setwd("C:/Work Files/Teaching/PSY 8170/Winter 2026/Class Exercises/Bayesian SEM")Bayesian SEM
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ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(tidybayes)Warning: package 'tidybayes' was built under R version 4.5.3library(psych)
Attaching package: 'psych'
The following objects are masked from 'package:ggplot2':
%+%, alphalibrary(knitr)
library(kableExtra)
Attaching package: 'kableExtra'
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group_rowslibrary(blavaan)Loading required package: Rcpp
This is blavaan 0.5-8
On multicore systems, we suggest use of future::plan("multicore") or
future::plan("multisession") for faster post-MCMC computations.library(loo)Warning: package 'loo' was built under R version 4.5.3This is loo version 2.9.0
- Online documentation and vignettes at mc-stan.org/loo
- As of v2.0.0 loo defaults to 1 core but we recommend using as many as possible. Use the 'cores' argument or set options(mc.cores = NUM_CORES) for an entire session.
- Windows 10 users: loo may be very slow if 'mc.cores' is set in your .Rprofile file (see https://github.com/stan-dev/loo/issues/94).library(corrplot)corrplot 0.95 loadedlibrary(performance)
library(lavaan)Warning: package 'lavaan' was built under R version 4.5.3This is lavaan 0.6-21
lavaan is FREE software! Please report any bugs.
Attaching package: 'lavaan'
The following object is masked from 'package:psych':
cor2covSEM_Data <- read.csv("HBAT example.csv")
names(SEM_Data) [1] "id" "JS1" "OC1" "OC2" "EP1" "OC3" "OC4" "EP2" "EP3" "AC1" "EP4" "JS2"
[13] "JS3" "AC2" "SI1" "JS4" "SI2" "JS5" "AC3" "SI3" "AC4" "SI4" "C1" "C2"
[25] "C3" "AGE" "EXP" "JP" "JS" "OC" "SI" "EP" "AC" colnames(SEM_Data)[1]<-"ID"
colnames(SEM_Data)[23]<-"Gender"
colnames(SEM_Data)[24]<-"Employee Type"
colnames(SEM_Data)[25]<-"Geographic Location"
str(SEM_Data)'data.frame': 400 obs. of 33 variables:
$ ID : int 1 2 3 4 5 6 7 8 9 10 ...
$ JS1 : int 5 3 4 4 5 6 2 2 4 5 ...
$ OC1 : int 3 0 6 7 2 5 6 4 9 5 ...
$ OC2 : int 5 5 10 7 10 8 10 9 10 9 ...
$ EP1 : int 10 10 10 10 10 8 9 10 8 10 ...
$ OC3 : int 10 3 10 10 9 7 10 9 10 9 ...
$ OC4 : int 10 7 10 7 9 7 9 7 10 10 ...
$ EP2 : int 10 10 10 10 9 10 9 10 6 10 ...
$ EP3 : int 5 10 10 9 10 7 9 10 8 8 ...
$ AC1 : int 1 2 1 2 1 1 2 1 3 2 ...
$ EP4 : int NA 7 7 7 6 7 6 7 3 7 ...
$ JS2 : int 4 4 2 5 4 6 3 2 5 3 ...
$ JS3 : int 3 3 2 4 3 5 6 1 1 2 ...
$ AC2 : int 2 1 4 1 1 2 4 1 4 4 ...
$ SI1 : int 4 5 5 5 5 5 5 3 3 4 ...
$ JS4 : int 3 2 3 2 2 3 4 1 1 2 ...
$ SI2 : int 4 4 5 4 5 4 5 4 3 4 ...
$ JS5 : int 23 43 60 33 58 62 11 21 80 33 ...
$ AC3 : int 1 1 1 1 2 1 3 1 3 1 ...
$ SI3 : int 3 4 5 3 3 3 5 4 2 3 ...
$ AC4 : int 1 1 2 1 2 1 3 3 1 4 ...
$ SI4 : int 3 4 5 4 4 3 4 2 2 3 ...
$ Gender : int 1 1 1 1 1 1 1 1 1 1 ...
$ Employee Type : int 0 1 1 0 1 0 1 1 0 0 ...
$ Geographic Location: int 1 1 1 1 1 1 1 1 1 1 ...
$ AGE : int 42 32 43 26 37 35 44 50 27 47 ...
$ EXP : num 6 5.8 1 3 14 8 12.5 0.2 0.3 5.3 ...
$ JP : int 5 4 5 5 5 4 5 5 4 5 ...
$ JS : num -0.22499 -0.55478 -0.51594 -0.13101 0.00117 ...
$ OC : num -0.364 -1.661 0.781 -0.33 0.321 ...
$ SI : num -0.37 0.388 1.281 0.222 0.641 ...
$ EP : num NA 0.868 0.868 0.659 0.435 ...
