W1_SR11 + W1_SR12
#Structural Model
## direct effect
SR ~ c*SE
## mediator
SR ~ b*FBP
FBP ~ a*SE
## indirect effect (a*b)
ab := a*b
## total effect
total := c + (a*b)
'
sem_fit <- sem(sem.model, data=writing, missing = "ml")
summary(sem_fit, fit.measures=TRUE, standardized=TRUE)lavaan 0.6-7 ended normally after 92 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 81
Number of observations 1509
Number of missing patterns 27
Model Test User Model:
Test statistic 1988.299
Degrees of freedom 296
P-value (Chi-square) 0.000
Model Test Baseline Model:
Test statistic 13338.258
Degrees of freedom 325
P-value 0.000
User Model versus Baseline Model:
Comparative Fit Index (CFI) 0.870
Tucker-Lewis Index (TLI) 0.857
Loglikelihood and Information Criteria:
Loglikelihood user model (H0) -48264.380
Loglikelihood unrestricted model (H1) -47270.231
Akaike (AIC) 96690.761
Bayesian (BIC) 97121.616
Sample-size adjusted Bayesian (BIC) 96864.301
Root Mean Square Error of Approximation:
RMSEA 0.062
90 Percent confidence interval - lower 0.059
90 Percent confidence interval - upper 0.064
P-value RMSEA <= 0.05 0.000
Standardized Root Mean Square Residual:
SRMR 0.050
Parameter Estimates:
Standard errors Standard
Information Observed
Observed information based on Hessian
Latent Variables:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
FBP =~
W1_FBP1 1.000 0.633 0.707
W1_FBP2 1.276 0.047 27.173 0.000 0.807 0.779
W1_FBP3 1.117 0.044 25.105 0.000 0.707 0.705
W1_FBP4 1.194 0.040 29.778 0.000 0.755 0.814
W1_FBP5 1.416 0.050 28.119 0.000 0.896 0.811
SE =~
W1_SE1 1.000 0.243 0.343
W1_SE2 2.274 0.190 11.942 0.000 0.552 0.625
W1_SE3 1.293 0.126 10.291 0.000 0.314 0.396
W1_SE4 2.873 0.236 12.166 0.000 0.697 0.695
W1_SE5 0.852 0.111 7.680 0.000 0.207 0.247
W1_SE6 2.654 0.214 12.391 0.000 0.644 0.729
W1_SE7 2.552 0.207 12.308 0.000 0.619 0.718
W1_SE8 2.559 0.217 11.768 0.000 0.621 0.609
W1_SE9 2.657 0.219 12.107 0.000 0.645 0.670
SR =~
W1_SR1 1.000 0.490 0.550
W1_SR2 1.201 0.070 17.251 0.000 0.588 0.588
W1_SR3 1.026 0.070 14.625 0.000 0.503 0.471
W1_SR4 0.738 0.065 11.329 0.000 0.361 0.342
W1_SR5 0.729 0.066 11.120 0.000 0.357 0.335
W1_SR6 1.344 0.074 18.180 0.000 0.658 0.643
W1_SR7 0.931 0.062 15.106 0.000 0.456 0.489
W1_SR8 1.068 0.068 15.638 0.000 0.523 0.511
W1_SR9 1.036 0.070 14.878 0.000 0.507 0.480
W1_SR10 1.228 0.073 16.846 0.000 0.601 0.570
W1_SR11 0.842 0.057 14.847 0.000 0.412 0.471
W1_SR12 1.320 0.077 17.073 0.000 0.646 0.586
Regressions:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
SR ~
SE (c) 1.127 0.117 9.611 0.000 0.558 0.558
FBP (b) 0.254 0.027 9.478 0.000 0.329 0.329
FBP ~
SE (a) 1.635 0.148 11.066 0.000 0.627 0.627
Intercepts:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.W1_FBP1 3.394 0.023 147.261 0.000 3.394 3.792
.W1_FBP2 2.941 0.027 110.275 0.000 2.941 2.840
