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tests/comparisons/Compare_to_ADANCO_and_matrixpls_cf_model.R
In cSEM: Composite-Based Structural Equation Modeling
#===============================================================================
#
# Topic: Compare results from cSEM (0.4.0.9000), ADANCO 2.2.1.,
# and matrixpls (v. 1.0.13)
#
# Type of model: common factor model
#
# Date: 19.07.2021
#
#===============================================================================
rm(list = ls())
require(cSEM)
require(xlsx)
require(matrixpls)
data("satisfaction", package = "cSEM")
path_to_results <- "tests/comparisons/results_cf_model_adanco_2_2_1_centroid.xls"
### Import ADANCO results ------------------------------------------------------
## Import weights
weights_ADANCO <- read.xlsx(path_to_results,
sheetName = "Weights",
startRow = 2, endRow = 29, colIndex = c(2:8),
colClasses = c("character", rep("numeric", 6)))
weights_ADANCO[is.na(weights_ADANCO)] <- 0
rownames(weights_ADANCO) <- weights_ADANCO$Indicator
weights_ADANCO <- weights_ADANCO[, -1]
## Import loadings
loadings_ADANCO <- read.xlsx(path_to_results,
sheetName = "Loadings",
startRow = 2, endRow = 29, colIndex = c(2:8),
colClasses = c("character", rep("numeric", 6)))
loadings_ADANCO[is.na(loadings_ADANCO)] <- 0
rownames(loadings_ADANCO) <- loadings_ADANCO$Indicator
loadings_ADANCO <- loadings_ADANCO[, -1]
## Import path
path_ADANCO <- read.xlsx(path_to_results,
sheetName = "Path Coefficients",
startRow = 3, endRow = 8, colIndex = c(2:7),
colClasses = c("character", rep("numeric", 5)))
path_ADANCO[is.na(path_ADANCO)] <- 0
rownames(path_ADANCO) <- path_ADANCO$c..IMAG....EXPE....QUAL....VAL....SAT..
path_ADANCO <- as.matrix(path_ADANCO[, -1])
## Import standardized scores
scores_ADANCO <- read.xlsx(path_to_results,
sheetName = "Standardized Construct Scores",
startRow = 2, endRow = 252, colIndex = c(3:8),
colClasses = rep("numeric", 5))
## Import Goodness of model fit (saturated)
gof_s_ADANCO <- read.xlsx(path_to_results,
sheetName = "Goodness of model fit (saturate",
startRow = 2, endRow = 5, colIndex = c(2:5),
colClasses = c("character", rep("numeric", 3)))
gof_s_ADANCO1 <- gof_s_ADANCO$Value
names(gof_s_ADANCO1) <- gof_s_ADANCO$c..SRMR....dULS....dG..
gof_s_ADANCO <- gof_s_ADANCO1
## Import Goodness of model fit (estimated)
gof_e_ADANCO <- read.xlsx(path_to_results,
sheetName = "Goodness of model fit (estimate",
startRow = 2, endRow = 5, colIndex = c(2:5),
colClasses = c("character", rep("numeric", 3)))
gof_e_ADANCO1 <- gof_e_ADANCO$Value
names(gof_e_ADANCO1) <- gof_e_ADANCO$c..SRMR....dULS....dG..
gof_e_ADANCO <- gof_e_ADANCO1
## Reliability
reliability_ADANCO <- read.xlsx(path_to_results,
sheetName = "Construct Reliability",
startRow = 2, endRow = 8, colIndex = c(2:5))
## AVE
ave_ADANCO <- read.xlsx(path_to_results,
sheetName = "Convergent Validity",
startRow = 2, endRow = 8, colIndex = c(2:3))
ave_name <- ave_ADANCO$Construct
ave_ADANCO <- ave_ADANCO$Average.variance.extracted..AVE.
