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:
- Pick a dataset and specify a model using lavaan syntax
- Use
csem()- 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$ModelA 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:
- Setting
.resample_methodincsem()to"jackknife"or"bootstrap"and subsequently using post-estimation functionssummarize()orinfer(). - The same result is achieved by passing a
cSEMResultsobject toresamplecSEMResults()and subsequently using post-estimation functionssummarize()orinfer().
# 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():
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")