$ AC : num -1.295 -1.257 -0.827 -1.257 -1.086 ...SEM_Data = SEM_Data %>% mutate(across(.cols=2:22, .fns=as.numeric))
SEM_Data$Gender<-factor(SEM_Data$Gender,
levels = c(0,1),
labels = c("Male", "Female"))
SEM_Data$`Employee Type`<-factor(SEM_Data$`Employee Type`,
levels = c(0,1),
labels = c("Part-Time", "Full-Time"))
SEM_Data$`Geographic Location`<-factor(SEM_Data$`Geographic Location`,
levels = c(0,1),
labels = c("Non-USA", "USA"))
describe(SEM_Data[,-1]) vars n mean sd median trimmed mad min max
JS1 1 400 4.20 1.34 4.00 4.22 1.48 1.00 7.00
OC1 2 400 4.89 2.53 5.00 4.92 2.97 0.00 10.00
OC2 3 400 8.42 2.19 9.00 8.89 1.48 0.00 10.00
EP1 4 400 8.53 1.83 9.00 8.85 1.48 0.00 10.00
OC3 5 400 8.65 1.75 9.00 8.99 1.48 0.00 10.00
OC4 6 400 8.40 2.05 9.00 8.83 1.48 0.00 10.00
EP2 7 400 8.85 1.63 9.00 9.17 1.48 0.00 10.00
EP3 8 400 8.93 1.33 9.00 9.16 1.48 0.00 10.00
AC1 9 400 2.76 1.39 3.00 2.70 1.48 1.00 5.00
EP4 10 399 5.83 1.39 6.00 6.06 1.48 1.00 7.00
JS2 11 400 4.20 1.37 4.00 4.22 1.48 1.00 7.00
JS3 12 400 3.21 1.32 3.00 3.22 1.48 1.00 6.00
AC2 13 400 3.55 1.73 4.00 3.57 1.48 1.00 6.00
SI1 14 400 4.20 0.87 4.00 4.33 1.48 1.00 5.00
JS4 15 400 2.67 1.28 3.00 2.58 1.48 1.00 5.00
SI2 16 400 4.20 0.88 4.00 4.33 1.48 1.00 5.00
JS5 17 400 54.82 20.59 55.50 54.83 22.98 0.00 100.00
AC3 18 400 2.78 1.42 3.00 2.72 1.48 1.00 5.00
SI3 19 400 3.47 1.02 3.00 3.50 1.48 1.00 5.00
AC4 20 399 3.21 1.61 3.00 3.14 1.48 1.00 6.00
SI4 21 400 3.48 0.97 4.00 3.52 1.48 1.00 5.00
Gender* 22 400 1.50 0.50 1.50 1.50 0.74 1.00 2.00
Employee Type* 23 400 1.52 0.50 2.00 1.53 0.00 1.00 2.00
Geographic Location* 24 400 1.50 0.50 1.50 1.50 0.74 1.00 2.00
AGE 25 399 43.38 7.14 43.00 43.36 7.41 24.00 62.00
EXP 26 399 8.64 3.62 8.60 8.68 3.56 0.10 25.00
JP 27 399 4.36 0.97 5.00 4.54 0.00 1.00 5.00
JS 28 400 0.00 0.92 -0.03 -0.01 0.96 -2.36 2.40
OC 29 400 0.00 0.93 0.27 0.16 0.76 -4.22 0.97
SI 30 400 0.00 0.95 0.10 0.10 0.83 -3.43 1.28
EP 31 399 0.00 0.93 0.13 0.15 1.09 -4.29 0.87
AC 32 399 0.00 0.95 -0.06 -0.02 1.27 -1.45 1.71
range skew kurtosis se
JS1 6.00 -0.09 -0.21 0.07
OC1 10.00 -0.13 -0.72 0.13
OC2 10.00 -2.07 4.52 0.11
EP1 10.00 -1.98 5.35 0.09
OC3 10.00 -2.03 5.24 0.09
OC4 10.00 -1.97 4.29 0.10
EP2 10.00 -2.11 5.71 0.08
EP3 10.00 -1.81 5.39 0.07
AC1 4.00 0.22 -1.22 0.07
EP4 6.00 -1.28 1.30 0.07
JS2 6.00 -0.03 -0.19 0.07
JS3 5.00 0.11 -0.69 0.07
AC2 5.00 -0.07 -1.32 0.09
SI1 4.00 -1.31 2.10 0.04
JS4 4.00 0.30 -0.97 0.06
SI2 4.00 -1.25 1.84 0.04
JS5 100.00 -0.02 -0.66 1.03
AC3 4.00 0.21 -1.25 0.07
SI3 4.00 0.00 -0.55 0.05
AC4 5.00 0.17 -1.11 0.08
SI4 4.00 -0.48 0.00 0.05
Gender* 1.00 0.00 -2.00 0.03
Employee Type* 1.00 -0.09 -2.00 0.03
Geographic Location* 1.00 0.00 -2.00 0.03
AGE 38.00 0.02 -0.26 0.36
EXP 24.90 0.10 0.86 0.18
JP 4.00 -1.33 0.69 0.05
JS 4.76 0.09 -0.39 0.05
OC 5.19 -1.73 3.53 0.05
SI 4.71 -1.06 1.41 0.05
EP 5.15 -1.39 2.09 0.05
AC 3.16 0.13 -1.25 0.05describe(SEM_Data[,-1])%>%
knitr::kable(digits = 3, format="html", booktabs=TRUE, caption="Table 1. Example Descriptives")%>%
kable_classic(full_width = F, html_font = "Cambria")| vars | n | mean | sd | median | trimmed | mad | min | max | range | skew | kurtosis | se | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| JS1 | 1 | 400 | 4.197 | 1.339 | 4.000 | 4.216 | 1.483 | 1.000 | 7.000 | 6.000 | -0.087 | -0.215 | 0.067 |
| OC1 | 2 | 400 | 4.888 | 2.525 | 5.000 | 4.922 | 2.965 | 0.000 | 10.000 | 10.000 | -0.130 | -0.723 | 0.126 |
| OC2 | 3 | 400 | 8.418 | 2.186 | 9.000 | 8.887 | 1.483 | 0.000 | 10.000 | 10.000 | -2.067 | 4.519 | 0.109 |
| EP1 | 4 | 400 | 8.528 | 1.831 | 9.000 | 8.853 | 1.483 | 0.000 | 10.000 | 10.000 | -1.983 | 5.354 | 0.092 |
| OC3 | 5 | 400 | 8.655 | 1.755 | 9.000 | 8.991 | 1.483 | 0.000 | 10.000 | 10.000 | -2.031 | 5.239 | 0.088 |
| OC4 | 6 | 400 | 8.405 | 2.053 | 9.000 | 8.828 | 1.483 | 0.000 | 10.000 | 10.000 | -1.973 | 4.294 | 0.103 |
| EP2 | 7 | 400 | 8.848 | 1.628 | 9.000 | 9.169 | 1.483 | 0.000 | 10.000 | 10.000 | -2.111 | 5.706 | 0.081 |
| EP3 | 8 | 400 | 8.928 | 1.335 | 9.000 | 9.159 | 1.483 | 0.000 | 10.000 | 10.000 | -1.810 | 5.391 | 0.067 |
| AC1 | 9 | 400 | 2.760 | 1.394 | 3.000 | 2.700 | 1.483 | 1.000 | 5.000 | 4.000 | 0.216 | -1.221 | 0.070 |
