Confirmatory Composite Analysis Using the R Package lavaan

This tutorial executes the CCA as described in Benitez et al. (2018) using the open-source R package lavaan. The lavaan package is devoted to covariance-based structural equation modeling. It can be obtained via CRAN.

In order to specify composite models in SPSS Amos, analysts can rely on the Henseler–Ogasawara specification (Schuberth, 2022; Henseler & Schuberth, 2021), i.e., they must specify emergent variables and excrescent variables. The figure below illustrates the specified model.


This tutorial executes the CCA as described in Benitez et al. (2018). The data and project files can be downloaded below:

Code:

ITFlexTutoriallavaannostartingincluding-weights.knit

Install the lavaan package:

install.packages("lavaan")

Load the lavaan package:

library(lavaan)
## This is lavaan 0.6-11.1682
## lavaan is FREE software! Please report any bugs.

Import the dataset. For that reason, please select the IT_Flex.xlsx file.

ITFlex <- as.data.frame(readxl::read_excel(choose.files()))

Specify the model using the the Henseler-Ogasawara specification (Schuberth, in press):

model_ITFlex = '

# Specification of the relationships between the observed variables ITCOMP1 - ITCOMP4
# and the emergent variable ITCOMP in terms of composite loadings.

ITCOMP =~ NA*ITCOMP1 + l11*ITCOMP1+ l21*ITCOMP2 + 1*ITCOMP3 + l41*ITCOMP4

ITCOMP~~vITCOMP*ITCOMP

# Specification of the relationships between the observed variables ITCOMP1 - ITCOMP4
# and their excrescent variables in terms of composite loadings.

nu11 =~ 1*ITCOMP1 + l22*ITCOMP2 + l32*ITCOMP3 + l42*ITCOMP4
nu12 =~ 0*ITCOMP1 + 1*ITCOMP2 + l33*ITCOMP3 + l43*ITCOMP4
nu13 =~ 0*ITCOMP1 + 0*ITCOMP2 + l34*ITCOMP3 + 1*ITCOMP4

nu11~~vnu11*nu11
nu12~~vnu12*nu12
nu13~~vnu13*nu13


# Specification of the relationships between the observed variables ITCONN1 - ITCONN4
# and the emergent variable ITCONN in terms of composite loadings.

ITCONN =~ NA*ITCONN1 + 1*ITCONN2 + ITCONN3 + ITCONN4

# Specification of the relationships between the observed variables ITCONN1 - ITCONN4
# and their excrescent variables in terms of composite loadings.

nu21 =~ 1*ITCONN1 + ITCONN2 + ITCONN3 + ITCONN4
nu22 =~ 0*ITCONN1 + ITCONN2 + 1*ITCONN3 + ITCONN4
nu23 =~ 0*ITCONN1 +  0*ITCONN2 + ITCONN3 + 1*ITCONN4


# Specification of the relationships between the observed variables MOD1 - MOD4
# and the emergent variable MOD in terms of composite loadings.

MOD =~ NA*MOD1 + MOD2 + 1*MOD3 +  MOD4

# Specification of the relationships between the observed variables MOD1 - MOD4
# and their excrescent variables in terms of composite loadings.

nu31 =~ 1*MOD1 + MOD2 + MOD3 + MOD4
nu32 =~ 0*MOD1 + 1*MOD2 + MOD3 + MOD4
nu33 =~ 0*MOD1 + 0*MOD2 + MOD3 + 1*MOD4

# Specification of the relationships between the observed variables ITPSF1 - ITPSF4
# and the emergent variable ITPSF in terms of composite loadings.