names(ave_ADANCO) <- ave_name
## HTMT
htmt_ADANCO <- read.xlsx(path_to_results,
sheetName = "Discriminant Validity Heterotr",
startRow = 2, endRow = 8, colIndex = c(3:8))
htmt_ADANCO <- as.matrix(htmt_ADANCO)
htmt_ADANCO <- apply(htmt_ADANCO, 2, as.numeric)
rownames(htmt_ADANCO) <- colnames(htmt_ADANCO)
htmt_ADANCO[is.na(htmt_ADANCO)] <- 0
### Fornell-Larcker Criterion
fl_ADANCO <- read.xlsx(path_to_results,
sheetName = "Fornell-Larcker Criterion",
startRow = 2, endRow = 8, colIndex = c(3:8))
fl_ADANCO <- as.matrix(fl_ADANCO)
fl_ADANCO <- apply(fl_ADANCO, 2, as.numeric)
fl_ADANCO[upper.tri(fl_ADANCO)] <- t(fl_ADANCO)[upper.tri(fl_ADANCO)]
rownames(fl_ADANCO) <- colnames(fl_ADANCO)
## R2
r2_ADANCO <- read.xlsx(path_to_results,
sheetName = "R-Squared",
startRow = 2, endRow = 7, colIndex = c(2:4))
## Cohens f2 (effect size)
f2_ADANCO <- read.xlsx(path_to_results,
sheetName = "Effect Overview",
startRow = 3, endRow = 17, colIndex = 6, header = FALSE,
colClasses = "numeric")
f2_ADANCO <- as.numeric(f2_ADANCO$X6)[!is.na(as.numeric(f2_ADANCO$X6))]
## Proxy cor
construct_cor_ADANCO <- read.xlsx(path_to_results,
sheetName = "Inter-Construct Correlations",
startRow = 2, endRow = 8, colIndex = c(3:8))
construct_cor_ADANCO <- as.matrix(construct_cor_ADANCO)
construct_cor_ADANCO[upper.tri(construct_cor_ADANCO)] <- t(construct_cor_ADANCO)[upper.tri(construct_cor_ADANCO)]
construct_cor_ADANCO <- apply(construct_cor_ADANCO, 2, as.numeric)
rownames(construct_cor_ADANCO) <- colnames(construct_cor_ADANCO)
## Model-implied indicator cor (saturated)
sigma_hat_saturated <- read.xlsx(path_to_results,
sheetName = "Impl_Cor Saturated Model",
startRow = 2, endRow = 29, colIndex = c(3:29))
sigma_hat_saturated <- as.matrix(sigma_hat_saturated)
rownames(sigma_hat_saturated) <- colnames(sigma_hat_saturated)
## Model-implied indicator cor (estimated)
sigma_hat_estimated <- read.xlsx(path_to_results,
sheetName = "Impl_Cor Estimated Model",
startRow = 2, endRow = 29, colIndex = c(3:29))
sigma_hat_estimated <- as.matrix(sigma_hat_estimated)
rownames(sigma_hat_estimated) <- colnames(sigma_hat_estimated)
### Load data and define model =================================================
# Model cSEM
model <- "
# Structural model
EXPE ~ IMAG
QUAL ~ EXPE
VAL ~ EXPE + QUAL
SAT ~ IMAG + EXPE + QUAL + VAL
LOY ~ IMAG + SAT
# Measurement model
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5
EXPE =~ expe1 + expe2 + expe3 + expe4 + expe5
QUAL =~ qual1 + qual2 + qual3 + qual4 + qual5
VAL =~ val1 + val2 + val3 + val4
SAT =~ sat1 + sat2 + sat3 + sat4
LOY =~ loy1 + loy2 + loy3 + loy4
"
### cSEM -----------------------------------------------------------------------
a1 <- csem(
.data = satisfaction,
.model = model,
.approach_weights = "PLS-PM",
.tolerance = 1e-06,
.PLS_modes = NULL,
.PLS_ignore_structural_model = FALSE,
.PLS_weight_scheme_inner = "centroid"
)
suma1 <- cSEM:::summarize(a1)
assa1 <- assess(a1)
### Matrixpls ------------------------------------------------------------------
a2 <- matrixpls(S = cor(satisfaction),
model = model,
standardize = TRUE,
parametersReflective = estimator.plscLoadings,
disattenuate = TRUE,
innerEstim = innerEstim.centroid,
ignoreInnerModel = FALSE,
outerEstim = outerEstim.modeA,
tol = 1e-06
)
suma2 <- summary(a2)
resid_matpls <- matrixpls:::residuals.matrixpls(a2, observed = FALSE)
W_matpls <- attr(a2, "W")
Lambda_matpls <- attr(a2, "reflective")
path_matpls <- attr(a2, "inner")
S_matpls <- attr(a2, "S")
vcv_proxy_matpls <- W_matpls %*% S_matpls %*% t(W_matpls)
vcv_construct_matpls <- attr(a2, "C")
Theta_matpls <- diag(1 - diag(Lambda_matpls %*% t(Lambda_matpls)))
sigma_hat_saturated_matpls <- Lambda_matpls %*% vcv_construct_matpls %*% t(Lambda_matpls) + Theta_matpls
sigma_hat_estimated_matpls <- matrixpls:::fitted.matrixpls(a2)