| EP4 | 10 | 399 | 5.830 | 1.395 | 6.000 | 6.056 | 1.483 | 1.000 | 7.000 | 6.000 | -1.280 | 1.301 | 0.070 |
| JS2 | 11 | 400 | 4.202 | 1.370 | 4.000 | 4.219 | 1.483 | 1.000 | 7.000 | 6.000 | -0.034 | -0.190 | 0.068 |
| JS3 | 12 | 400 | 3.215 | 1.316 | 3.000 | 3.216 | 1.483 | 1.000 | 6.000 | 5.000 | 0.107 | -0.692 | 0.066 |
| AC2 | 13 | 400 | 3.553 | 1.726 | 4.000 | 3.566 | 1.483 | 1.000 | 6.000 | 5.000 | -0.070 | -1.324 | 0.086 |
| SI1 | 14 | 400 | 4.202 | 0.871 | 4.000 | 4.334 | 1.483 | 1.000 | 5.000 | 4.000 | -1.310 | 2.095 | 0.044 |
| JS4 | 15 | 400 | 2.668 | 1.281 | 3.000 | 2.584 | 1.483 | 1.000 | 5.000 | 4.000 | 0.301 | -0.965 | 0.064 |
| SI2 | 16 | 400 | 4.205 | 0.877 | 4.000 | 4.331 | 1.483 | 1.000 | 5.000 | 4.000 | -1.252 | 1.839 | 0.044 |
| JS5 | 17 | 400 | 54.818 | 20.594 | 55.500 | 54.834 | 22.980 | 0.000 | 100.000 | 100.000 | -0.023 | -0.658 | 1.030 |
| AC3 | 18 | 400 | 2.775 | 1.419 | 3.000 | 2.719 | 1.483 | 1.000 | 5.000 | 4.000 | 0.206 | -1.249 | 0.071 |
| SI3 | 19 | 400 | 3.473 | 1.016 | 3.000 | 3.497 | 1.483 | 1.000 | 5.000 | 4.000 | 0.003 | -0.550 | 0.051 |
| AC4 | 20 | 399 | 3.211 | 1.612 | 3.000 | 3.140 | 1.483 | 1.000 | 6.000 | 5.000 | 0.171 | -1.113 | 0.081 |
| SI4 | 21 | 400 | 3.480 | 0.968 | 4.000 | 3.522 | 1.483 | 1.000 | 5.000 | 4.000 | -0.481 | 0.005 | 0.048 |
| Gender* | 22 | 400 | 1.500 | 0.501 | 1.500 | 1.500 | 0.741 | 1.000 | 2.000 | 1.000 | 0.000 | -2.005 | 0.025 |
| Employee Type* | 23 | 400 | 1.522 | 0.500 | 2.000 | 1.528 | 0.000 | 1.000 | 2.000 | 1.000 | -0.090 | -1.997 | 0.025 |
| Geographic Location* | 24 | 400 | 1.500 | 0.501 | 1.500 | 1.500 | 0.741 | 1.000 | 2.000 | 1.000 | 0.000 | -2.005 | 0.025 |
| AGE | 25 | 399 | 43.383 | 7.138 | 43.000 | 43.364 | 7.413 | 24.000 | 62.000 | 38.000 | 0.019 | -0.256 | 0.357 |
| EXP | 26 | 399 | 8.639 | 3.620 | 8.600 | 8.683 | 3.558 | 0.100 | 25.000 | 24.900 | 0.097 | 0.856 | 0.181 |
| JP | 27 | 399 | 4.358 | 0.974 | 5.000 | 4.536 | 0.000 | 1.000 | 5.000 | 4.000 | -1.332 | 0.695 | 0.049 |
| JS | 28 | 400 | 0.000 | 0.920 | -0.026 | -0.010 | 0.964 | -2.358 | 2.402 | 4.759 | 0.093 | -0.393 | 0.046 |
| OC | 29 | 400 | 0.000 | 0.934 | 0.268 | 0.160 | 0.760 | -4.218 | 0.969 | 5.187 | -1.729 | 3.528 | 0.047 |
| SI | 30 | 400 | 0.000 | 0.947 | 0.104 | 0.096 | 0.831 | -3.426 | 1.281 | 4.708 | -1.055 | 1.410 | 0.047 |
| EP | 31 | 399 | 0.000 | 0.932 | 0.130 | 0.148 | 1.094 | -4.286 | 0.868 | 5.154 | -1.392 | 2.091 | 0.047 |
| AC | 32 | 399 | 0.000 | 0.946 | -0.062 | -0.019 | 1.267 | -1.450 | 1.712 | 3.162 | 0.130 | -1.253 | 0.047 |
#JS = Job Satisfaction
#OC = Organizational Commitment
#EP = Environmental Support
#AC = Attitude Toward Co-Workers
#SI = Stay Intention
#All variables coded with higher scores indicating higher levels of the construct
SEM_Data_NM <- na.omit(SEM_Data)dpriors() nu alpha lambda beta
"normal(0,32)" "normal(0,10)" "normal(0,10)" "normal(0,10)"
theta psi rho ibpsi
"gamma(1,.5)[sd]" "gamma(1,.5)[sd]" "beta(1,1)" "wishart(3,iden)"
tau
"normal(0,1.5)" | Parameter | Meaning | Default Prior |
|---|---|---|
| nu | Observed intercepts | Normal(0, 32) |
| alpha | Latent intercepts | Normal(0, 10) |
| lambda | Factor loadings | Normal(0, 10) |
| beta | Regression paths | Normal(0, 10) |
| theta | Residual variances (observed) | Gamma(1, 0.5) |
| psi | Residual variances (latent) | Gamma(1, 0.5) |
| rho | Correlations | Beta(1, 1) |
| ibpsi | Latent covariance matrix | Wishart |
| tau | Thresholds (ordinal only) | Normal(0, 1.5) |
BayesM1 <- '
Env_Supp =~ EP1 + EP2 + EP3 + EP4
Att_Cowrk =~ AC1 + AC2 + AC3 + AC4
Org_Comm =~ OC1 + OC2 + OC3 + OC4
Job_Sat =~ JS1 + JS2 + JS3 + JS4
Stay_Int =~ SI1 + SI2 + SI3 + SI4
Job_Sat ~ Env_Supp + Att_Cowrk + Org_Comm
Stay_Int ~ Env_Supp + Att_Cowrk + Org_Comm + Job_Sat
Env_Supp ~~ Att_Cowrk
Env_Supp ~~ Org_Comm
Att_Cowrk ~~ Org_Comm
'
B_fit1 <- bsem(BayesM1, data = SEM_Data_NM)
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Computing post-estimation metrics (including lvs if requested)...summary(B_fit1, standardized = TRUE, fit.measures = TRUE, rsquare = TRUE)blavaan 0.5.8 ended normally after 1000 iterations
Estimator BAYES
Optimization method MCMC
Number of model parameters 50
Number of observations 398
Statistic MargLogLik PPP
Value -12377.126 0.021
Parameter Estimates:
Latent Variables:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Env_Supp =~
EP1 1.000 1.261 0.690
EP2 1.059 0.076 0.920 1.216 1.335 0.814
EP3 0.823 0.062 0.710 0.952 1.038 0.780
EP4 0.918 0.066 0.797 1.055 1.157 0.823
Att_Cowrk =~
AC1 1.000 1.141 0.819
AC2 1.248 0.070 1.119 1.388 1.424 0.821
AC3 1.046 0.057 0.939 1.160 1.194 0.837
AC4 1.155 0.065 1.032 1.287 1.318 0.815
Org_Comm =~
OC1 1.000 1.432 0.570
OC2 1.370 0.121 1.167 1.636 1.963 0.889
OC3 0.816 0.084 0.666 0.999 1.169 0.661
OC4 1.218 0.109 1.027 1.462 1.745 0.841
Job_Sat =~
JS1 1.000 0.987 0.735
JS2 1.036 0.084 0.886 1.213 1.022 0.741
JS3 0.936 0.081 0.791 1.107 0.924 0.697
JS4 0.927 0.080 0.778 1.094 0.915 0.709
Stay_Int =~
SI1 1.000 0.713 0.812
SI2 1.074 0.055 0.971 1.186 0.765 0.865
SI3 1.065 0.067 0.935 1.203 0.759 0.742
SI4 1.169 0.063 1.054 1.304 0.833 0.853
Rhat Prior
1.000 normal(0,10)
1.000 normal(0,10)
0.999 normal(0,10)
1.001 normal(0,10)
0.999 normal(0,10)
1.001 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
Regressions:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Job_Sat ~
Env_Supp 0.147 0.056 0.036 0.257 0.187 0.187
Att_Cowrk -0.048 0.053 -0.148 0.055 -0.055 -0.055
Org_Comm 0.078 0.050 -0.019 0.177 0.114 0.114
Stay_Int ~
Env_Supp 0.199 0.036 0.132 0.271 0.353 0.353
Att_Cowrk 0.073 0.031 0.012 0.135 0.117 0.117
Org_Comm 0.164 0.032 0.104 0.230 0.330 0.330
Job_Sat 0.049 0.036 -0.021 0.118 0.067 0.067
Rhat Prior
1.000 normal(0,10)
0.999 normal(0,10)
0.999 normal(0,10)
1.000 normal(0,10)
0.999 normal(0,10)
1.000 normal(0,10)
0.999 normal(0,10)
Covariances:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Env_Supp ~~
Att_Cowrk 0.358 0.088 0.193 0.540 0.249 0.249
Org_Comm 0.884 0.143 0.629 1.187 0.490 0.490
Att_Cowrk ~~
Org_Comm 0.491 0.105 0.299 0.708 0.300 0.300
Rhat Prior
1.000 lkj_corr(1)
0.999 lkj_corr(1)
1.000 lkj_corr(1)
Variances:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
.EP1 1.747 0.150 1.476 2.049 1.747 0.524
.EP2 0.910 0.095 0.738 1.103 0.910 0.338
.EP3 0.693 0.065 0.576 0.824 0.693 0.391
.EP4 0.636 0.067 0.511 0.778 0.636 0.322
.AC1 0.640 0.061 0.525 0.766 0.640 0.330
.AC2 0.985 0.092 0.814 1.177 0.985 0.327
.AC3 0.609 0.063 0.493 0.740 0.609 0.299
.AC4 0.881 0.083 0.726 1.059 0.881 0.336
.OC1 4.263 0.323 3.667 4.939 4.263 0.675
.OC2 1.017 0.157 0.728 1.317 1.017 0.209
.OC3 1.763 0.143 1.507 2.061 1.763 0.563
.OC4 1.258 0.141 0.991 1.543 1.258 0.292
.JS1 0.828 0.082 0.681 0.996 0.828 0.460
.JS2 0.861 0.087 0.700 1.049 0.861 0.452
.JS3 0.901 0.081 0.755 1.069 0.901 0.514
.JS4 0.829 0.078 0.684 0.993 0.829 0.498
.SI1 0.263 0.024 0.217 0.312 0.263 0.341
.SI2 0.198 0.021 0.158 0.240 0.198 0.252
.SI3 0.471 0.039 0.398 0.553 0.471 0.450
.SI4 0.260 0.027 0.210 0.319 0.260 0.272
Env_Supp 1.589 0.217 1.187 2.038 1.000 1.000
Att_Cowrk 1.302 0.136 1.053 1.584 1.000 1.000
Org_Comm 2.051 0.358 1.386 2.794 1.000 1.000
.Job_Sat 0.913 0.124 0.681 1.173 0.937 0.937
.Stay_Int 0.290 0.033 0.229 0.359 0.571 0.571
Rhat Prior
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
R-Square:
Estimate
EP1 0.476
EP2 0.662
EP3 0.609
EP4 0.678
AC1 0.670
AC2 0.673
AC3 0.701
AC4 0.664
OC1 0.325
OC2 0.791
OC3 0.437
OC4 0.708
JS1 0.540
JS2 0.548
JS3 0.486
JS4 0.502
SI1 0.659
SI2 0.748
SI3 0.550
SI4 0.728
Job_Sat 0.063
Stay_Int 0.429plot(B_fit1, pars = 16:22, plot.type = "trace")
plot(B_fit1, pars = 16:22, plot.type = "intervals")
BayesM2 <- '
Env_Supp =~ EP1 + prior("normal(0,1)")*EP2 + EP3 + EP4
Att_Cowrk =~ AC1 + AC2 + AC3 + AC4
Org_Comm =~ OC1 + OC2 + OC3 + OC4
Job_Sat =~ JS1 + JS2 + JS3 + JS4
Stay_Int =~ SI1 + SI2 + SI3 + SI4
Job_Sat ~ Env_Supp + prior("normal(0.3,0.1)")*Att_Cowrk + Org_Comm
Stay_Int ~ Env_Supp + Att_Cowrk + Org_Comm + prior("normal(0.5,0.1)")*Job_Sat
Env_Supp ~~ Att_Cowrk
Env_Supp ~~ Org_Comm
Att_Cowrk ~~ Org_Comm
'
B_fit2 <- bsem(BayesM2, data = SEM_Data_NM)
SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.000613 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 6.13 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1: 16.611 seconds (Total)
Chain 1:
SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 2).
Chain 2:
Chain 2: Gradient evaluation took 0.000526 seconds
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Chain 2: Adjust your expectations accordingly!
