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cSEM: Composite-based SEM

Purpose

Estimate, analyse, test, and study linear, nonlinear, hierarchical and multi-group structural equation models using composite-based approaches and procedures, including estimation techniques such as partial least squares path modeling (PLS-PM) and its derivatives (PLSc, OrdPLSc, robustPLSc), generalized structured component analysis (GSCA), generalized structured component analysis with uniqueness terms (GSCAm), generalized canonical correlation analysis (GCCA), principal component analysis (PCA), factor score regression (FSR) using sum score, regression or Bartlett scores (including bias correction using Croon’s approach), as well as several tests and typical post-estimation procedures (e.g., verify admissibility of the estimates, assess the model fit, test the model fit, compute confidence intervals, compare groups, etc.).

News (2022-05-09):

  • predict() function is now able to predict categorical indicators (a procedure known as OrdPLScPredict).

  • Use singular value decomposition in GSCAm to deal with large datasets, which allows for large datasets (thanks to Heungsun Hwang)

Installation

The package is available on CRAN:

install.packages("cSEM")

To install the development version, which is recommended, use:

# install.packages("devtools")
devtools::install_github("FloSchuberth/cSEM")

Getting started

The best place to get started is the cSEM-website.

Basic usage

The basic usage is illustrated below.

Usually, using cSEM is the same 3 step procedure:

  1. Pick a dataset and specify a model using lavaan syntax
  2. Use csem()
  3. Apply one of the post-estimation functions listed below on the resulting object.

Post-Estimation Functions

There are five major post-estimation verbs, three test family functions and three do-family of function:

  • assess() : assess the model using common quality criteria
  • infer() : calculate common inferential quantities (e.g., standard errors, confidence intervals)
  • predict() : predict endogenous indicator values
  • summarize() : summarize the results
  • verify() : verify admissibility of the estimates

Tests are performed by using the test family of functions. Currently, the following tests are implemented:

  • testOMF() : performs a test for overall model fit
  • testMICOM() : performs a test for composite measurement invariance
  • testMGD() : performs several tests to assess multi-group differences
  • testHausman() : performs the regression-based Hausman test to test for endogeneity

Other miscellaneous post-estimation functions belong do the do-family of functions. Currently, three do functions are implemented:

  • doIPMA(): performs an importance-performance matrix analysis
  • doNonlinearEffectsAnalysis(): performs a nonlinear effects analysis such as floodlight and surface analysis
  • doRedundancyAnalysis(): performs a redundancy analysis

All functions require a cSEMResults object.

Example

Models are defined using lavaan syntax with some slight modifications (see the Specifying a model section on the cSEM-website). For illustration we use the build-in and well-known satisfaction dataset.

require(cSEM)
    
## Note: The operator "<~" tells cSEM that the construct to its left is modeled
##       as a composite.
##       The operator "=~" tells cSEM that the construct to its left is modeled
##       as a common factor.
##       The operator "~" tells cSEM which are the dependent (left-hand side) and
##       independent variables (right-hand side).
    
model <- "
# Structural model
EXPE ~ IMAG
QUAL ~ EXPE
VAL  ~ EXPE + QUAL
SAT  ~ IMAG + EXPE + QUAL + VAL 
LOY  ~ IMAG + SAT

# Composite model
IMAG <~ imag1 + imag2 + imag3
EXPE <~ expe1 + expe2 + expe3 
QUAL <~ qual1 + qual2 + qual3 + qual4 + qual5
VAL  <~ val1  + val2  + val3

# Reflective measurement model
SAT  =~ sat1  + sat2  + sat3  + sat4
LOY  =~ loy1  + loy2  + loy3  + loy4
"

The estimation is conducted using the csem() function.

# Estimate using defaults
res <- csem(.data = satisfaction, .model = model)
res
## ________________________________________________________________________________
## ----------------------------------- Overview -----------------------------------
## 
## Estimation was successful.
## 
## The result is a list of class cSEMResults with list elements:
## 
##  - Estimates
##  - Information
## 
## To get an overview or help type:
## 
##  - ?cSEMResults
##  - str(<object-name>)
##  - listviewer::jsondedit(<object-name>, mode = 'view')
## 
## If you wish to access the list elements directly type e.g. 
## 
##  - <object-name>$Estimates
## 
## Available postestimation commands:
## 
##  - assess(<object-name>)
##  - infer(<object-name)
##  - predict(<object-name>)
##  - summarize(<object-name>)
##  - verify(<object-name>)
## ________________________________________________________________________________

This is equal to:

csem(
   .data                        = satisfaction,
   .model                       = model,
   .approach_cor_robust         = "none",
   .approach_nl                 = "sequential",
   .approach_paths              = "OLS",
   .approach_weights            = "PLS-PM",
   .conv_criterion              = "diff_absolute",
   .disattenuate                = TRUE,
   .dominant_indicators         = NULL,
   .estimate_structural         = TRUE,
   .id                          = NULL,
   .iter_max                    = 100,
   .normality                   = FALSE,
   .PLS_approach_cf             = "dist_squared_euclid",
   .PLS_ignore_structural_model = FALSE,
   .PLS_modes                   = NULL,
   .PLS_weight_scheme_inner     = "path",
   .reliabilities               = NULL,
   .starting_values             = NULL,
   .tolerance                   = 1e-05,
   .resample_method             = "none", 
   .resample_method2            = "none",
   .R                           = 499,
   .R2                          = 199,
   .handle_inadmissibles        = "drop",
   .user_funs                   = NULL,
   .eval_plan                   = "sequential",
   .seed                        = NULL,
   .sign_change_option          = "none"
    )

The result is always a named list of class cSEMResults.

To access list elements use $:

res$Estimates$Loading_estimates 
res$Information$Model

A useful tool to examine a list is the listviewer package. If you are new to cSEM this might be a good way to familiarize yourself with the structure of a cSEMResults object.

listviewer::jsonedit(res, mode = "view") # requires the listviewer package.