ITPSF =~ NA*ITPSF1 + 1*ITPSF2 + ITPSF3 + ITPSF4

# Specification of the relationships between the observed variables ITPSF1 - ITPSF4
# and their excrescent variables in terms of composite loadings.

nu41 =~ 1*ITPSF1 + ITPSF2 + ITPSF3 + ITPSF4
nu42 =~ 0*ITPSF1 + ITPSF2 + 1*ITPSF3 + ITPSF4
nu43 =~ 0*ITPSF1 + 0*ITPSF2 + ITPSF3 + 1*ITPSF4


# Speciifcation of the covariances among the emergent variables
ITCOMP ~~ ITCONN + MOD + ITPSF
ITCONN ~~ MOD + ITPSF
MOD ~~ ITPSF


# The H-O specification assumes that the excrescent variables are uncorrelated.
# Therefore, the covariance between the excrescent variables is fixed to 0:

nu11 ~~ 0*nu12 + 0*nu13 + 0*nu21 + 0*nu22 + 0*nu23 + 0*nu31 + 0*nu32 + 0*nu33
nu11 ~~ 0*nu41 + 0*nu42 + 0*nu43
nu12 ~~ 0*nu13 + 0*nu21 + 0*nu22 + 0*nu23 + 0*nu31 + 0*nu32 + 0*nu33
nu12 ~~ 0*nu41 + 0*nu42 + 0*nu43
nu13 ~~ 0*nu21 + 0*nu22 + 0*nu23 + 0*nu31 + 0*nu32 + 0*nu33
nu13 ~~ 0*nu41 + 0*nu42 + 0*nu43

nu21 ~~ 0*nu22 + 0*nu23 + 0*nu31 + 0*nu32 + 0*nu33
nu21 ~~ 0*nu41 + 0*nu42 + 0*nu43
nu22 ~~ 0*nu23 + 0*nu31 + 0*nu32 + 0*nu33
nu22 ~~ 0*nu41 + 0*nu42 + 0*nu43
nu23 ~~ 0*nu31 + 0*nu32 + 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43

nu31 ~~ 0*nu32 + 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43
nu32 ~~ 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43
nu33 ~~ 0*nu41 + 0*nu42 + 0*nu43

nu41 ~~ 0*nu42 + 0*nu43
nu42 ~~ 0*nu43

# Moreover, the H-O specification assumes that the excrescent variables are uncorrelated
# with the emergent and latent variables. Therefore, the covariances between
# the emergent and the excrescent varibales are fixed to 0:

ITCOMP ~~ 0*nu11 + 0*nu12 + 0*nu13 + 0*nu21 + 0*nu22 + 0*nu23
ITCOMP ~~ 0*nu31 + 0*nu32 + 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43

ITCONN =~ 0*nu11 + 0*nu12 + 0*nu13 + 0*nu21 + 0*nu22 + 0*nu23
ITCONN =~ 0*nu31 + 0*nu32 + 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43

MOD ~~ 0*nu11 + 0*nu12 + 0*nu13 + 0*nu21 + 0*nu22 + 0*nu23
MOD ~~ 0*nu31 + 0*nu32 + 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43

ITPSF ~~ 0*nu11 + 0*nu12 + 0*nu13 + 0*nu21 + 0*nu22 + 0*nu23
ITPSF ~~ 0*nu31 + 0*nu32 + 0*nu33 + 0*nu41 + 0*nu42 + 0*nu43

# In lavaan, the =~ command is originally used to specify a common factor model,
# which assumes that each observed variable is affected by a random measurement error.
# It is assumed that the observed variables forming composites are free from
# random measurement error. Therefore, the variances of the random measurement errors
# originally attached to the observed variables by the common factor model are fixed to 0:

ITCOMP1~~0*ITCOMP1
ITCOMP2~~0*ITCOMP2
ITCOMP3~~0*ITCOMP3
ITCOMP4~~0*ITCOMP4
ITCONN1~~0*ITCONN1
ITCONN2~~0*ITCONN2
ITCONN3~~0*ITCONN3
ITCONN4~~0*ITCONN4
MOD1~~0*MOD1
MOD2~~0*MOD2
MOD3~~0*MOD3
MOD4~~0*MOD4
ITPSF1~~0*ITPSF1
ITPSF2~~0*ITPSF2
ITPSF3~~0*ITPSF3
ITPSF4~~0*ITPSF4