.W1_FBP3 3.232 0.026 125.156 0.000 3.232 3.224
.W1_FBP4 3.245 0.024 135.924 0.000 3.245 3.500
.W1_FBP5 2.800 0.028 98.440 0.000 2.800 2.534
.W1_SE1 3.552 0.018 194.684 0.000 3.552 5.018
.W1_SE2 2.963 0.023 130.449 0.000 2.963 3.359
.W1_SE3 3.355 0.020 164.465 0.000 3.355 4.234
.W1_SE4 2.862 0.026 110.737 0.000 2.862 2.853
.W1_SE5 3.133 0.022 145.393 0.000 3.133 3.744
.W1_SE6 3.084 0.023 135.653 0.000 3.084 3.493
.W1_SE7 3.166 0.022 142.529 0.000 3.166 3.670
.W1_SE8 2.751 0.026 104.818 0.000 2.751 2.698
.W1_SE9 2.903 0.025 117.137 0.000 2.903 3.016
.W1_SR1 3.206 0.023 139.602 0.000 3.206 3.601
.W1_SR2 2.576 0.026 99.917 0.000 2.576 2.574
.W1_SR3 2.710 0.027 98.553 0.000 2.710 2.539
.W1_SR4 2.815 0.027 103.474 0.000 2.815 2.665
.W1_SR5 2.631 0.027 95.762 0.000 2.631 2.466
.W1_SR6 2.542 0.026 96.493 0.000 2.542 2.485
.W1_SR7 3.109 0.024 129.462 0.000 3.109 3.336
.W1_SR8 2.789 0.026 105.833 0.000 2.789 2.725
.W1_SR9 2.845 0.027 104.595 0.000 2.845 2.695
.W1_SR10 2.721 0.027 100.079 0.000 2.721 2.577
.W1_SR11 3.179 0.023 141.229 0.000 3.179 3.636
.W1_SR12 2.981 0.028 105.010 0.000 2.981 2.704
.FBP 0.000 0.000 0.000
SE 0.000 0.000 0.000
.SR 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
.W1_FBP1 0.401 0.017 23.683 0.000 0.401 0.500
.W1_FBP2 0.422 0.019 21.667 0.000 0.422 0.393
.W1_FBP3 0.506 0.021 24.067 0.000 0.506 0.503
.W1_FBP4 0.290 0.015 19.961 0.000 0.290 0.337
.W1_FBP5 0.418 0.021 20.310 0.000 0.418 0.342
.W1_SE1 0.442 0.016 26.852 0.000 0.442 0.883
.W1_SE2 0.474 0.019 24.727 0.000 0.474 0.609
.W1_SE3 0.529 0.020 26.663 0.000 0.529 0.843
.W1_SE4 0.520 0.022 23.367 0.000 0.520 0.517
.W1_SE5 0.658 0.024 27.179 0.000 0.658 0.939
.W1_SE6 0.365 0.016 22.449 0.000 0.365 0.468
.W1_SE7 0.361 0.016 22.862 0.000 0.361 0.485
.W1_SE8 0.654 0.026 24.813 0.000 0.654 0.629
.W1_SE9 0.511 0.021 24.013 0.000 0.511 0.551
.W1_SR1 0.553 0.022 25.348 0.000 0.553 0.698
.W1_SR2 0.656 0.027 24.700 0.000 0.656 0.655
.W1_SR3 0.887 0.034 26.073 0.000 0.887 0.778
.W1_SR4 0.986 0.037 26.824 0.000 0.986 0.883
.W1_SR5 1.011 0.038 26.842 0.000 1.011 0.888
.W1_SR6 0.613 0.026 23.809 0.000 0.613 0.586
.W1_SR7 0.660 0.026 25.844 0.000 0.660 0.761
.W1_SR8 0.774 0.030 25.707 0.000 0.774 0.739
.W1_SR9 0.857 0.033 26.025 0.000 0.857 0.769
.W1_SR10 0.753 0.030 25.126 0.000 0.753 0.676
.W1_SR11 0.595 0.023 26.089 0.000 0.595 0.778
.W1_SR12 0.798 0.032 24.925 0.000 0.798 0.656
.FBP 0.243 0.017 13.939 0.000 0.607 0.607
SE 0.059 0.009 6.378 0.000 1.000 1.000
.SR 0.084 0.009 9.340 0.000 0.350 0.350
Defined Parameters:
Estimate Std.Err z-value P(>|z|) Std.lv Std.all
ab 0.416 0.054 7.731 0.000 0.206 0.206
total 1.543 0.142 10.868 0.000 0.764 0.764Same model, but with bootstrapped standard errors (I’m only doing 10 here because it takes forever) and 95% confidence intervals!