### Compare ====================================================================
# Note (19.12.2019): Apparently ADANCO has a bug. If you change the weighting scheme
# from Factor to Centroid nothing changes, i.e., the ADANCO always uses the
# factor scheme.
# Note (19.07.2021): This issue has been fixed in version 2.2.1. Now centroid and
# factorial scheme yield different results
## Compare weights
a1$Estimates$Weight_estimates - t(weights_ADANCO) # identical at the 8th sig digit
a1$Estimates$Weight_estimates - W_matpls # identical
## Compare loadings
a1$Estimates$Loading_estimates - t(loadings_ADANCO) # identical at the 8th sig digit
a1$Estimates$Loading_estimates - t(Lambda_matpls) # identical
## Compare path
a1$Estimates$Path_estimates[-1, -6] - t(path_ADANCO) # identical at the 8th sig digit
a1$Estimates$Path_estimates - path_matpls # identical
## Compare proxy/composite correlation matrix (C in cSEM)
a1$Estimates$Proxy_VCV - cor(scores_ADANCO) # identical at the 8th sig digit
a1$Estimates$Proxy_VCV - vcv_proxy_matpls # identical
## Compare construct correlation matrix (P in cSEM)
a1$Estimates$Construct_VCV - construct_cor_ADANCO # identical at the 8th sig digit
a1$Estimates$Construct_VCV - vcv_construct_matpls # identical
## Compare model_implied indicator cor (saturated)
round(fit(a1, .saturated = TRUE) - sigma_hat_saturated, 8) # identical at the 8th sig digit
fit(a1, .saturated = TRUE) - sigma_hat_saturated_matpls # identical
## Compare model_implied indicator cor (estimated)
round(fit(a1) - sigma_hat_estimated, 6) # Identical
round(fit(a1) - sigma_hat_estimated_matpls, 6) # Differences for blocks of SAT and LOY
# See: fit function for explanation why.
## Compare model_implied indicator cor of constructs
# We have:
# Sigma = Lambda V_eta Lambda' + Theta
# Lambda' (Sigma - Theta ) Lambda = (Lambda'Lambda) V_eta (Lambda' Lambda)
# V_eta = (Lambda' Lambda)^-1 Lambda' (Sigma - Theta ) Lambda (Lambda' Lambda)^-1
#
# V_eta matrixpls
V_eta_matpls <- solve(t(Lambda_matpls) %*% Lambda_matpls) %*% t(Lambda_matpls) %*%
(sigma_hat_estimated_matpls - Theta_matpls) %*% Lambda_matpls %*%
solve(t(Lambda_matpls) %*% Lambda_matpls)
round(fit(a1, .type_vcv = "construct") - V_eta_matpls, 8)
# main diagonal elements differ, i.e., model-implied construct variances are not
# 1 (which they should be). This causes the blocks of those constructs that
# dont have a variance of 1 to be wrong in "sigma_hat_estimated_matpls".
## V_eta for ADANCO
V_eta_ADANCO <- solve(t(Lambda_matpls) %*% Lambda_matpls) %*% t(Lambda_matpls) %*%
(sigma_hat_estimated - Theta_matpls) %*% Lambda_matpls %*%
solve(t(Lambda_matpls) %*% Lambda_matpls)
round(fit(a1, .type_vcv = "construct") - V_eta_ADANCO, 8) # identical to the 8th digit