# Specify weights:
w1:= (-l32 + l22*l33 + l34*l42 - l22*l34*l43)/(
  1 - l11*l32 - l21*l33 + l11*l22*l33 - l34*l41 + l11*l34*l42 + 
   l21* l34* l43 - l11* l22* l34* l43)
w2:= (-l33 + l34*l43)/(1 - l11*l32 - l21*l33 + 
    l11*l22*l33 - l34*l41 + l11*l34*l42 + l21*l34*l43 - l11*l22*l34*l43)
w3:= 1/(1 - l11*l32 - l21*l33 + l11*l22*l33 -
    l34*l41 + l11*l34*l42 + l21*l34*l43 - l11*l22*l34*l43)
w4:= -l34/(1 - l11*l32 - l21*l33 + l11*l22*l33 -
    l34*l41 + l11*l34*l42 + l21*l34*l43 - l11*l22*l34*l43)

vITCOMP1 := l11^2*vITCOMP + vnu11
vITCOMP2 := l21^2*vITCOMP + l22^2*vnu11 + vnu12
vITCOMP3 := vITCOMP + l32^2*vnu11 + l33^2 * vnu12 + l34^2*vnu13
vITCOMP4 := l41^2*vITCOMP + l42^2*vnu11 + l43^2*vnu12 + vnu13

w1std := w1*(vITCOMP1/vITCOMP)^(1/2)
w2std := w2*(vITCOMP2/vITCOMP)^(1/2)
w3std := w3*(vITCOMP3/vITCOMP)^(1/2)
w4std := w4*(vITCOMP4/vITCOMP)^(1/2)
'

Estimate the model maximum-likelihood:

out <- sem(data = ITFlex, model = model_ITFlex)

Return model summary:

summary(out,standardize = T)
## lavaan 0.6-11.1682 ended normally after 179 iterations
## 
##   Estimator                                         ML
##   Optimization method                           NLMINB
##   Number of model parameters                        58
##                                                       
##   Number of observations                           100
##                                                       
## Model Test User Model:
##                                                       
##   Test statistic                               130.326
##   Degrees of freedom                                78
##   P-value (Chi-square)                           0.000
## 
## Parameter Estimates:
## 
##   Standard errors                             Standard
##   Information                                 Expected
##   Information saturated (h1) model          Structured
## 
## Latent Variables:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   ITCOMP =~                                                             
##     ITCOMP1  (l11)    0.677    0.160    4.229    0.000    0.721    0.594
##     ITCOMP2  (l21)    0.746    0.132    5.657    0.000    0.794    0.668
##     ITCOMP3           1.000                               1.065    0.949
##     ITCOMP4  (l41)    0.648    0.123    5.257    0.000    0.690    0.674
##   nu11 =~                                                               
##     ITCOMP1           1.000                               0.977    0.805
##     ITCOMP2  (l22)    0.091    0.138    0.654    0.513    0.088    0.074
##     ITCOMP3  (l32)   -0.287    0.140   -2.053    0.040   -0.280   -0.250
##     ITCOMP4  (l42)   -0.044    0.125   -0.350    0.726   -0.043   -0.042
##   nu12 =~                                                               
##     ITCOMP1           0.000                               0.000    0.000
##     ITCOMP2           1.000                               0.881    0.741
##     ITCOMP3  (l33)   -0.041    0.158   -0.256    0.798   -0.036   -0.032
##     ITCOMP4  (l43)    0.060    0.139    0.432    0.666    0.053    0.052
##   nu13 =~                                                               
##     ITCOMP1           0.000                               0.000    0.000
##     ITCOMP2           0.000                               0.000    0.000
##     ITCOMP3  (l34)   -0.282    0.208   -1.354    0.176   -0.212   -0.189
##     ITCOMP4           1.000                               0.753    0.736
##   ITCONN =~                                                             
##     ITCONN1           0.607    0.167    3.643    0.000    0.464    0.471
##     ITCONN2           1.000                               0.765    0.724
##     ITCONN3           1.700    0.307    5.531    0.000    1.300    0.921
##     ITCONN4           0.909    0.205    4.436    0.000    0.695    0.660
##   nu21 =~                                                               
##     ITCONN1           1.000                               0.871    0.882
##     ITCONN2           0.153    0.123    1.251    0.211    0.134    0.126
##     ITCONN3          -0.280    0.176   -1.588    0.112   -0.244   -0.173
##     ITCONN4          -0.315    0.137   -2.304    0.021   -0.274   -0.260
##   nu22 =~                                                               
##     ITCONN1           0.000                               0.000    0.000
##     ITCONN2          -2.144    1.168   -1.835    0.066   -0.717   -0.678
##     ITCONN3           1.000                               0.334    0.237
##     ITCONN4           0.222    0.375    0.592    0.554    0.074    0.070
##   nu23 =~                                                               
##     ITCONN1           0.000                               0.000    0.000
##     ITCONN2           0.000                               0.000    0.000
##     ITCONN3          -0.488    0.298   -1.639    0.101   -0.360   -0.255
##     ITCONN4           1.000                               0.738    0.701
##   MOD =~                                                                
##     MOD1              0.885    0.198    4.469    0.000    0.665    0.620
##     MOD2              1.183    0.184    6.417    0.000    0.888    0.784
##     MOD3              1.000                               0.751    0.751
##     MOD4              0.960    0.193    4.964    0.000    0.721    0.754
##   nu31 =~                                                               
##     MOD1              1.000                               0.841    0.785
##     MOD2             -0.036    0.146   -0.246    0.806   -0.030   -0.027
##     MOD3             -0.094    0.134   -0.701    0.483   -0.079   -0.079
##     MOD4             -0.251    0.133   -1.892    0.059   -0.212   -0.221
##   nu32 =~                                                               
##     MOD1              0.000                               0.000    0.000
##     MOD2              1.000                               0.702    0.620
##     MOD3              0.075    0.178    0.422    0.673    0.053    0.053
##     MOD4             -0.773    0.221   -3.497    0.000   -0.543   -0.568
##   nu33 =~                                                               
##     MOD1              0.000                               0.000    0.000
##     MOD2              0.000                               0.000    0.000
##     MOD3             -2.799    2.107   -1.328    0.184   -0.654   -0.654
##     MOD4              1.000                               0.234    0.244
##   ITPSF =~                                                              
##     ITPSF1            1.529    0.361    4.239    0.000    0.816    0.829
##     ITPSF2            1.000                               0.533    0.576
##     ITPSF3            1.326    0.398    3.335    0.001    0.707    0.779
##     ITPSF4            1.160    0.331    3.510    0.000    0.619    0.670
##   nu41 =~                                                               
##     ITPSF1            1.000                               0.551    0.560
##     ITPSF2            0.236    0.297    