Apply post-estimation functions:

## Get a summary
summarize(res) 
## ________________________________________________________________________________
## ----------------------------------- Overview -----------------------------------
## 
##  General information:
##  ------------------------
##  Estimation status                  = Ok
##  Number of observations             = 250
##  Weight estimator                   = PLS-PM
##  Inner weighting scheme             = "path"
##  Type of indicator correlation      = Pearson
##  Path model estimator               = OLS
##  Second-order approach              = NA
##  Type of path model                 = Linear
##  Disattenuated                      = Yes (PLSc)
## 
##  Construct details:
##  ------------------
##  Name  Modeled as     Order         Mode      
## 
##  IMAG  Composite      First order   "modeB"   
##  EXPE  Composite      First order   "modeB"   
##  QUAL  Composite      First order   "modeB"   
##  VAL   Composite      First order   "modeB"   
##  SAT   Common factor  First order   "modeA"   
##  LOY   Common factor  First order   "modeA"   
## 
## ----------------------------------- Estimates ----------------------------------
## 
## Estimated path coefficients:
## ============================
##   Path           Estimate  Std. error   t-stat.   p-value
##   EXPE ~ IMAG      0.4714          NA        NA        NA
##   QUAL ~ EXPE      0.8344          NA        NA        NA
##   VAL ~ EXPE       0.0457          NA        NA        NA
##   VAL ~ QUAL       0.7013          NA        NA        NA
##   SAT ~ IMAG       0.2450          NA        NA        NA
##   SAT ~ EXPE      -0.0172          NA        NA        NA
##   SAT ~ QUAL       0.2215          NA        NA        NA
##   SAT ~ VAL        0.5270          NA        NA        NA
##   LOY ~ IMAG       0.1819          NA        NA        NA
##   LOY ~ SAT        0.6283          NA        NA        NA
## 
## Estimated loadings:
## ===================
##   Loading          Estimate  Std. error   t-stat.   p-value
##   IMAG =~ imag1      0.6306          NA        NA        NA
##   IMAG =~ imag2      0.9246          NA        NA        NA
##   IMAG =~ imag3      0.9577          NA        NA        NA
##   EXPE =~ expe1      0.7525          NA        NA        NA
##   EXPE =~ expe2      0.9348          NA        NA        NA
##   EXPE =~ expe3      0.7295          NA        NA        NA
##   QUAL =~ qual1      0.7861          NA        NA        NA
##   QUAL =~ qual2      0.9244          NA        NA        NA
##   QUAL =~ qual3      0.7560          NA        NA        NA
##   QUAL =~ qual4      0.7632          NA        NA        NA
##   QUAL =~ qual5      0.7834          NA        NA        NA
##   VAL =~ val1        0.9518          NA        NA        NA
##   VAL =~ val2        0.8056          NA        NA        NA
##   VAL =~ val3        0.6763          NA        NA        NA
##   SAT =~ sat1        0.9243          NA        NA        NA
##   SAT =~ sat2        0.8813          NA        NA        NA
##   SAT =~ sat3        0.7127          NA        NA        NA
##   SAT =~ sat4        0.7756          NA        NA        NA
##   LOY =~ loy1        0.9097          NA        NA        NA
##   LOY =~ loy2        0.5775          NA        NA        NA
##   LOY =~ loy3        0.9043          NA        NA        NA
##   LOY =~ loy4        0.4917          NA        NA        NA
## 
## Estimated weights:
## ==================
##   Weight           Estimate  Std. error   t-stat.   p-value
##   IMAG <~ imag1      0.0156          NA        NA        NA
##   IMAG <~ imag2      0.4473          NA        NA        NA
##   IMAG <~ imag3      0.6020          NA        NA        NA
##   EXPE <~ expe1      0.2946          NA        NA        NA
##   EXPE <~ expe2      0.6473          NA        NA        NA
##   EXPE <~ expe3      0.2374          NA        NA        NA
##   QUAL <~ qual1      0.2370          NA        NA        NA
##   QUAL <~ qual2      0.4712          NA        NA        NA
##   QUAL <~ qual3      0.1831          NA        NA        NA
##   QUAL <~ qual4      0.1037          NA        NA        NA
##   QUAL <~ qual5      0.2049          NA        NA        NA
##   VAL <~ val1        0.7163          NA        NA        NA
##   VAL <~ val2        0.2202          NA        NA        NA
##   VAL <~ val3        0.2082          NA        NA        NA
##   SAT <~ sat1        0.3209          NA        NA        NA
##   SAT <~ sat2        0.3059          NA        NA        NA
##   SAT <~ sat3        0.2474          NA        NA        NA
##   SAT <~ sat4        0.2692          NA        NA        NA
##   LOY <~ loy1        0.3834          NA        NA        NA
##   LOY <~ loy2        0.2434          NA        NA        NA
##   LOY <~ loy3        0.3812          NA        NA        NA
##   LOY <~ loy4        0.2073          NA        NA        NA
## 
## Estimated indicator correlations:
## =================================
##   Correlation       Estimate  Std. error   t-stat.   p-value
##   imag1 ~~ imag2      0.6437          NA        NA        NA
##   imag1 ~~ imag3      0.5433          NA        NA        NA
##   imag2 ~~ imag3      0.7761          NA        NA        NA
##   expe1 ~~ expe2      0.5353          NA        NA        NA
##   expe1 ~~ expe3      0.4694          NA        NA        NA
##   expe2 ~~ expe3      0.5467          NA        NA        NA
##   qual1 ~~ qual2      0.6053          NA        NA        NA
##   qual1 ~~ qual3      0.5406          NA        NA        NA
##   qual1 ~~ qual4      0.5662          NA        NA        NA
##   qual1 ~~ qual5      0.5180          NA        NA        NA
##   qual2 ~~ qual3      0.6187          NA        NA        NA
##   qual2 ~~ qual4      0.6517          NA        NA        NA
##   qual2 ~~ qual5      0.6291          NA        NA        NA
##   qual3 ~~ qual4      0.4752          NA        NA        NA
##   qual3 ~~ qual5      0.5074          NA        NA        NA
##   qual4 ~~ qual5      0.6402          NA        NA        NA
##   val1 ~~ val2        0.6344          NA        NA        NA
##   val1 ~~ val3        0.4602          NA        NA        NA
##   val2 ~~ val3        0.6288          NA        NA        NA
## 
## ------------------------------------ Effects -----------------------------------
## 
## Estimated total effects:
## ========================
##   Total effect    Estimate  Std. error   t-stat.   p-value
##   EXPE ~ IMAG       0.4714          NA        NA        NA
##   QUAL ~ IMAG       0.3933          NA        NA        NA
##   QUAL ~ EXPE       0.8344          NA        NA        NA
##   VAL ~ IMAG        