### Quality criteria -------------------------------------------------------------
## Overall model fit
# SRMR, dG dL
# Note : the fitted function in ADANCO is not correct. Reason: the model-implied
# construct correlation matrix does not always have ones on its main diagonal,
# i.e. the variance of some constructs (those deeper down the nomologial net).
# Note (19.07.2021): fixed in ADANCO version 2.2.1
## Distance measures for saturated model
cSEM:::calculateSRMR(a1, .saturated = TRUE) - gof_s_ADANCO["SRMR"] # identical at the 8th sig digit
cSEM:::calculateDL(a1, .saturated = TRUE) - gof_s_ADANCO["dULS"] # identical at the 8th sig digit
cSEM:::calculateDG(a1, .saturated = TRUE) - gof_s_ADANCO["dG"] # identical at the 8th sig digit
# no measures for matrixpls
## Distance measures for estimated model
cSEM:::calculateSRMR(a1) - gof_e_ADANCO["SRMR"] # identical at the 8th sig digit
cSEM:::calculateDL(a1) - gof_e_ADANCO["dULS"] # identical at the 8th sig digit
cSEM:::calculateDG(a1) - gof_e_ADANCO["dG"] # identical at the 8th sig digit
cSEM:::calculateSRMR(a1) - resid_matpls$indices[1] # different, since model-implied vcv is different
# for dg and DL no measure for matrixpls
## R2
assa1$R2 - r2_ADANCO$Coefficient.of.determination..R2. # identical at the 8th sig digit
assa1$R2 - suma2$r2[-1] # identical to matrixpls
## R2 adjusted
assa1$R2_adj - r2_ADANCO$Adjusted.R2 # identical at the 8th sig digit
# no measures for matrixpls
## AVE
assa1$AVE - ave_ADANCO # identical at the 8th sig digit
assa1$AVE - suma2$ave$ave # identical to matrixpls
## HTMT
assa1$HTMT$values - htmt_ADANCO # identical to ADANCO
assa1$HTMT$values - suma2$htmt # identical to matrixpls
## Fornell-Larcker
assa1$`Fornell-Larcker` - fl_ADANCO # identical to ADANCO
# no measure for matrixpls
## Cohens f^2
f2_ADANCO
assa1$F2 # identical to ADANCO
# no measure for matrixpls
## Reliability
assa1$Reliability$`Dijkstra-Henselers_rho_A` - reliability_ADANCO$Dijkstra.Henseler.s.rho...U.03C1.A. # identical to ADNACO
assa1$Reliability$Joereskogs_rho - reliability_ADANCO$Jรถreskog.s.rho...U.03C1.c. # identical to ADANCO
assa1$Reliability$Cronbachs_alpha - reliability_ADANCO$Cronbach.s.alpha.a. # identical ADANCO
assa1$Reliability$Joereskogs_rho - suma2$cr # identical to matrixpls
## GoF
assa1$GoF - suma2$gof # identical to matrixpls
# no measure for ADANCO
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#===============================================================================
#
# Topic: Compare results from cSEM (0.4.0.9000), ADANCO 2.2.1.,
# and matrixpls (v. 1.0.13)
#
# Type of model: common factor model
#
# Date: 19.07.2021
#
#===============================================================================
rm(list = ls())
require(cSEM)
require(xlsx)
require(matrixpls)
data("satisfaction", package = "cSEM")
path_to_results <- "tests/comparisons/results_cf_model_adanco_2_2_1_centroid.xls"
### Import ADANCO results ------------------------------------------------------
## Import weights
weights_ADANCO <- read.xlsx(path_to_results,
sheetName = "Weights",
startRow = 2, endRow = 29, colIndex = c(2:8),
colClasses = c("character", rep("numeric", 6)))
weights_ADANCO[is.na(weights_ADANCO)] <- 0
rownames(weights_ADANCO) <- weights_ADANCO$Indicator
weights_ADANCO <- weights_ADANCO[, -1]
## Import loadings
loadings_ADANCO <- read.xlsx(path_to_results,
sheetName = "Loadings",
startRow = 2, endRow = 29, colIndex = c(2:8),
colClasses = c("character", rep("numeric", 6)))
loadings_ADANCO[is.na(loadings_ADANCO)] <- 0
rownames(loadings_ADANCO) <- loadings_ADANCO$Indicator
loadings_ADANCO <- loadings_ADANCO[, -1]
## Import path
path_ADANCO <- read.xlsx(path_to_results,
sheetName = "Path Coefficients",
startRow = 3, endRow = 8, colIndex = c(2:7),
colClasses = c("character", rep("numeric", 5)))
path_ADANCO[is.na(path_ADANCO)] <- 0
rownames(path_ADANCO) <- path_ADANCO$c..IMAG....EXPE....QUAL....VAL....SAT..
