cSEM Tutorial for Confirmatory Composite Analysis
Get the data here.
Install the recent version of cSEM:
devtools::install_github("FloSchuberth/cSEM")
install.packages("readxl")Load the cSEM package:
library(cSEM)##
## Attaching package: 'cSEM'## The following object is masked from 'package:stats':
##
## predict## The following object is masked from 'package:grDevices':
##
## savePlotImport the dataset. For that reason, please select the IT_Flex.xlsx file.
ITFlex <- as.data.frame(readxl::read_excel(choose.files()))Specify the model with a saturated structural model:
model_IT_Fex="
# Composite models
ITComp <~ ITCOMP1 + ITCOMP2 + ITCOMP3 + ITCOMP4
Modul <~ MOD1 + MOD2 + MOD3 + MOD4
ITConn <~ ITCONN1 + ITCONN2 + ITCONN3 + ITCONN4
ITPers <~ ITPSF1 + ITPSF2 + ITPSF3 + ITPSF4
# Saturated structural model
ITPers ~ ITComp + Modul + ITConn
Modul ~ ITComp + ITConn
ITConn ~ ITComp
"Estimate the model using MAXVAR:
out <- csem(.data = ITFlex,
.model = model_IT_Fex,
.approach_weights = "MAXVAR",
.resample_method = "bootstrap",
.dominant_indicators = c("ITComp" = "ITCOMP1","ITConn"="ITCONN1",
"Modul"="MOD1","ITPers"="ITPSF1"))Return model summary:
summarize(out)## ________________________________________________________________________________
## ----------------------------------- Overview -----------------------------------
##
## General information:
## ------------------------
## Estimation status = Ok
## Number of observations = 100
## Weight estimator = MAXVAR
## Type of indicator correlation = Pearson
## Path model estimator = OLS
## Second-order approach = NA
## Type of path model = Linear
## Disattenuated = No
##
## Resample information:
## ---------------------
## Resample method = "bootstrap"
## Number of resamples = 499
## Number of admissible results = 499
## Approach to handle inadmissibles = "drop"
## Sign change option = "none"
## Random seed = 1628426985
##
## Construct details:
## ------------------
## Name Modeled as Order
##
## ITComp Composite First order
## ITConn Composite First order
## Modul Composite First order
## ITPers Composite First order
##
## ----------------------------------- Estimates ----------------------------------
##
## Estimated path coefficients:
## ============================
## CI_percentile
## Path Estimate Std. error t-stat. p-value 95%
## ITConn ~ ITComp 0.6014 0.0871 6.9022 0.0000 [ 0.4634; 0.7480 ]
## Modul ~ ITComp 0.3702 0.1069 3.4625 0.0005 [ 0.1463; 0.5595 ]
## Modul ~ ITConn 0.3878 0.1098 3.5321 0.0004 [ 0.2063; 0.5988 ]
## ITPers ~ ITComp 0.0182 0.1306 0.1392 0.8893 [-0.2183; 0.2986 ]
## ITPers ~ ITConn 0.2420 0.1127 2.1473 0.0318 [ 0.0370; 0.4882 ]
## ITPers ~ Modul 0.4243 0.1121 3.7858 0.0002 [ 0.1931; 0.6104 ]
##
## Estimated loadings:
## ===================
## CI_percentile
## Loading Estimate Std. error t-stat. p-value 95%
## ITComp =~ ITCOMP1 0.6048 0.1256 4.8166 0.0000 [ 0.3292; 0.8256 ]
## ITComp =~ ITCOMP2 0.5964 0.1442 4.1353 0.0000 [ 0.2768; 0.8214 ]
## ITComp =~ ITCOMP3 0.9272 0.0792 11.7090 