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Chain 2: 16.185 seconds (Total)
Chain 2:
SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000521 seconds
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Chain 3: 15.96 seconds (Total)
Chain 3:
Computing post-estimation metrics (including lvs if requested)...summary(B_fit2, standardized = TRUE, fit.measures = TRUE, rsquare = TRUE)blavaan 0.5.8 ended normally after 1000 iterations
Estimator BAYES
Optimization method MCMC
Number of model parameters 50
Number of observations 398
Statistic MargLogLik PPP
Value -12380.061 0.012
Parameter Estimates:
Latent Variables:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Env_Supp =~
EP1 1.000 1.267 0.692
EP2 1.052 0.072 0.921 1.201 1.333 0.813
EP3 0.820 0.061 0.707 0.943 1.039 0.781
EP4 0.914 0.063 0.799 1.044 1.158 0.824
Att_Cowrk =~
AC1 1.000 1.139 0.818
AC2 1.251 0.072 1.116 1.400 1.425 0.820
AC3 1.048 0.058 0.936 1.165 1.193 0.837
AC4 1.157 0.067 1.032 1.295 1.318 0.815
Org_Comm =~
OC1 1.000 1.433 0.570
OC2 1.370 0.120 1.165 1.634 1.963 0.889
OC3 0.817 0.083 0.669 0.993 1.171 0.661
OC4 1.218 0.108 1.021 1.453 1.746 0.842
Job_Sat =~
JS1 1.000 0.978 0.730
JS2 1.047 0.085 0.894 1.217 1.024 0.741
JS3 0.949 0.082 0.795 1.114 0.928 0.700
JS4 0.941 0.080 0.787 1.105 0.920 0.711
Stay_Int =~
SI1 1.000 0.722 0.816
SI2 1.067 0.053 0.969 1.172 0.770 0.865
SI3 1.059 0.067 0.930 1.194 0.764 0.744
SI4 1.162 0.061 1.045 1.287 0.839 0.855
Rhat Prior
1.000 normal(0,1)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
0.999 normal(0,10)
0.999 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.002 normal(0,10)
1.001 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.001 normal(0,10)
1.001 normal(0,10)
Regressions:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Job_Sat ~
Env_Supp 0.132 0.056 0.024 0.241 0.172 0.172
Att_Cowrk 0.030 0.048 -0.065 0.123 0.034 0.034
Org_Comm 0.061 0.049 -0.034 0.160 0.089 0.089
Stay_Int ~
Env_Supp 0.192 0.034 0.125 0.262 0.336 0.336
Att_Cowrk 0.075 0.031 0.015 0.135 0.118 0.118
Org_Comm 0.161 0.032 0.102 0.229 0.320 0.320
Job_Sat 0.102 0.035 0.034 0.173 0.139 0.139
Rhat Prior
1.000 normal(0,10)
0.999 normal(0.3,0.1)
1.000 normal(0,10)
0.999 normal(0,10)
0.999 normal(0,10)
0.999 normal(0,10)
0.999 normal(0.5,0.1)
Covariances:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Env_Supp ~~
Att_Cowrk 0.356 0.089 0.187 0.539 0.246 0.246
Org_Comm 0.888 0.138 0.633 1.170 0.489 0.489
Att_Cowrk ~~
Org_Comm 0.488 0.106 0.297 0.718 0.299 0.299
Rhat Prior
0.999 lkj_corr(1)
1.000 lkj_corr(1)
1.000 lkj_corr(1)
Variances:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
.EP1 1.744 0.145 1.469 2.036 1.744 0.521
.EP2 0.910 0.094 0.738 1.104 0.910 0.339
.EP3 0.692 0.064 0.575 0.827 0.692 0.391
.EP4 0.632 0.065 0.513 0.768 0.632 0.320
.AC1 0.642 0.062 0.531 0.770 0.642 0.331
.AC2 0.988 0.094 0.816 1.178 0.988 0.327
.AC3 0.609 0.061 0.498 0.735 0.609 0.300
.AC4 0.880 0.083 0.729 1.052 0.880 0.336
.OC1 4.264 0.328 3.682 4.945 4.264 0.675
.OC2 1.019 0.153 0.730 1.328 1.019 0.209
.OC3 1.766 0.137 1.511 2.053 1.766 0.563
.OC4 1.257 0.138 0.994 1.537 1.257 0.292
.JS1 0.839 0.082 0.688 1.014 0.839 0.467
.JS2 0.863 0.090 0.699 1.051 0.863 0.451
.JS3 0.898 0.081 0.746 1.072 0.898 0.510
.JS4 0.826 0.080 0.681 0.993 0.826 0.494
.SI1 0.262 0.024 0.217 0.312 0.262 0.335
.SI2 0.200 0.022 0.159 0.245 0.200 0.252
.SI3 0.471 0.039 0.399 0.552 0.471 0.446
.SI4 0.259 0.027 0.207 0.313 0.259 0.269
Env_Supp 1.605 0.211 1.235 2.050 1.000 1.000
Att_Cowrk 1.297 0.139 1.045 1.593 1.000 1.000
Org_Comm 2.054 0.359 1.415 2.817 1.000 1.000
.Job_Sat 0.901 0.121 0.680 1.150 0.942 0.942
.Stay_Int 0.294 0.034 0.232 0.364 0.564 0.564
Rhat Prior
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.001 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.001 gamma(1,.5)[sd]
1.001 gamma(1,.5)[sd]
R-Square:
Estimate
EP1 0.479
EP2 0.661
EP3 0.609
EP4 0.680
AC1 0.669
AC2 0.673
AC3 0.700
AC4 0.664
OC1 0.325
OC2 0.791
OC3 0.437
OC4 0.708
JS1 0.533
JS2 0.549
JS3 0.490
JS4 0.506
SI1 0.665
SI2 0.748
SI3 0.554
SI4 0.731
Job_Sat 0.058
Stay_Int 0.436blavFitIndices(B_fit2)Warning:
50 (12.6%) p_waic estimates greater than 0.4. We recommend trying loo instead.Warning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.Posterior mean (EAP) of devm-based fit indices:
BRMSEA BGammaHat adjBGammaHat BMc
0.036 0.986 0.972 0.931 coef(B_fit2) %>%
kable(
digits = 3,
format = "html",
booktabs = TRUE,
caption = "Model 2: Posterior Estimates"
) %>%
kable_classic(full_width = FALSE, html_font = "Cambria")| x | |
|---|---|
| Env_Supp=~EP2 | 1.05233595 |
| Env_Supp=~EP3 | 0.82010711 |
| Env_Supp=~EP4 | 0.91421937 |
| Att_Cowrk=~AC2 | 1.25114540 |
| Att_Cowrk=~AC3 | 1.04758351 |
| Att_Cowrk=~AC4 | 1.15722824 |
| Org_Comm=~OC2 | 1.36955130 |
| Org_Comm=~OC3 | 0.81688520 |
| Org_Comm=~OC4 | 1.21818121 |
| Job_Sat=~JS2 | 1.04724357 |
| Job_Sat=~JS3 | 0.94890311 |
| Job_Sat=~JS4 | 0.94064472 |
| Stay_Int=~SI2 | 1.06683519 |
| Stay_Int=~SI3 | 1.05858992 |
| Stay_Int=~SI4 | 1.16191087 |
| Job_Sat~Env_Supp | 0.13245396 |
| Job_Sat~Att_Cowrk | 0.02955331 |
| Job_Sat~Org_Comm | 0.06057994 |
| Stay_Int~Env_Supp | 0.19169864 |
| Stay_Int~Att_Cowrk | 0.07497001 |
| Stay_Int~Org_Comm | 0.16101549 |
| Stay_Int~Job_Sat | 0.10229977 |
| Env_Supp~~Att_Cowrk | 0.35558831 |
| Env_Supp~~Org_Comm | 0.88817317 |
| Att_Cowrk~~Org_Comm | 0.48830706 |
| EP1~~EP1 | 1.74413939 |
| EP2~~EP2 | 0.91030435 |
| EP3~~EP3 | 0.69189179 |
| EP4~~EP4 | 0.63204949 |
| AC1~~AC1 | 0.64199507 |
| AC2~~AC2 | 0.98840975 |
| AC3~~AC3 | 0.60905525 |
| AC4~~AC4 | 0.87989178 |
| OC1~~OC1 | 4.26417874 |
| OC2~~OC2 | 1.01933829 |
| OC3~~OC3 | 1.76558950 |
| OC4~~OC4 | 1.25657745 |
| JS1~~JS1 | 0.83926723 |
| JS2~~JS2 | 0.86262649 |
| JS3~~JS3 | 0.89777894 |
| JS4~~JS4 | 0.82582345 |
| SI1~~SI1 | 0.26228228 |
| SI2~~SI2 | 0.19953398 |
| SI3~~SI3 | 0.47108229 |
| SI4~~SI4 | 0.25876541 |
| Env_Supp~~Env_Supp | 1.60510164 |
| Att_Cowrk~~Att_Cowrk | 1.29664341 |
| Org_Comm~~Org_Comm | 2.05444113 |
| Job_Sat~~Job_Sat | 0.90051979 |
| Stay_Int~~Stay_Int | 0.29395682 |
# Convergence (Rhat should be ~1)
blavInspect(B_fit2, "rhat") Env_Supp=~EP2 Env_Supp=~EP3 Env_Supp=~EP4
0.9997795 0.9997582 0.9997945
Att_Cowrk=~AC2 Att_Cowrk=~AC3 Att_Cowrk=~AC4
0.9998579 0.9994991 0.9993860
Org_Comm=~OC2 Org_Comm=~OC3 Org_Comm=~OC4
1.0001280 0.9998580 0.9997512
Job_Sat=~JS2 Job_Sat=~JS3 Job_Sat=~JS4
1.0020571 1.0008162 0.9999660
Stay_Int=~SI2 Stay_Int=~SI3 Stay_Int=~SI4
1.0001916 1.0010021 1.0007905
Job_Sat~Env_Supp Job_Sat~Att_Cowrk Job_Sat~Org_Comm
0.9998379 0.9994700 0.9995112
Stay_Int~Env_Supp Stay_Int~Att_Cowrk Stay_Int~Org_Comm
0.9993286 0.9992264 0.9994762
Stay_Int~Job_Sat Env_Supp~~Att_Cowrk Env_Supp~~Org_Comm
0.9992499 0.9994078 1.0000468
Att_Cowrk~~Org_Comm EP1~~EP1 EP2~~EP2
0.9997015 0.9993212 0.9998598
EP3~~EP3 EP4~~EP4 AC1~~AC1
0.9993281 0.9998082 0.9997120
AC2~~AC2 AC3~~AC3 AC4~~AC4
0.9996619 0.9992538 0.9991569
OC1~~OC1 OC2~~OC2 OC3~~OC3
0.9991976 0.9994420 0.9991603
OC4~~OC4 JS1~~JS1 JS2~~JS2
0.9993225 1.0002440 1.0005617
JS3~~JS3 JS4~~JS4 SI1~~SI1
0.9994241 0.9992051 0.9995742
SI2~~SI2 SI3~~SI3 SI4~~SI4
0.9996769 0.9994502 0.9994870
Env_Supp~~Env_Supp Att_Cowrk~~Att_Cowrk Org_Comm~~Org_Comm
0.9998454 1.0003942 1.0001945
Job_Sat~~Job_Sat Stay_Int~~Stay_Int
1.0010082 1.0005460 # Trace plots
plot(B_fit2, pars = 16:22, plot.type = "trace")
# Credible intervals
plot(B_fit2, pars = 16:22, plot.type = "intervals")
B_fit3 <- bsem(
BayesM2,
data = SEM_Data_NM,
dp = dpriors(lambda = "normal(1,5)")
)
SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 1).
Chain 1:
Chain 1: Gradient evaluation took 0.000589 seconds
Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 5.89 seconds.
Chain 1: Adjust your expectations accordingly!
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Chain 1:
Chain 1: Elapsed Time: 5.783 seconds (Warm-up)
Chain 1: 10.343 seconds (Sampling)
Chain 1: 16.126 seconds (Total)
Chain 1:
SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 2).
Chain 2:
Chain 2: Gradient evaluation took 0.000529 seconds
Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 5.29 seconds.
Chain 2: Adjust your expectations accordingly!
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Chain 2: 15.452 seconds (Total)
Chain 2:
SAMPLING FOR MODEL 'stanmarg' NOW (CHAIN 3).
Chain 3:
Chain 3: Gradient evaluation took 0.000607 seconds
Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 6.07 seconds.
Chain 3: Adjust your expectations accordingly!