sem_fit_boot <- sem(sem.model, data = writing, se = "bootstrap", bootstrap = 10, missing = "ml")lavaan WARNING:
The variance-covariance matrix of the estimated parameters (vcov)
does not appear to be positive definite! The smallest eigenvalue
(= -4.807122e-16) is smaller than zero. This may be a symptom that
the model is not identified.summary(sem_fit_boot, standardized=TRUE, ci = .95)lavaan 0.6-7 ended normally after 92 iterations
Estimator ML
Optimization method NLMINB
Number of free parameters 81
Number of observations 1509
Number of missing patterns 27
Model Test User Model:
Test statistic 1988.299
Degrees of freedom 296
P-value (Chi-square) 0.000extreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpointsextreme order statistics used as endpoints
Parameter Estimates:
Standard errors Bootstrap
Number of requested bootstrap draws 10
Number of successful bootstrap draws 10
Latent Variables:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
FBP =~
W1_FBP1 1.000 1.000 1.000 0.633 0.707
W1_FBP2 1.276 0.056 22.708 0.000 1.196 1.386 0.807 0.779
W1_FBP3 1.117 0.041 26.983 0.000 1.058 1.191 0.707 0.705
W1_FBP4 1.194 0.035 34.125 0.000 1.125 1.253 0.755 0.814
W1_FBP5 1.416 0.065 21.917 0.000 1.331 1.517 0.896 0.811
SE =~
W1_SE1 1.000 1.000 1.000 0.243 0.343
W1_SE2 2.274 0.277 8.198 0.000 1.989 2.960 0.552 0.625
W1_SE3 1.293 0.099 13.087 0.000 1.270 1.592 0.314 0.396
W1_SE4 2.873 0.358 8.021 0.000 2.483 3.724 0.697 0.695
W1_SE5 0.852 0.099 8.591 0.000 0.701 1.042 0.207 0.247
W1_SE6 2.654 0.309 8.599 0.000 2.236 3.311 0.644 0.729
W1_SE7 2.552 0.323 7.909 0.000 2.204 3.296 0.619 0.718
W1_SE8 2.559 0.253 10.096 0.000 2.258 3.155 0.621 0.609
W1_SE9 2.657 0.341 7.796 0.000 2.238 3.339 0.645 0.670
SR =~
W1_SR1 1.000 1.000 1.000 0.490 0.550
W1_SR2 1.201 0.057 20.907 0.000 1.107 1.287 0.588 0.588
W1_SR3 1.026 0.044 23.230 0.000 0.916 1.050 0.503 0.471
W1_SR4 0.738 0.038 19.251 0.000 0.637 0.775 0.361 0.342
W1_SR5 0.729 0.045 16.189 0.000 0.668 0.801 0.357 0.335
W1_SR6 1.344 0.056 23.907 0.000 1.262 1.435 0.658 0.643
W1_SR7 0.931 0.077 12.081 0.000 0.837 1.089 0.456 0.489
W1_SR8 1.068 0.090 11.929 0.000 0.923 1.258 0.523 0.511
W1_SR9 1.036 0.091 11.332 0.000 0.896 1.207 0.507 0.480
W1_SR10 1.228 0.067 18.440 0.000 1.099 1.312 0.601 0.570