0.792    0.428    0.130    0.140
##     ITPSF3           -0.902    0.347   -2.597    0.009   -0.497   -0.548
##     ITPSF4           -0.546    0.340   -1.605    0.108   -0.301   -0.326
##   nu42 =~                                                               
##     ITPSF1            0.000                               0.000    0.000
##     ITPSF2           -6.439   10.633   -0.606    0.545   -0.746   -0.805
##     ITPSF3            1.000                               0.116    0.128
##     ITPSF4           -0.674    2.265   -0.297    0.766   -0.078   -0.085
##   nu43 =~                                                               
##     ITPSF1            0.000                               0.000    0.000
##     ITPSF2            0.000                               0.000    0.000
##     ITPSF3           -0.410    0.397   -1.033    0.302   -0.250   -0.276
##     ITPSF4            1.000                               0.611    0.662
##   ITCONN =~                                                             
##     nu11              0.000                               0.000    0.000
##     nu12              0.000                               0.000    0.000
##     nu13              0.000                               0.000    0.000
##     nu21              0.000                               0.000    0.000
##     nu22              0.000                               0.000    0.000
##     nu23              0.000                               0.000    0.000
##     nu31              0.000                               0.000    0.000
##     nu32              0.000                               0.000    0.000
##     nu33              0.000                               0.000    0.000
##     nu41              0.000                               0.000    0.000
##     nu42              0.000                               0.000    0.000
##     nu43              0.000                               0.000    0.000
## 
## Covariances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##   ITCOMP ~~                                                             
##     ITCONN            0.517    0.122    4.252    0.000    0.635    0.635
##     MOD               0.472    0.111    4.240    0.000    0.591    0.591
##     ITPSF             0.221    0.080    2.768    0.006    0.390    0.390
##   ITCONN ~~                                                             
##     MOD               0.340    0.091    3.742    0.000    0.592    0.592
##     ITPSF             0.202    0.070    2.872    0.004    0.496    0.496
##   MOD ~~                                                                
##     ITPSF             0.238    0.077    3.080    0.002    0.593    0.593
##  .nu11 ~~                                                               
##    .nu12              0.000                               0.000    0.000
##    .nu13              0.000                               0.000    0.000
##    .nu21              0.000                               0.000    0.000
##    .nu22              0.000                               0.000    0.000
##    .nu23              0.000                               0.000    0.000
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu12 ~~                                                               
##    .nu13              0.000                               0.000    0.000
##    .nu21              0.000                               0.000    0.000
##    .nu22              0.000                               0.000    0.000
##    .nu23              0.000                               0.000    0.000
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu13 ~~                                                               
##    .nu21              0.000                               0.000    0.000
##    .nu22              0.000                               0.000    0.000
##    .nu23              0.000                               0.000    0.000
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu21 ~~                                                               
##    .nu22              0.000                               0.000    0.000
##    .nu23              0.000                               0.000    0.000
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu22 ~~                                                               
##    .nu23              0.000                               0.000    0.000
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu23 ~~                                                               
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu31 ~~                                                               
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu32 ~~                                                               
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu33 ~~                                                               
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu41 ~~                                                               
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu42 ~~                                                               
##    .nu43              0.000                               0.000    0.000
##   ITCOMP ~~                                                             
##    .nu11              0.000                               0.000    0.000
##    .nu12              0.000                               0.000    0.000
##    .nu13              0.000                               0.000    0.000
##    .nu21              0.000                               0.000    0.000
##    .nu22              0.000                               0.000    0.000
##    .nu23              0.000                               0.000    0.000
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu11 ~~                                                               