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Chain 3: 15.486 seconds (Total)
Chain 3:
Computing post-estimation metrics (including lvs if requested)...summary(B_fit3, standardized = TRUE, fit.measures = TRUE, rsquare = TRUE)blavaan 0.5.8 ended normally after 1000 iterations
Estimator BAYES
Optimization method MCMC
Number of model parameters 50
Number of observations 398
Statistic MargLogLik PPP
Value -12370.436 0.016
Parameter Estimates:
Latent Variables:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Env_Supp =~
EP1 1.000 1.268 0.693
EP2 1.051 0.073 0.919 1.207 1.333 0.813
EP3 0.819 0.061 0.707 0.947 1.038 0.780
EP4 0.914 0.065 0.794 1.055 1.158 0.824
Att_Cowrk =~
AC1 1.000 1.141 0.818
AC2 1.250 0.070 1.120 1.397 1.426 0.821
AC3 1.046 0.058 0.938 1.167 1.194 0.837
AC4 1.158 0.066 1.037 1.297 1.321 0.816
Org_Comm =~
OC1 1.000 1.426 0.568
OC2 1.374 0.120 1.163 1.637 1.960 0.889
OC3 0.819 0.081 0.677 1.001 1.168 0.660
OC4 1.222 0.107 1.031 1.460 1.743 0.841
Job_Sat =~
JS1 1.000 0.975 0.728
JS2 1.048 0.083 0.895 1.226 1.022 0.740
JS3 0.950 0.079 0.804 1.108 0.927 0.700
JS4 0.942 0.081 0.792 1.112 0.919 0.712
Stay_Int =~
SI1 1.000 0.722 0.816
SI2 1.066 0.055 0.962 1.175 0.770 0.865
SI3 1.060 0.068 0.933 1.201 0.765 0.745
SI4 1.162 0.063 1.043 1.292 0.839 0.855
Rhat Prior
1.003 normal(0,1)
1.002 normal(1,5)
1.003 normal(1,5)
0.999 normal(1,5)
0.999 normal(1,5)
1.000 normal(1,5)
1.001 normal(1,5)
1.000 normal(1,5)
1.002 normal(1,5)
1.000 normal(1,5)
1.000 normal(1,5)
1.000 normal(1,5)
1.001 normal(1,5)
1.000 normal(1,5)
1.000 normal(1,5)
Regressions:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Job_Sat ~
Env_Supp 0.131 0.056 0.022 0.242 0.171 0.171
Att_Cowrk 0.029 0.047 -0.061 0.121 0.033 0.033
Org_Comm 0.060 0.050 -0.037 0.162 0.088 0.088
Stay_Int ~
Env_Supp 0.192 0.034 0.127 0.259 0.337 0.337
Att_Cowrk 0.075 0.031 0.015 0.135 0.118 0.118
Org_Comm 0.162 0.032 0.101 0.228 0.319 0.319
Job_Sat 0.103 0.036 0.033 0.174 0.139 0.139
Rhat Prior
0.999 normal(0,10)
1.000 normal(0.3,0.1)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
1.000 normal(0,10)
0.999 normal(0.5,0.1)
Covariances:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
Env_Supp ~~
Att_Cowrk 0.357 0.088 0.194 0.534 0.247 0.247
Org_Comm 0.882 0.137 0.632 1.168 0.488 0.488
Att_Cowrk ~~
Org_Comm 0.488 0.105 0.297 0.701 0.300 0.300
Rhat Prior
0.999 lkj_corr(1)
1.000 lkj_corr(1)
1.000 lkj_corr(1)
Variances:
Estimate Post.SD pi.lower pi.upper Std.lv Std.all
.EP1 1.739 0.151 1.468 2.057 1.739 0.520
.EP2 0.911 0.091 0.747 1.107 0.911 0.339
.EP3 0.693 0.065 0.578 0.829 0.693 0.392
.EP4 0.634 0.066 0.510 0.767 0.634 0.321
.AC1 0.642 0.063 0.530 0.774 0.642 0.330
.AC2 0.985 0.093 0.813 1.174 0.985 0.326
.AC3 0.610 0.058 0.504 0.732 0.610 0.300
.AC4 0.879 0.081 0.731 1.049 0.879 0.335
.OC1 4.266 0.326 3.660 4.947 4.266 0.677
.OC2 1.016 0.157 0.721 1.339 1.016 0.209
.OC3 1.766 0.144 1.504 2.064 1.766 0.564
.OC4 1.258 0.142 0.989 1.548 1.258 0.293
.JS1 0.842 0.084 0.692 1.014 0.842 0.469
.JS2 0.863 0.084 0.707 1.029 0.863 0.452
.JS3 0.896 0.084 0.738 1.070 0.896 0.511
.JS4 0.823 0.077 0.681 0.981 0.823 0.494
.SI1 0.262 0.025 0.217 0.313 0.262 0.335
.SI2 0.199 0.021 0.158 0.242 0.199 0.251
.SI3 0.470 0.039 0.399 0.549 0.470 0.445
.SI4 0.259 0.027 0.210 0.316 0.259 0.269
Env_Supp 1.607 0.216 1.222 2.070 1.000 1.000
Att_Cowrk 1.302 0.139 1.043 1.592 1.000 1.000
Org_Comm 2.035 0.337 1.405 2.731 1.000 1.000
.Job_Sat 0.897 0.120 0.678 1.150 0.943 0.943
.Stay_Int 0.294 0.034 0.233 0.366 0.563 0.563
Rhat Prior
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
1.001 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.001 gamma(1,.5)[sd]
0.999 gamma(1,.5)[sd]
1.000 gamma(1,.5)[sd]
R-Square:
Estimate
EP1 0.480
EP2 0.661
EP3 0.608
EP4 0.679
AC1 0.670
AC2 0.674
AC3 0.700
AC4 0.665
OC1 0.323
OC2 0.791
OC3 0.436
OC4 0.707
JS1 0.531
JS2 0.548
JS3 0.489
JS4 0.506
SI1 0.665
SI2 0.749
SI3 0.555
SI4 0.731
Job_Sat 0.057
Stay_Int 0.437coef(B_fit3) %>%
kable(
digits = 3,
format = "html",
booktabs = TRUE,
caption = "Model 3: Posterior Estimates (Weak Priors)"
) %>%
kable_classic(full_width = FALSE, html_font = "Cambria")| x | |
|---|---|
| Env_Supp=~EP2 | 1.05103875 |
| Env_Supp=~EP3 | 0.81855025 |
| Env_Supp=~EP4 | 0.91353201 |
| Att_Cowrk=~AC2 | 1.24989473 |
| Att_Cowrk=~AC3 | 1.04636762 |
| Att_Cowrk=~AC4 | 1.15797210 |
| Org_Comm=~OC2 | 1.37412178 |