0.2974          NA        NA        NA
##   VAL ~ EXPE        0.6309          NA        NA        NA
##   VAL ~ QUAL        0.7013          NA        NA        NA
##   SAT ~ IMAG        0.4807          NA        NA        NA
##   SAT ~ EXPE        0.5001          NA        NA        NA
##   SAT ~ QUAL        0.5911          NA        NA        NA
##   SAT ~ VAL         0.5270          NA        NA        NA
##   LOY ~ IMAG        0.4840          NA        NA        NA
##   LOY ~ EXPE        0.3142          NA        NA        NA
##   LOY ~ QUAL        0.3714          NA        NA        NA
##   LOY ~ VAL         0.3311          NA        NA        NA
##   LOY ~ SAT         0.6283          NA        NA        NA
## 
## Estimated indirect effects:
## ===========================
##   Indirect effect    Estimate  Std. error   t-stat.   p-value
##   QUAL ~ IMAG          0.3933          NA        NA        NA
##   VAL ~ IMAG           0.2974          NA        NA        NA
##   VAL ~ EXPE           0.5852          NA        NA        NA
##   SAT ~ IMAG           0.2357          NA        NA        NA
##   SAT ~ EXPE           0.5173          NA        NA        NA
##   SAT ~ QUAL           0.3696          NA        NA        NA
##   LOY ~ IMAG           0.3020          NA        NA        NA
##   LOY ~ EXPE           0.3142          NA        NA        NA
##   LOY ~ QUAL           0.3714          NA        NA        NA
##   LOY ~ VAL            0.3311          NA        NA        NA
## ________________________________________________________________________________
## Verify admissibility of the results
verify(res) 
## ________________________________________________________________________________
## 
## Verify admissibility:
## 
##   admissible
## 
## Details:
## 
##   Code   Status    Description
##   1      ok        Convergence achieved                                   
##   2      ok        All absolute standardized loading estimates <= 1       
##   3      ok        Construct VCV is positive semi-definite                
##   4      ok        All reliability estimates <= 1                         
##   5      ok        Model-implied indicator VCV is positive semi-definite  
## ________________________________________________________________________________
## Test overall model fit
testOMF(res)
## ________________________________________________________________________________
## --------- 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                      0.6493      0.3263  
##  SRMR                    0.0940      0.0530  
##  dL                      2.2340      0.7099  
##  dML                     2.9219      1.6308  
##  
## 
## Decision: 
## 
##                          Significance level
##  Distance measure          95%   
##  dG                      reject  
##  SRMR                    reject  
##  dL                      reject  
##  dML                     reject  
##  
## Additional information:
## 
##  Out of 499 bootstrap replications 476 are admissible.
##  See ?verify() for what constitutes an inadmissible result.
## 
##  The seed used was: 980464158
## ________________________________________________________________________________
## Assess the model
assess(res)
## ________________________________________________________________________________
## 
##  Construct        AVE           R2          R2_adj    
##  SAT            0.6851        0.7624        0.7585    
##  LOY            0.5552        0.5868        0.5834    
##  EXPE             NA          0.2222        0.2190    
##  QUAL             NA          0.6963        0.6951    
##  VAL              NA          0.5474        0.5438    
## 
## -------------- Common (internal consistency) reliability estimates -------------
## 
##  Construct Cronbachs_alpha   Joereskogs_rho   Dijkstra-Henselers_rho_A 
##  SAT        0.8940           0.8960                0.9051          
##  LOY        0.8194           0.8237                0.8761          
## 
## ----------- Alternative (internal consistency) reliability estimates -----------
## 
##  Construct       RhoC         RhoC_mm    RhoC_weighted
##  SAT            0.8960        0.8938        0.9051    
##  LOY            0.8237        0.8011        0.8761    
## 
##  Construct  RhoC_weighted_mm     RhoT      RhoT_weighted
##  SAT            0.9051        0.8940        0.8869    
##  LOY            0.8761        0.8194        0.7850    
## 
## --------------------------- Distance and fit measures --------------------------
## 
##  Geodesic distance             = 0.6493432
##  Squared Euclidean distance    = 2.23402
##  ML distance                   = 2.921932
## 
##  Chi_square       = 727.5611
##  Chi_square_df    = 3.954137
##  CFI              = 0.8598825
##  CN               = 75.14588
##  GFI              = 0.7280612
##  IFI              = 0.8615598
##  NFI              = 0.8229918
##  NNFI             = 0.8240917
##  RMSEA            = 0.108922
##  RMS_theta        = 0.05069299
##  SRMR             = 0.09396871
## 
##  Degrees of freedom       = 184
## 
## --------------------------- Model selection criteria ---------------------------
## 
##  Construct        AIC          AICc          AICu     
##  EXPE          -59.8152      192.2824      -57.8072   
##  QUAL          -294.9343     -42.8367      -292.9263  
##  VAL           -193.2127      58.9506      -190.1945  
##  SAT           -350.2874     -97.9418      -345.2368  
##  LOY           -215.9322      36.2311      -212.9141  
## 
##  Construct        BIC           FPE           GM      
##  EXPE          -52.7723       0.7872       259.8087   
##  QUAL          -287.8914      0.3074       271.8568   
##  VAL           -182.6483      0.4617       312.7010   
##  SAT           -332.6801      0.2463       278.2973   
##  LOY           -205.3678      0.4216       291.0665   
## 
##  Construct        HQ            HQc       Mallows_Cp  
##  EXPE          -56.9806      -56.8695       2.7658    
##  QUAL          -292.0997     -291.9886      14.8139   
##  VAL           -188.9608     -188.7516      52.1366   
##  SAT           -343.2010     -342.7088      10.6900   
##  LOY           -211.6804     -211.4711      30.5022   
## 
## ----------------------- Variance inflation factors (VIFs) ----------------------
## 
##   Dependent construct: 'VAL'
## 
##  Independent construct    VIF value 
##  EXPE                      3.2928   
##  QUAL                      3.2928   
## 
##   Dependent construct: 'SAT'
## 
##  Independent construct    VIF value 
##  EXPE                      3.2985   
##  QUAL                      4.4151   
##  IMAG                      1.7280   
##  VAL                       2.6726   
## 
##   Dependent construct: 