0.0000 [ 0.7128; 0.9886 ]
## ITComp =~ ITCOMP4 0.7164 0.1199 5.9771 0.0000 [ 0.4262; 0.8792 ]
## ITConn =~ ITCONN1 0.4205 0.1360 3.0927 0.0020 [ 0.1208; 0.6656 ]
## ITConn =~ ITCONN2 0.6899 0.1277 5.4028 0.0000 [ 0.4004; 0.8518 ]
## ITConn =~ ITCONN3 0.9100 0.1047 8.6885 0.0000 [ 0.7226; 0.9767 ]
## ITConn =~ ITCONN4 0.7354 0.1229 5.9827 0.0000 [ 0.5139; 0.8910 ]
## Modul =~ MOD1 0.6137 0.1265 4.8527 0.0000 [ 0.2907; 0.7783 ]
## Modul =~ MOD2 0.7714 0.0785 9.8312 0.0000 [ 0.5576; 0.8868 ]
## Modul =~ MOD3 0.7599 0.0834 9.1115 0.0000 [ 0.5629; 0.8850 ]
## Modul =~ MOD4 0.7636 0.0887 8.6051 0.0000 [ 0.5625; 0.8999 ]
## ITPers =~ ITPSF1 0.7956 0.1137 6.9988 0.0000 [ 0.4999; 0.9404 ]
## ITPers =~ ITPSF2 0.6493 0.1515 4.2867 0.0000 [ 0.2525; 0.8536 ]
## ITPers =~ ITPSF3 0.7974 0.1214 6.5682 0.0000 [ 0.4722; 0.9468 ]
## ITPers =~ ITPSF4 0.6628 0.1476 4.4901 0.0000 [ 0.3204; 0.8799 ]
##
## Estimated weights:
## ==================
## CI_percentile
## Weight Estimate Std. error t-stat. p-value 95%
## ITComp <~ ITCOMP1 0.2798 0.1559 1.7944 0.0727 [-0.0111; 0.5998 ]
## ITComp <~ ITCOMP2 -0.1123 0.1859 -0.6041 0.5458 [-0.4616; 0.2461 ]
## ITComp <~ ITCOMP3 0.7449 0.1889 3.9444 0.0001 [ 0.3177; 1.0759 ]
## ITComp <~ ITCOMP4 0.2891 0.1842 1.5695 0.1165 [-0.0753; 0.6088 ]
## ITConn <~ ITCONN1 0.1321 0.1641 0.8049 0.4209 [-0.2066; 0.4551 ]
## ITConn <~ ITCONN2 0.1986 0.1808 1.0980 0.2722 [-0.1907; 0.5009 ]
## ITConn <~ ITCONN3 0.6056 0.1402 4.3189 0.0000 [ 0.3119; 0.8524 ]
## ITConn <~ ITCONN4 0.3486 0.1663 2.0963 0.0361 [ 0.0433; 0.6593 ]
## Modul <~ MOD1 0.1739 0.1467 1.1854 0.2359 [-0.1585; 0.4292 ]
## Modul <~ MOD2 0.4265 0.1590 2.6830 0.0073 [ 0.1255; 0.6987 ]
## Modul <~ MOD3 0.2181 0.1583 1.3779 0.1682 [-0.0933; 0.5494 ]
## Modul <~ MOD4 0.5220 0.1264 4.1281 0.0000 [ 0.2671; 0.7580 ]
## ITPers <~ ITPSF1 0.4565 0.2121 2.1525 0.0314 [ 0.0205; 0.8613 ]
## ITPers <~ ITPSF2 0.1953 0.2288 0.8534 0.3934 [-0.3277; 0.6127 ]
## ITPers <~ ITPSF3 0.5127 0.1966 2.6075 0.0091 [ 0.1555; 0.8903 ]
## ITPers <~ ITPSF4 0.1527 0.2454 0.6223 0.5337 [-0.3252; 0.6258 ]
##
## Estimated indicator correlations:
## =================================
## CI_percentile
## Correlation Estimate Std. error t-stat. p-value 95%
## ITCOMP1 ~~ ITCOMP2 0.4564 0.0918 4.9725 0.0000 [ 0.2510; 0.6084 ]
## ITCOMP1 ~~ ITCOMP3 0.3629 0.1017 3.5690 0.0004 [ 0.1497; 0.5548 ]
## ITCOMP1 ~~ ITCOMP4 0.3666 0.0937 3.9109 0.0001 [ 0.1439; 0.5341 ]
## ITCOMP2 ~~ ITCOMP3 0.5917 0.0820 7.2196 0.0000 [ 0.4181; 0.7260 ]
## ITCOMP2 ~~ ITCOMP4 0.4852 0.0877 5.5350 0.0000 [ 0.2976; 0.6509 ]
## ITCOMP3 ~~ ITCOMP4 0.5092 0.1024 4.9716 0.0000 [ 0.2904; 0.6817 ]
## ITCONN1 ~~ ITCONN2 0.4521 0.0991 4.5601 0.0000 [ 0.2490; 0.6213 ]
## ITCONN1 ~~ ITCONN3 0.2813 0.1066 2.6385 0.0083 [ 0.0649; 0.4925 ]
## ITCONN1 ~~ ITCONN4 0.0811 0.1086 0.7468 0.4552 [-0.1283; 0.3045 ]
## ITCONN2 ~~ ITCONN3 0.4841 0.0972 4.9802 0.0000 [ 0.2717; 0.6529 ]
## ITCONN2 ~~ ITCONN4 0.3970 0.0786 5.0528 0.0000 [ 0.2335; 0.5373 ]
## ITCONN3 ~~ ITCONN4 