##     MOD               0.000                               0.000    0.000
##  .nu12 ~~                                                               
##     MOD               0.000                               0.000    0.000
##  .nu13 ~~                                                               
##     MOD               0.000                               0.000    0.000
##  .nu21 ~~                                                               
##     MOD               0.000                               0.000    0.000
##  .nu22 ~~                                                               
##     MOD               0.000                               0.000    0.000
##  .nu23 ~~                                                               
##     MOD               0.000                               0.000    0.000
##   MOD ~~                                                                
##    .nu31              0.000                               0.000    0.000
##    .nu32              0.000                               0.000    0.000
##    .nu33              0.000                               0.000    0.000
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
##  .nu11 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu12 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu13 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu21 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu22 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu23 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu31 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu32 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##  .nu33 ~~                                                               
##     ITPSF             0.000                               0.000    0.000
##   ITPSF ~~                                                              
##    .nu41              0.000                               0.000    0.000
##    .nu42              0.000                               0.000    0.000
##    .nu43              0.000                               0.000    0.000
## 
## Variances:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     ITCOMP  (vITC)    1.133    0.194    5.847    0.000    1.000    1.000
##    .nu11    (vn11)    0.954    0.200    4.764    0.000    1.000    1.000
##    .nu12    (vn12)    0.776    0.174    4.461    0.000    1.000    1.000
##    .nu13    (vn13)    0.567    0.134    4.236    0.000    1.000    1.000
##    .ITCOMP1           0.000                               0.000    0.000
##    .ITCOMP2           0.000                               0.000    0.000
##    .ITCOMP3           0.000                               0.000    0.000
##    .ITCOMP4           0.000                               0.000    0.000
##    .ITCONN1           0.000                               0.000    0.000
##    .ITCONN2           0.000                               0.000    0.000
##    .ITCONN3           0.000                               0.000    0.000
##    .ITCONN4           0.000                               0.000    0.000
##    .MOD1              0.000                               0.000    0.000
##    .MOD2              0.000                               0.000    0.000
##    .MOD3              0.000                               0.000    0.000
##    .MOD4              0.000                               0.000    0.000
##    .ITPSF1            0.000                               0.000    0.000
##    .ITPSF2            0.000                               0.000    0.000
##    .ITPSF3            0.000                               0.000    0.000
##    .ITPSF4            0.000                               0.000    0.000
##     ITCONN            0.585    0.178    3.284    0.001    1.000    1.000
##    .nu21              0.758    0.134    5.647    0.000    1.000    1.000
##    .nu22              0.112    0.102    1.091    0.275    1.000    1.000
##    .nu23              0.545    0.155    3.512    0.000    1.000    1.000
##     MOD               0.564    0.158    3.565    0.000    1.000    1.000
##    .nu31              0.708    0.146    4.860    0.000    1.000    1.000
##    .nu32              0.493    0.140    3.526    0.000    1.000    1.000
##    .nu33              0.055    0.071    0.770    0.441    1.000    1.000
##     ITPSF             0.285    0.136    2.088    0.037    1.000    1.000
##    .nu41              0.304    0.121    2.501    0.012    1.000    1.000
##    .nu42              0.013    0.043    0.313    0.754    1.000    1.000
##    .nu43              0.373    0.167    2.230    0.026    1.000    1.000
## 
## Defined Parameters:
##                    Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
##     w1                0.212    0.099    2.140    0.032    0.209    0.198
##     w2                0.017    0.126    0.134    0.893    0.018    0.017
##     w3                0.714    0.131    5.449    0.000    0.729    0.773
##     w4                0.201    0.129    1.564    0.118    0.155    0.146
##     vITCOMP1          1.474    0.208    7.071    0.000    1.520    1.353
##     vITCOMP2          1.414    0.200    7.071    0.000    1.638    1.452
##     vITCOMP3          1.258    0.178    7.071    0.000    1.125    1.099
##     vITCOMP4          1.047    0.148    7.071    0.000    1.480    1.459
##     w1std             0.241    0.119    2.022    0.043    0.258    0.230
##     w2std             0.019    0.141    0.134    0.893    0.023    0.021
##     w3std             0.752    0.115    6.524    0.000    0.773    0.810
##     w4std             0.193    0.127    1.518    0.129    0.188    0.177

References:

Benitez, J., Ray, G., & Henseler, J. (2018). Impact of information technology infrastructure flexibility on mergers and acquisitions. MIS Quarterly, 42(1), 25–43, https://doi.org/10.25300/MISQ/2018/13245.

Henseler, J., & Schuberth, F. (2021). Confirmatory composite analysis. In J. Henseler (Ed.), Composite-based Structural Equation Modeling: Analyzing Latent and Emergent Variables (pp. 179–201). The Guilford Press.

Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software48(2), 1–36. https://doi.org/10.18637/jss.v048.i02

Schuberth, F. (2022). The Henseler–Ogasawara specification of composites in structural equation modeling: A tutorial. Psychological Methods, in press, https://doi.org/10.1037/met0000432