'LOY'
## 
##  Independent construct    VIF value 
##  IMAG                      1.9345   
##  SAT                       1.9345   
## 
## -------------- Variance inflation factors (VIFs) for modeB weights -------------
## 
##   Construct: 'IMAG'
## 
##  Weight    VIF value 
##  imag1      1.7215   
##  imag2      3.0515   
##  imag3      2.5356   
## 
##   Construct: 'EXPE'
## 
##  Weight    VIF value 
##  expe1      1.4949   
##  expe2      1.6623   
##  expe3      1.5212   
## 
##   Construct: 'QUAL'
## 
##  Weight    VIF value 
##  qual1      1.8401   
##  qual2      2.5005   
##  qual3      1.7796   
##  qual4      2.1557   
##  qual5      2.0206   
## 
##   Construct: 'VAL'
## 
##  Weight    VIF value 
##  val1       1.6912   
##  val2       2.2049   
##  val3       1.6714   
## 
## -------------------------- Effect sizes (Cohen's f^2) --------------------------
## 
##   Dependent construct: 'EXPE'
## 
##  Independent construct       f^2    
##  IMAG                      0.2856   
## 
##   Dependent construct: 'QUAL'
## 
##  Independent construct       f^2    
##  EXPE                      2.2928   
## 
##   Dependent construct: 'VAL'
## 
##  Independent construct       f^2    
##  EXPE                      0.0014   
##  QUAL                      0.3301   
## 
##   Dependent construct: 'SAT'
## 
##  Independent construct       f^2    
##  IMAG                      0.1462   
##  EXPE                      0.0004   
##  QUAL                      0.0468   
##  VAL                       0.4373   
## 
##   Dependent construct: 'LOY'
## 
##  Independent construct       f^2    
##  IMAG                      0.0414   
##  SAT                       0.4938   
## 
## ----------------------- Discriminant validity assessment -----------------------
## 
##  Heterotrait-monotrait ratio of correlations matrix (HTMT matrix)
## 
##           SAT LOY
## SAT 1.0000000   0
## LOY 0.7432489   1
## 
## 
##  Advanced heterotrait-monotrait ratio of correlations matrix (HTMT2 matrix)
## 
##           SAT LOY
## SAT 1.0000000   0
## LOY 0.7140046   1
## 
## 
##  Fornell-Larcker matrix
## 
##           SAT       LOY
## SAT 0.6851491 0.5696460
## LOY 0.5696460 0.5551718
## 
## 
## ------------------------------------ Effects -----------------------------------
## 
## Estimated total effects:
## ========================
##   Total effect    Estimate  Std. error   t-stat.   p-value
##   EXPE ~ IMAG       0.4714          NA        NA        NA
##   QUAL ~ IMAG       0.3933          NA        NA        NA
##   QUAL ~ EXPE       0.8344          NA        NA        NA
##   VAL ~ IMAG        0.2974          NA        NA        NA
##   VAL ~ EXPE        0.6309          NA        NA        NA
##   VAL ~ QUAL        0.7013          NA        NA        NA
##   SAT ~ IMAG        0.4807          NA        NA        NA
##   SAT ~ EXPE        0.5001          NA        NA        NA
##   SAT ~ QUAL        0.5911          NA        NA        NA
##   SAT ~ VAL         0.5270          NA        NA        NA
##   LOY ~ IMAG        0.4840          NA        NA        NA
##   LOY ~ EXPE        0.3142          NA        NA        NA
##   LOY ~ QUAL        0.3714          NA        NA        NA
##   LOY ~ VAL         0.3311          NA        NA        NA
##   LOY ~ SAT         0.6283          NA        NA        NA
## 
## Estimated indirect effects:
## ===========================
##   Indirect effect    Estimate  Std. error   t-stat.   p-value
##   QUAL ~ IMAG          0.3933          NA        NA        NA
##   VAL ~ IMAG           0.2974          NA        NA        NA
##   VAL ~ EXPE           0.5852          NA        NA        NA
##   SAT ~ IMAG           0.2357          NA        NA        NA
##   SAT ~ EXPE           0.5173          NA        NA        NA
##   SAT ~ QUAL           0.3696          NA        NA        NA
##   LOY ~ IMAG           0.3020          NA        NA        NA
##   LOY ~ EXPE           0.3142          NA        NA        NA
##   LOY ~ QUAL           0.3714          NA        NA        NA
##   LOY ~ VAL            0.3311          NA        NA        NA
## ________________________________________________________________________________
## Predict indicator scores of endogenous constructs
predict(res)
## ________________________________________________________________________________
## ----------------------------------- Overview -----------------------------------
## 
##  Number of obs. training            = 225
##  Number of obs. test                = 25
##  Number of cv folds                 = 10
##  Number of repetitions              = 1
##  Handle inadmissibles               = stop
##  Estimator target                   = 'PLS-PM'
##  Estimator benchmark                = 'lm'
##  Disattenuation target              = 'TRUE'
##  Disattenuation benchmark           = 'FALSE'
##  Approach to predict                = 'earliest'
## 
## ------------------------------ Prediction metrics ------------------------------
## 
## 
##   Name      MAE target  MAE benchmark  RMSE target RMSE benchmark   Q2_predict
##   expe1         1.4681         1.6013       1.9215         2.1197       0.0435
##   expe2         1.4233         1.5085       1.9455         2.0427       0.1907
##   expe3         1.6278         1.7411       2.1223         2.2187       0.1224
##   qual1         1.4835         1.5636       1.9342         2.0818       0.1115
##   qual2         1.5822         1.5459       2.0474         2.0710       0.2111
##   qual3         1.7312         1.7355       2.2205         2.2806       0.1176
##   qual4         1.2308         1.2007       1.5951         1.6432       0.2345
##   qual5         1.5032         1.5178       1.9349         1.9653       0.1958
##   val1          1.4477         1.3711       1.8707         1.7731       0.2481
##   val2          1.2276         1.2270       1.6515         1.7353       0.1713
##   val3          1.4746         1.3913       1.9619         1.9351       0.1520
##   sat1          1.2565         1.2362       1.6547         1.6278       0.3319
##   sat2          1.2372         1.2051       1.6465         1.6348       0.3035
##   sat3          1.3398         1.2889       1.6715         1.7256       0.2105
##   sat4          1.3171         1.2679       1.6718         1.6510       0.2734
##   loy1          1.7100         1.6798       2.2523         2.2520       0.2581
##   loy2          1.4907         1.4904       1.9127         1.9860       0.1354
##   loy3          1.7170         1.6789       2.2952         2.2773       0.2609
##   loy4          1.7045         1.7085       2.1899         2.3266       0.0850
## ________________________________________________________________________________