0.4908 0.0966 5.0802 0.0000 [ 0.2747; 0.6546 ]
## MOD1 ~~ MOD2 0.4652 0.0924 5.0345 0.0000 [ 0.2838; 0.6223 ]
## MOD1 ~~ MOD3 0.4036 0.0836 4.8246 0.0000 [ 0.2262; 0.5539 ]
## MOD1 ~~ MOD4 0.2939 0.0922 3.1863 0.0014 [ 0.1018; 0.4604 ]
## MOD2 ~~ MOD3 0.6237 0.0576 10.8218 0.0000 [ 0.5010; 0.7245 ]
## MOD2 ~~ MOD4 0.2453 0.0930 2.6379 0.0083 [ 0.0697; 0.4324 ]
## MOD3 ~~ MOD4 0.3939 0.0970 4.0605 0.0000 [ 0.1802; 0.5661 ]
## ITPSF1 ~~ ITPSF2 0.5557 0.0812 6.8416 0.0000 [ 0.3749; 0.7039 ]
## ITPSF1 ~~ ITPSF3 0.3387 0.1001 3.3826 0.0007 [ 0.1345; 0.5077 ]
## ITPSF1 ~~ ITPSF4 0.3727 0.1075 3.4684 0.0005 [ 0.1523; 0.5598 ]
## ITPSF2 ~~ ITPSF3 0.2691 0.1165 2.3098 0.0209 [ 0.0023; 0.4756 ]
## ITPSF2 ~~ ITPSF4 0.4083 0.1079 3.7824 0.0002 [ 0.1798; 0.5984 ]
## ITPSF3 ~~ ITPSF4 0.5075 0.0810 6.2679 0.0000 [ 0.3398; 0.6579 ]
##
## ------------------------------------ Effects -----------------------------------
##
## Estimated total effects:
## ========================
## CI_percentile
## Total effect Estimate Std. error t-stat. p-value 95%
## ITConn ~ ITComp 0.6014 0.0871 6.9022 0.0000 [ 0.4634; 0.7480 ]
## Modul ~ ITComp 0.6035 0.0671 8.9965 0.0000 [ 0.4840; 0.7412 ]
## Modul ~ ITConn 0.3878 0.1098 3.5321 0.0004 [ 0.2063; 0.5988 ]
## ITPers ~ ITComp 0.4197 0.1021 4.1121 0.0000 [ 0.2508; 0.6364 ]
## ITPers ~ ITConn 0.4065 0.1061 3.8308 0.0001 [ 0.2277; 0.6144 ]
## ITPers ~ Modul 0.4243 0.1121 3.7858 0.0002 [ 0.1931; 0.6104 ]
##
## Estimated indirect effects:
## ===========================
## CI_percentile
## Indirect effect Estimate Std. error t-stat. p-value 95%
## Modul ~ ITComp 0.2332 0.0688 3.3897 0.0007 [ 0.1341; 0.3913 ]
## ITPers ~ ITComp 0.4016 0.0769 5.2212 0.0000 [ 0.2659; 0.5679 ]
## ITPers ~ ITConn 0.1645 0.0679 2.4227 0.0154 [ 0.0575; 0.3033 ]
## ________________________________________________________________________________Assess the overall model fit:
outoverall=testOMF(out)
outoverall## ________________________________________________________________________________
## --------- Test for overall model fit based on Beran & Srivastava (1985) --------
##
## Null hypothesis:
##
## ┌──────────────────────────────────────────────────────────────────┐
## │ │
## │ H0: The model-implied indicator covariance matrix equals the │
## │ population indicator covariance matrix. │
## │ │
## └──────────────────────────────────────────────────────────────────┘
##
## Test statistic and critical value:
##
## Critical value
## Distance measure Test statistic 95%
## dG 0.2762 0.2954
## SRMR 0.0651 0.0688
## dL 0.5763 0.6443
## dML 1.3221 1.3838
##
##
## Decision:
##
## Significance level
## Distance measure 95%
## dG Do not reject
## SRMR Do not reject
## dL Do not reject
## dML Do not reject
##
## Additional information:
##
## Out of 499 bootstrap replications 499 are admissible.
## See ?verify() for what constitutes an inadmissible result.
##
## The seed used was: -713308418
## ________________________________________________________________________________