| Org_Comm=~OC3 | 0.81854151 |
| Org_Comm=~OC4 | 1.22210175 |
| Job_Sat=~JS2 | 1.04763953 |
| Job_Sat=~JS3 | 0.95031831 |
| Job_Sat=~JS4 | 0.94221068 |
| Stay_Int=~SI2 | 1.06640464 |
| Stay_Int=~SI3 | 1.06003615 |
| Stay_Int=~SI4 | 1.16165132 |
| Job_Sat~Env_Supp | 0.13145365 |
| Job_Sat~Att_Cowrk | 0.02863180 |
| Job_Sat~Org_Comm | 0.06025761 |
| Stay_Int~Env_Supp | 0.19213552 |
| Stay_Int~Att_Cowrk | 0.07475601 |
| Stay_Int~Org_Comm | 0.16160594 |
| Stay_Int~Job_Sat | 0.10287073 |
| Env_Supp~~Att_Cowrk | 0.35747782 |
| Env_Supp~~Org_Comm | 0.88226780 |
| Att_Cowrk~~Org_Comm | 0.48822021 |
| EP1~~EP1 | 1.73913610 |
| EP2~~EP2 | 0.91119635 |
| EP3~~EP3 | 0.69313202 |
| EP4~~EP4 | 0.63424619 |
| AC1~~AC1 | 0.64178274 |
| AC2~~AC2 | 0.98523863 |
| AC3~~AC3 | 0.61001729 |
| AC4~~AC4 | 0.87889912 |
| OC1~~OC1 | 4.26625460 |
| OC2~~OC2 | 1.01624000 |
| OC3~~OC3 | 1.76648259 |
| OC4~~OC4 | 1.25755173 |
| JS1~~JS1 | 0.84206019 |
| JS2~~JS2 | 0.86305014 |
| JS3~~JS3 | 0.89643282 |
| JS4~~JS4 | 0.82335190 |
| SI1~~SI1 | 0.26239286 |
| SI2~~SI2 | 0.19901222 |
| SI3~~SI3 | 0.46998620 |
| SI4~~SI4 | 0.25903218 |
| Env_Supp~~Env_Supp | 1.60735527 |
| Att_Cowrk~~Att_Cowrk | 1.30166097 |
| Org_Comm~~Org_Comm | 2.03472117 |
| Job_Sat~~Job_Sat | 0.89701453 |
| Stay_Int~~Stay_Int | 0.29371767 |
blavInspect(B_fit3, "rhat") Env_Supp=~EP2 Env_Supp=~EP3 Env_Supp=~EP4
1.0030587 1.0021384 1.0029584
Att_Cowrk=~AC2 Att_Cowrk=~AC3 Att_Cowrk=~AC4
0.9993566 0.9992504 0.9995370
Org_Comm=~OC2 Org_Comm=~OC3 Org_Comm=~OC4
1.0010065 1.0000329 1.0016103
Job_Sat=~JS2 Job_Sat=~JS3 Job_Sat=~JS4
1.0003696 1.0001723 1.0001136
Stay_Int=~SI2 Stay_Int=~SI3 Stay_Int=~SI4
1.0006708 1.0002865 1.0002660
Job_Sat~Env_Supp Job_Sat~Att_Cowrk Job_Sat~Org_Comm
0.9994825 0.9995212 0.9995135
Stay_Int~Env_Supp Stay_Int~Att_Cowrk Stay_Int~Org_Comm
0.9999417 0.9996804 1.0001914
Stay_Int~Job_Sat Env_Supp~~Att_Cowrk Env_Supp~~Org_Comm
0.9991264 0.9993867 0.9999587
Att_Cowrk~~Org_Comm EP1~~EP1 EP2~~EP2
1.0001407 0.9999626 0.9995925
EP3~~EP3 EP4~~EP4 AC1~~AC1
0.9992713 0.9996599 0.9998458
AC2~~AC2 AC3~~AC3 AC4~~AC4
1.0004493 0.9995111 0.9991987
OC1~~OC1 OC2~~OC2 OC3~~OC3
0.9992383 1.0000208 0.9991289
OC4~~OC4 JS1~~JS1 JS2~~JS2
0.9991520 0.9994850 1.0000345
JS3~~JS3 JS4~~JS4 SI1~~SI1
0.9993771 0.9996318 0.9994349
SI2~~SI2 SI3~~SI3 SI4~~SI4
1.0000492 0.9993937 0.9996801
Env_Supp~~Env_Supp Att_Cowrk~~Att_Cowrk Org_Comm~~Org_Comm
1.0014152 0.9992559 1.0005315
Job_Sat~~Job_Sat Stay_Int~~Stay_Int
0.9994102 0.9999358 plot(B_fit3, pars = 16:22, plot.type = "trace")
plot(B_fit3, pars = 16:22, plot.type = "intervals")
blavCompare(B_fit1, B_fit2)Replacing NAs in `r_eff` with 1sWarning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.Replacing NAs in `r_eff` with 1sWarning: Some Pareto k diagnostic values are too high. See help('pareto-k-diagnostic') for details.Warning:
49 (12.3%) p_waic estimates greater than 0.4. We recommend trying loo instead.Warning:
50 (12.6%) p_waic estimates greater than 0.4. We recommend trying loo instead.
WAIC estimates:
object1: 24528.125
object2: 24532.055
ELPD difference & SE:
-1.965 2.051
LOO estimates:
object1: 24526.464
object2: 24530.093
ELPD difference & SE:
-1.814 1.864
Laplace approximation to the log-Bayes factor
(experimental; positive values favor object1): 2.935 Sample Write Up
A Bayesian structural equation model was estimated to examine relationships among latent constructs. Model estimation showed excellent convergence, with all R-hat values close to 1.00 and well-mixed trace plots, indicating stable posterior sampling. Overall model fit was strong according to posterior predictive fit indices, including BRMSEA = 0.036, BGammaHat = 0.986, adjusted BGammaHat = 0.973, and BMc = 0.931, all indicating good to excellent global fit. Predictive model comparison using LOO and WAIC indicated no meaningful differences in out-of-sample predictive performance across alternative prior specifications, suggesting robust predictive equivalence. However, posterior predictive checks indicated potential localized misfit (PPP = 0.015), suggesting that while the model captures the overall covariance structure well, it may not fully reproduce certain finer-grained aspects of the observed data. Taken together, results suggest a well-identified and stable model with strong global fit and predictive robustness, alongside minor localized discrepancies in model-data reproduction.