Resampling and Inference

By default no inferential statistics are calculated since most composite-based estimators have no closed-form expressions for standard errors. Resampling is used instead. cSEM mostly relies on the bootstrap procedure (although jackknife is implemented as well) to estimate standard errors, test statistics, and critical quantiles.

cSEM offers two ways for resampling:

  1. Setting .resample_method in csem() to "jackknife" or "bootstrap" and subsequently using post-estimation functions summarize() or infer().
  2. The same result is achieved by passing a cSEMResults object to resamplecSEMResults() and subsequently using post-estimation functions summarize() or infer().
# Setting `.resample_method`
b1 <- csem(.data = satisfaction, .model = model, .resample_method = "bootstrap")
# Using resamplecSEMResults()
b2 <- resamplecSEMResults(res)

The summarize() function reports the inferential statistics:

summarize(b1)
## ________________________________________________________________________________
## ----------------------------------- Overview -----------------------------------
## 
##  General information:
##  ------------------------
##  Estimation status                  = Ok
##  Number of observations             = 250
##  Weight estimator                   = PLS-PM
##  Inner weighting scheme             = "path"
##  Type of indicator correlation      = Pearson
##  Path model estimator               = OLS
##  Second-order approach              = NA
##  Type of path model                 = Linear
##  Disattenuated                      = Yes (PLSc)
## 
##  Resample information:
##  ---------------------
##  Resample method                    = "bootstrap"
##  Number of resamples                = 499
##  Number of admissible results       = 487
##  Approach to handle inadmissibles   = "drop"
##  Sign change option                 = "none"
##  Random seed                        = -558304815
## 
##  Construct details:
##  ------------------
##  Name  Modeled as     Order         Mode      
## 
##  IMAG  Composite      First order   "modeB"   
##  EXPE  Composite      First order   "modeB"   
##  QUAL  Composite      First order   "modeB"   
##  VAL   Composite      First order   "modeB"   
##  SAT   Common factor  First order   "modeA"   
##  LOY   Common factor  First order   "modeA"   
## 
## ----------------------------------- Estimates ----------------------------------
## 
## Estimated path coefficients:
## ============================
##                                                              CI_percentile   
##   Path           Estimate  Std. error   t-stat.   p-value         95%        
##   EXPE ~ IMAG      0.4714      0.0645    7.3038    0.0000 [ 0.3572; 0.5912 ] 
##   QUAL ~ EXPE      0.8344      0.0239   34.8885    0.0000 [ 0.7835; 0.8732 ] 
##   VAL ~ EXPE       0.0457      0.0830    0.5505    0.5820 [-0.1025; 0.2206 ] 
##   VAL ~ QUAL       0.7013      0.0796    8.8114    0.0000 [ 0.5327; 0.8562 ] 
##   SAT ~ IMAG       0.2450      0.0541    4.5315    0.0000 [ 0.1378; 0.3406 ] 
##   SAT ~ EXPE      -0.0172      0.0702   -0.2457    0.8059 [-0.1644; 0.1206 ] 
##   SAT ~ QUAL       0.2215      0.1034    2.1427    0.0321 [ 0.0491; 0.4451 ] 
##   SAT ~ VAL        0.5270      0.0878    5.9992    0.0000 [ 0.3340; 0.6845 ] 
##   LOY ~ IMAG       0.1819      0.0799    2.2764    0.0228 [ 0.0531; 0.3645 ] 
##   LOY ~ SAT        0.6283      0.0827    7.5987    0.0000 [ 0.4545; 0.7812 ] 
## 
## Estimated loadings:
## ===================
##                                                                CI_percentile   
##   Loading          Estimate  Std. error   t-stat.   p-value         95%        
##   IMAG =~ imag1      0.6306      0.0982    6.4240    0.0000 [ 0.4163; 0.8001 ] 
##   IMAG =~ imag2      0.9246      0.0414   22.3433    0.0000 [ 0.8208; 0.9761 ] 
##   IMAG =~ imag3      0.9577      0.0286   33.4955    0.0000 [ 0.8813; 0.9945 ] 
##   EXPE =~ expe1      0.7525      0.0759    9.9200    0.0000 [ 0.5820; 0.8621 ] 
##   EXPE =~ expe2      0.9348      0.0277   33.7516    0.0000 [ 0.8571; 0.9717 ] 
##   EXPE =~ expe3      0.7295      0.0700   10.4149    0.0000 [ 0.5649; 0.8461 ] 
##   QUAL =~ qual1      0.7861      0.0657   11.9741    0.0000 [ 0.6252; 0.8846 ] 
##   QUAL =~ qual2      0.9244      0.0218   42.4976    0.0000 [ 0.8691; 0.9566 ] 
##   QUAL =~ qual3      0.7560      0.0595   12.7096    0.0000 [ 0.6145; 0.8500 ] 
##   QUAL =~ qual4      0.7632      0.0531   14.3660    0.0000 [ 0.6453; 0.8510 ] 
##   QUAL =~ qual5      0.7834      0.0440   17.7936    0.0000 [ 0.6891; 0.8574 ] 
##   VAL =~ val1        0.9518      0.0246   38.6484    0.0000 [ 0.8941; 0.9854 ] 
##   VAL =~ val2        0.8056      0.0647   12.4583    0.0000 [ 0.6711; 0.9056 ] 
##   VAL =~ val3        0.6763      0.0733    9.2279    0.0000 [ 0.5271; 0.8104 ] 
##   SAT =~ sat1        0.9243      0.0240   38.5351    0.0000 [ 0.8710; 0.9662 ] 
##   SAT =~ sat2        0.8813      0.0308   28.6399    0.0000 [ 0.8099; 0.9273 ] 
##   SAT =~ sat3        0.7127      0.0550   12.9677    0.0000 [ 0.5923; 0.8009 ] 
##   SAT =~ sat4        0.7756      0.0500   15.5128    0.0000 [ 0.6697; 0.8675 ] 
##   LOY =~ loy1        0.9097      0.0501   18.1412    0.0000 [ 0.7959; 0.9838 ] 
##   LOY =~ loy2        0.5775      0.0833    6.9336    0.0000 [ 0.4093; 0.7281 ] 
##   LOY =~ loy3        0.9043      0.0428   21.1431    0.0000 [ 0.8068; 0.9688 ] 
##   LOY =~ loy4        0.4917      0.1016    4.8403    0.0000 [ 0.2938; 0.6902 ] 
## 
## Estimated weights:
## ==================
##                                                                CI_percentile   
##   Weight           Estimate  Std. error   t-stat.   p-value         95%        
##   IMAG <~ imag1      0.0156      0.1192    0.1312    0.8956 [-0.2039; 0.2429 ] 
##   IMAG <~ imag2      0.4473      0.1540    2.9037    0.0037 [ 0.1171; 0.7296 ] 
##   IMAG <~ imag3      0.6020      0.1389    4.3349    0.0000 [ 0.3265; 0.8840 ] 
##   EXPE <~ expe1      0.2946      0.1121    2.6281    0.0086 [ 0.0595; 