W1_SR11 0.842 0.058 14.593 0.000 0.755 0.948 0.412 0.471
W1_SR12 1.320 0.075 17.715 0.000 1.216 1.470 0.646 0.586
Regressions:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
SR ~
SE (c) 1.127 0.187 6.031 0.000 0.944 1.572 0.558 0.558
FBP (b) 0.254 0.022 11.409 0.000 0.213 0.283 0.329 0.329
FBP ~
SE (a) 1.635 0.176 9.288 0.000 1.501 2.069 0.627 0.627
Intercepts:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.W1_FBP1 3.394 0.017 200.782 0.000 3.359 3.421 3.394 3.792
.W1_FBP2 2.941 0.026 114.238 0.000 2.906 3.001 2.941 2.840
.W1_FBP3 3.232 0.020 162.358 0.000 3.201 3.267 3.232 3.224
.W1_FBP4 3.245 0.016 198.363 0.000 3.231 3.278 3.245 3.500
.W1_FBP5 2.800 0.026 106.768 0.000 2.771 2.860 2.800 2.534
.W1_SE1 3.552 0.013 275.605 0.000 3.544 3.579 3.552 5.018
.W1_SE2 2.963 0.022 136.341 0.000 2.931 3.011 2.963 3.359
.W1_SE3 3.355 0.019 176.406 0.000 3.327 3.387 3.355 4.234
.W1_SE4 2.862 0.023 124.430 0.000 2.805 2.896 2.862 2.853
.W1_SE5 3.133 0.024 133.136 0.000 3.078 3.172 3.133 3.744
.W1_SE6 3.084 0.028 108.585 0.000 3.038 3.140 3.084 3.493
.W1_SE7 3.166 0.022 145.207 0.000 3.125 3.202 3.166 3.670
.W1_SE8 2.751 0.020 140.236 0.000 2.730 2.796 2.751 2.698
.W1_SE9 2.903 0.014 214.867 0.000 2.897 2.935 2.903 3.016
.W1_SR1 3.206 0.028 115.531 0.000 3.167 3.255 3.206 3.601
.W1_SR2 2.576 0.028 91.139 0.000 2.538 2.640 2.576 2.574
.W1_SR3 2.710 0.035 78.046 0.000 2.677 2.798 2.710 2.539
.W1_SR4 2.815 0.032 87.306 0.000 2.776 2.882 2.815 2.665
.W1_SR5 2.631 0.025 104.664 0.000 2.613 2.688 2.631 2.466
.W1_SR6 2.542 0.029 86.442 0.000 2.507 2.624 2.542 2.485
.W1_SR7 3.109 0.021 151.183 0.000 3.082 3.146 3.109 3.336
.W1_SR8 2.789 0.014 194.336 0.000 2.752 2.807 2.789 2.725
.W1_SR9 2.845 0.021 133.668 0.000 2.807 2.888 2.845 2.695
.W1_SR10 2.721 0.023 119.529 0.000 2.697 2.772 2.721 2.577
.W1_SR11 3.179 0.030 105.958 0.000 3.137 3.232 3.179 3.636
.W1_SR12 2.981 0.017 174.294 0.000 2.968 3.023 2.981 2.704
.FBP 0.000 0.000 0.000 0.000 0.000
SE 0.000 0.000 0.000 0.000 0.000
.SR 0.000 0.000 0.000 0.000 0.000
Variances:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
.W1_FBP1 0.401 0.022 17.968 0.000 0.362 0.442 0.401 0.500
.W1_FBP2 0.422 0.027 15.793 0.000 0.386 0.469 0.422 0.393
.W1_FBP3 0.506 0.019 26.337 0.000 0.481 0.543 0.506 0.503