0.4870 ] 
##   EXPE <~ expe2      0.6473      0.0785    8.2469    0.0000 [ 0.4702; 0.7858 ] 
##   EXPE <~ expe3      0.2374      0.0902    2.6320    0.0085 [ 0.0560; 0.4173 ] 
##   QUAL <~ qual1      0.2370      0.0889    2.6667    0.0077 [ 0.0688; 0.4078 ] 
##   QUAL <~ qual2      0.4712      0.0739    6.3735    0.0000 [ 0.3344; 0.6058 ] 
##   QUAL <~ qual3      0.1831      0.0783    2.3383    0.0194 [ 0.0237; 0.3205 ] 
##   QUAL <~ qual4      0.1037      0.0585    1.7722    0.0764 [-0.0022; 0.2202 ] 
##   QUAL <~ qual5      0.2049      0.0603    3.3952    0.0007 [ 0.0849; 0.3109 ] 
##   VAL <~ val1        0.7163      0.0987    7.2574    0.0000 [ 0.5053; 0.8754 ] 
##   VAL <~ val2        0.2202      0.0939    2.3457    0.0190 [ 0.0601; 0.4145 ] 
##   VAL <~ val3        0.2082      0.0634    3.2811    0.0010 [ 0.0952; 0.3370 ] 
##   SAT <~ sat1        0.3209      0.0156   20.5742    0.0000 [ 0.2963; 0.3535 ] 
##   SAT <~ sat2        0.3059      0.0141   21.6609    0.0000 [ 0.2808; 0.3365 ] 
##   SAT <~ sat3        0.2474      0.0119   20.8686    0.0000 [ 0.2233; 0.2707 ] 
##   SAT <~ sat4        0.2692      0.0125   21.5568    0.0000 [ 0.2471; 0.2966 ] 
##   LOY <~ loy1        0.3834      0.0271   14.1384    0.0000 [ 0.3314; 0.4345 ] 
##   LOY <~ loy2        0.2434      0.0288    8.4639    0.0000 [ 0.1803; 0.2913 ] 
##   LOY <~ loy3        0.3812      0.0273   13.9809    0.0000 [ 0.3275; 0.4349 ] 
##   LOY <~ loy4        0.2073      0.0377    5.4925    0.0000 [ 0.1325; 0.2795 ] 
## 
## Estimated indicator correlations:
## =================================
##                                                                 CI_percentile   
##   Correlation       Estimate  Std. error   t-stat.   p-value         95%        
##   imag1 ~~ imag2      0.6437      0.0660    9.7459    0.0000 [ 0.5046; 0.7537 ] 
##   imag1 ~~ imag3      0.5433      0.0692    7.8542    0.0000 [ 0.3989; 0.6627 ] 
##   imag2 ~~ imag3      0.7761      0.0393   19.7338    0.0000 [ 0.6929; 0.8385 ] 
##   expe1 ~~ expe2      0.5353      0.0584    9.1611    0.0000 [ 0.4000; 0.6434 ] 
##   expe1 ~~ expe3      0.4694      0.0587    8.0001    0.0000 [ 0.3451; 0.5749 ] 
##   expe2 ~~ expe3      0.5467      0.0606    9.0141    0.0000 [ 0.4078; 0.6554 ] 
##   qual1 ~~ qual2      0.6053      0.0568   10.6494    0.0000 [ 0.4852; 0.7079 ] 
##   qual1 ~~ qual3      0.5406      0.0568    9.5226    0.0000 [ 0.4302; 0.6485 ] 
##   qual1 ~~ qual4      0.5662      0.0671    8.4422    0.0000 [ 0.4362; 0.6877 ] 
##   qual1 ~~ qual5      0.5180      0.0642    8.0657    0.0000 [ 0.3943; 0.6359 ] 
##   qual2 ~~ qual3      0.6187      0.0552   11.2007    0.0000 [ 0.5043; 0.7127 ] 
##   qual2 ~~ qual4      0.6517      0.0613   10.6365    0.0000 [ 0.5252; 0.7516 ] 
##   qual2 ~~ qual5      0.6291      0.0545   11.5384    0.0000 [ 0.5168; 0.7250 ] 
##   qual3 ~~ qual4      0.4752      0.0627    7.5821    0.0000 [ 0.3551; 0.5928 ] 
##   qual3 ~~ qual5      0.5074      0.0609    8.3332    0.0000 [ 0.3957; 0.6226 ] 
##   qual4 ~~ qual5      0.6402      0.0579   11.0481    0.0000 [ 0.5187; 0.7365 ] 
##   val1 ~~ val2        0.6344      0.0539   11.7782    0.0000 [ 0.5247; 0.7355 ] 
##   val1 ~~ val3        0.4602      0.0702    6.5561    0.0000 [ 0.3208; 0.5949 ] 
##   val2 ~~ val3        0.6288      0.0611   10.2953    0.0000 [ 0.5148; 0.7399 ] 
## 
## ------------------------------------ Effects -----------------------------------
## 
## Estimated total effects:
## ========================
##                                                               CI_percentile   
##   Total effect    Estimate  Std. error   t-stat.   p-value         95%        
##   EXPE ~ IMAG       0.4714      0.0645    7.3038    0.0000 [ 0.3572; 0.5912 ] 
##   QUAL ~ IMAG       0.3933      0.0605    6.5021    0.0000 [ 0.2854; 0.5030 ] 
##   QUAL ~ EXPE       0.8344      0.0239   34.8885    0.0000 [ 0.7835; 0.8732 ] 
##   VAL ~ IMAG        0.2974      0.0600    4.9526    0.0000 [ 0.1930; 0.4247 ] 
##   VAL ~ EXPE        0.6309      0.0507   12.4388    0.0000 [ 0.5356; 0.7312 ] 
##   VAL ~ QUAL        0.7013      0.0796    8.8114    0.0000 [ 0.5327; 0.8562 ] 
##   SAT ~ IMAG        0.4807      0.0667    7.2079    0.0000 [ 0.3445; 0.6084 ] 
##   SAT ~ EXPE        0.5001      0.0569    8.7964    0.0000 [ 0.3856; 0.6051 ] 
##   SAT ~ QUAL        0.5911      0.0934    6.3297    0.0000 [ 0.4312; 0.7866 ] 
##   SAT ~ VAL         0.5270      0.0878    5.9992    0.0000 [ 0.3340; 0.6845 ] 
##   LOY ~ IMAG        0.4840      0.0671    7.2176    0.0000 [ 0.3701; 0.6248 ] 
##   LOY ~ EXPE        0.3142      0.0540    5.8235    0.0000 [ 0.2088; 0.4148 ] 
##   LOY ~ QUAL        0.3714      0.0800    4.6407    0.0000 [ 0.2269; 0.5264 ] 
##   LOY ~ VAL         0.3311      0.0769    4.3039    0.0000 [ 0.1797; 0.4755 ] 
##   LOY ~ SAT         0.6283      0.0827    7.5987    0.0000 [ 0.4545; 0.7812 ] 
## 
## Estimated indirect effects:
## ===========================
##                                                                  CI_percentile   
##   Indirect effect    Estimate  Std. error   t-stat.   p-value         95%        
##   QUAL ~ IMAG          0.3933      0.0605    6.5021    0.0000 [ 0.2854; 0.5030 ] 
##   VAL ~ IMAG           0.2974      0.0600    4.9526    0.0000 [ 0.1930; 0.4247 ] 
##   VAL ~ EXPE           0.5852      0.0680    8.6095    0.0000 [ 0.4469; 0.7188 ] 
##   SAT ~ IMAG           0.2357      0.0487    4.8406    0.0000 [ 0.1469; 0.3346 ] 
##   SAT ~ EXPE           0.5173      0.0663    7.7999    0.0000 [ 0.3961; 0.6611 ] 
##   SAT ~ QUAL           0.3696      0.0630    5.8700    0.0000 [ 0.2426; 0.4801 ] 
##   LOY ~ IMAG           0.3020      0.0554    5.4563    0.0000 [ 0.1934; 0.4106 ] 
##   LOY ~ EXPE           0.3142      0.0540    5.8235    0.0000 [ 0.2088; 0.4148 ] 
##   LOY ~ QUAL           0.3714      0.0800    4.6407    0.0000 [ 0.2269; 0.5264 ] 
##   LOY ~ VAL            0.3311      0.0769    4.3039    0.0000 [ 0.1797; 0.4755 ] 
## ________________________________________________________________________________

Several bootstrap-based confidence intervals are implemented, see ?infer():

infer(b1, .quantity = c("CI_standard_z", "CI_percentile")) # no print method yet

Both bootstrap and jackknife resampling support platform-independent multiprocessing as well as setting random seeds via the future framework. For multiprocessing simply set .eval_plan = "multisession" in which case the maximum number of available cores is used if not on Windows. On Windows as many separate R instances are opened in the background as there are cores available instead. Note that this naturally has some overhead so for a small number of resamples multiprocessing will not always be faster compared to sequential (single core) processing (the default). Seeds are set via the .seed argument.

b <- csem(
  .data            = satisfaction,
  .model           = model, 
  .resample_method = "bootstrap",
  .R               = 999,
  .seed            = 98234,
  .eval_plan       = "multisession")

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Install

install.packages('cSEM')

Monthly Downloads

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Version

0.6.0

License

GPL-3

Issues

63

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Stars

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Forks

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Maintainer

Florian Schuberth

Last Published

February 25th, 2025

Functions in cSEM (0.6.0)

args_assess_dotdotdot

Complete list of assess()'s ... arguments
calculateAVE

Average variance extracted (AVE)
args_default

Show argument defaults or candidates
assess

Assess model
cSEM-package

cSEM: A package for composite-based structural equation modeling
calculate2ndStage

Internal: Second/Third stage of the two-stage approach for second order constructs
calculateCompositeVCV

Internal: Calculate composite variance-covariance matrix
Yooetal2000

Data: Yooetal2000
adjustAlpha

Internal: Multiple testing correction
buildDotCode

Internal: Build DOT code for the SEM plot, including construct correlations.
calculateFR