.W1_FBP4 0.290 0.017 16.992 0.000 0.243 0.302 0.290 0.337
.W1_FBP5 0.418 0.024 17.128 0.000 0.369 0.463 0.418 0.342
.W1_SE1 0.442 0.017 25.580 0.000 0.401 0.460 0.442 0.883
.W1_SE2 0.474 0.028 16.767 0.000 0.424 0.523 0.474 0.609
.W1_SE3 0.529 0.018 28.969 0.000 0.490 0.546 0.529 0.843
.W1_SE4 0.520 0.009 60.046 0.000 0.502 0.528 0.520 0.517
.W1_SE5 0.658 0.017 38.356 0.000 0.620 0.682 0.658 0.939
.W1_SE6 0.365 0.015 25.032 0.000 0.337 0.384 0.365 0.468
.W1_SE7 0.361 0.020 18.300 0.000 0.330 0.412 0.361 0.485
.W1_SE8 0.654 0.029 22.469 0.000 0.615 0.713 0.654 0.629
.W1_SE9 0.511 0.031 16.390 0.000 0.457 0.568 0.511 0.551
.W1_SR1 0.553 0.024 22.721 0.000 0.521 0.591 0.553 0.698
.W1_SR2 0.656 0.030 22.181 0.000 0.599 0.700 0.656 0.655
.W1_SR3 0.887 0.036 24.476 0.000 0.838 0.936 0.887 0.778
.W1_SR4 0.986 0.030 33.385 0.000 0.921 1.015 0.986 0.883
.W1_SR5 1.011 0.032 31.538 0.000 0.939 1.064 1.011 0.888
.W1_SR6 0.613 0.031 20.072 0.000 0.574 0.698 0.613 0.586
.W1_SR7 0.660 0.023 29.130 0.000 0.611 0.680 0.660 0.761
.W1_SR8 0.774 0.029 26.396 0.000 0.744 0.860 0.774 0.739
.W1_SR9 0.857 0.032 26.960 0.000 0.809 0.910 0.857 0.769
.W1_SR10 0.753 0.030 25.284 0.000 0.694 0.794 0.753 0.676
.W1_SR11 0.595 0.019 31.304 0.000 0.561 0.616 0.595 0.778
.W1_SR12 0.798 0.029 27.401 0.000 0.753 0.846 0.798 0.656
.FBP 0.243 0.022 10.859 0.000 0.207 0.279 0.607 0.607
SE 0.059 0.013 4.536 0.000 0.038 0.080 1.000 1.000
.SR 0.084 0.011 7.593 0.000 0.061 0.097 0.350 0.350
Defined Parameters:
Estimate Std.Err z-value P(>|z|) ci.lower ci.upper Std.lv Std.all
ab 0.416 0.053 7.884 0.000 0.363 0.520 0.206 0.206
total 1.543 0.223 6.923 0.000 1.337 2.082 0.764 0.764To obtain R Squared Values
lavInspect(sem_fit, "r2")W1_FBP1 W1_FBP2 W1_FBP3 W1_FBP4 W1_FBP5 W1_SE1 W1_SE2 W1_SE3 W1_SE4 W1_SE5 W1_SE6
0.500 0.607 0.497 0.663 0.658 0.117 0.391 0.157 0.483 0.061 0.532
W1_SE7 W1_SE8 W1_SE9 W1_SR1 W1_SR2 W1_SR3 W1_SR4 W1_SR5 W1_SR6 W1_SR7 W1_SR8
0.515 0.371 0.449 0.302 0.345 0.222 0.117 0.112 0.414 0.239 0.261
W1_SR9 W1_SR10 W1_SR11 W1_SR12 FBP SR
0.231 0.324 0.222 0.344 0.393 0.650 Visualize it with a path diagram
semPlot::semPaths(sem_fit, whatLabels = "standardized", residuals = FALSE)
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