Internal: ANOVA F-test statistic
calculateDf

Degrees of freedom
calculateConstructVCV

Internal: Calculate construct variance-covariance matrix
calculateHTMT

HTMT
calculateEffects

Internal: Calculate direct, indirect and total effect
calculateGoF

Goodness of Fit (GoF)
calculateFLCriterion

Fornell-Larcker criterion
calculateCorrectionFactors

Internal: Calculate PLSc correction factors
calculateIndicatorCor

Internal: Calculate indicator correlation matrix
calculateModelSelectionCriteria

Model selection criteria
calculateMAE

Internal: Calculate prediction metrics
calculateOuterWeightsPLS

Internal: Calculate the outer weights for PLS-PM
calculateDistance

Internal: Matrix difference
calculateParameterDifference

Internal: Parameter differences across groups
calculateInnerWeightsPLS

Internal: Calculate the inner weights for PLS-PM
calculateVIFModeB

Calculate variance inflation factors (VIF) for weights obtained by PLS Mode B
calculateWeightsGSCA

Calculate composite weights using GSCA
calculateRelativeGoF

Relative Goodness of Fit (relative GoF)
calculatePr

Internal: Calculation of the CDF used in Henseler et al. (2009)
classifyConstructs

Internal: Classify structural model terms by type
cleanNode

Internal: Clean a node name.
calculateReliabilities

Internal: Calculate Reliabilities
calculateWeightsGSCAm

Calculate weights using GSCAm
calculateWeightsKettenring

Calculate composite weights using GCCA
checkConvergence

Internal: Check convergence
calculateWeightsPCA

Calculate composite weights using principal component analysis (PCA)
calculateWeightsPLS

Calculate composite weights using PLS-PM
check_connection

Internal: Check whether two indicators belong to the same construct.
calculateWeightsUnit

Calculate composite weights using unit weights
calculatef2

Calculate Cohen's f^2
dgp_2ndorder_cf_of_c

Data: Second order common factor of composites
distance_measures

Calculate difference between S and Sigma_hat
convertModel

Internal: Convert second order cSEMModel
csem_test

cSEMTest
csem

Composite-based SEM
csem_results

cSEMResults
csem_arguments

cSEMArguments
doIPMA

Do an importance-performance matrix analysis
fit

Model-implied indicator or construct variance-covariance matrix
fit_measures

Model fit measures
doRedundancyAnalysis

Do a redundancy analysis
doNonlinearEffectsAnalysis

Do a nonlinear effects analysis
exportToExcel

Export to Excel (.xlsx)
estimatePath

Internal: Estimate the structural coefficients
csem_summary

cSEMSummarize
csem_model

cSEMModel
getConstructScores

Get construct scores
firstOrderMeasurementEdges

Internal: firstOrderMeasurementEdges
getParameterNames

Internal: Parameter names
foreman

Internal: Composite-based SEM
get_significance_stars

Internal: get significance stars
infer

Inference
getRelevantParameters

Internal: Extract relevant parameters from several cSEMResults_multi
handleArgs

Internal: Handle arguments
moments

Internal: Calculate consistent moments of a nonlinear model
plot.cSEMIPMA

cSEMIPMA method for plot()
parseModel

Parse lavaan model
nonlinear_estimation_utilities

Internal: Utility functions for the estimation of nonlinear models
inference_helper

Internal: Helper for infer()
plot.cSEMResults_multi

cSEMResults method for plot() for multiple groups.
plot.cSEMNonlinearEffects

cSEMNonlinearEffects method for plot()
getValuesFloodlight

Internal: Helper for doNonlinearEffectsAnalysis()
plot.cSEMResults_2ndorder

cSEMResults method for plot() for second-order models.
predict

Predict indicator scores
print.cSEMPredict

cSEMPredict method for print()
plot.cSEMPredict

cSEMPredict method for plot()
print.cSEMAssess

cSEMAssess method for print()
print.cSEMPlotPredict

cSEMPlotPredict method for print()
plot.cSEMResults_default

cSEMResults method for plot()
print.cSEMTestMICOM

cSEMTestMICOM method for print()
print.cSEMTestMGD

cSEMTestMGD method for print()
print.cSEMResults

cSEMResults method for print()
print.cSEMTestCVPAT

cSEMTestCVPAT method for print()
print.cSEMTestHausman

cSEMTestHausman method for print()
print.cSEMNonlinearEffects

cSEMNonlinearEffectsAnalysis method for print()
print.cSEMTestOMF

cSEMTestOMF method for print()
save_single_plot

Internal: save_single_plot Helper function to save a single DiagrammeR plot based on the file extension
savePlot

savePlot
print.cSEMSummarize

cSEMSummarize method for print()
processData

Internal: Process data
reliability

Reliability
resampleData

Resample data
resamplecSEMResults

Resample cSEMResults
scaleWeights

Internal: Scale weights
setDominantIndicator

Internal: Set the dominant indicator
setStartingValues

Internal: Set starting values
secondOrderMeasurementEdges

Internal: secondOrderMeasurementEdges
print.cSEMVerify

cSEMVerify method for print()
satisfaction_gender

Data: satisfaction including gender
satisfaction

Data: satisfaction
testOMF

Test for overall model fit
testCVPAT

Perform a Cross-Validated Predictive Ability Test (CVPAT)
verify

Verify admissibility
testMICOM

Test measurement invariance of composites
testMGD

Tests for multi-group comparisons
threecommonfactors

Data: threecommonfactors
testHausman

Regression-based Hausman test
structureTestMGDDecisions

Internal: get structured cSEMTestMGD results
summarize

Summarize model
BergamiBagozzi2000

Data: BergamiBagozzi2000
Anime

Data: Anime
Sigma_Summers_composites

Data: Summers
Benitezetal2020

Data: Benitezetal2020
Switching

Data: Switching
ITFlex

Data: ITFlex
LancelotMiltgenetal2016

Data: LancelotMiltgenetal2016
PoliticalDemocracy

Data: political democracy
SQ

Data: SQ
Russett

Data: Russett