path_ADANCO <- as.matrix(path_ADANCO[, -1])
## Import standardized scores
scores_ADANCO <- read.xlsx(path_to_results,
sheetName = "Standardized Construct Scores",
startRow = 2, endRow = 252, colIndex = c(3:8),
colClasses = rep("numeric", 5))
## Import Goodness of model fit (saturated)
gof_s_ADANCO <- read.xlsx(path_to_results,
sheetName = "Goodness of model fit (saturate",
startRow = 2, endRow = 5, colIndex = c(2:5),
colClasses = c("character", rep("numeric", 3)))
gof_s_ADANCO1 <- gof_s_ADANCO$Value
names(gof_s_ADANCO1) <- gof_s_ADANCO$c..SRMR....dULS....dG..
gof_s_ADANCO <- gof_s_ADANCO1
## Import Goodness of model fit (estimated)
gof_e_ADANCO <- read.xlsx(path_to_results,
sheetName = "Goodness of model fit (estimate",
startRow = 2, endRow = 5, colIndex = c(2:5),
colClasses = c("character", rep("numeric", 3)))
gof_e_ADANCO1 <- gof_e_ADANCO$Value
names(gof_e_ADANCO1) <- gof_e_ADANCO$c..SRMR....dULS....dG..
gof_e_ADANCO <- gof_e_ADANCO1
## Reliability
reliability_ADANCO <- read.xlsx(path_to_results,
sheetName = "Construct Reliability",
startRow = 2, endRow = 8, colIndex = c(2:5))
## AVE
ave_ADANCO <- read.xlsx(path_to_results,
sheetName = "Convergent Validity",
startRow = 2, endRow = 8, colIndex = c(2:3))
ave_name <- ave_ADANCO$Construct
ave_ADANCO <- ave_ADANCO$Average.variance.extracted..AVE.
names(ave_ADANCO) <- ave_name
## HTMT
htmt_ADANCO <- read.xlsx(path_to_results,
sheetName = "Discriminant Validity Heterotr",
startRow = 2, endRow = 8, colIndex = c(3:8))
htmt_ADANCO <- as.matrix(htmt_ADANCO)
htmt_ADANCO <- apply(htmt_ADANCO, 2, as.numeric)
rownames(htmt_ADANCO) <- colnames(htmt_ADANCO)
htmt_ADANCO[is.na(htmt_ADANCO)] <- 0
### Fornell-Larcker Criterion
fl_ADANCO <- read.xlsx(path_to_results,
sheetName = "Fornell-Larcker Criterion",
startRow = 2, endRow = 8, colIndex = c(3:8))
fl_ADANCO <- as.matrix(fl_ADANCO)
fl_ADANCO <- apply(fl_ADANCO, 2, as.numeric)
fl_ADANCO[upper.tri(fl_ADANCO)] <- t(fl_ADANCO)[upper.tri(fl_ADANCO)]
rownames(fl_ADANCO) <- colnames(fl_ADANCO)
## R2
r2_ADANCO <- read.xlsx(path_to_results,
sheetName = "R-Squared",
startRow = 2, endRow = 7, colIndex = c(2:4))
## Cohens f2 (effect size)
f2_ADANCO <- read.xlsx(path_to_results,
sheetName = "Effect Overview",
startRow = 3, endRow = 17, colIndex = 6, header = FALSE,
colClasses = "numeric")
f2_ADANCO <- as.numeric(f2_ADANCO$X6)[!is.na(as.numeric(f2_ADANCO$X6))]
## Proxy cor
construct_cor_ADANCO <- read.xlsx(path_to_results,
sheetName = "Inter-Construct Correlations",
startRow = 2, endRow = 8, colIndex = c(3:8))
construct_cor_ADANCO <- as.matrix(construct_cor_ADANCO)
construct_cor_ADANCO[upper.tri(construct_cor_ADANCO)] <- t(construct_cor_ADANCO)[upper.tri(construct_cor_ADANCO)]
construct_cor_ADANCO <- apply(construct_cor_ADANCO, 2, as.numeric)
rownames(construct_cor_ADANCO) <- colnames(construct_cor_ADANCO)
## Model-implied indicator cor (saturated)
sigma_hat_saturated <- read.xlsx(path_to_results,
sheetName = "Impl_Cor Saturated Model",
startRow = 2, endRow = 29, colIndex = c(3:29))
sigma_hat_saturated <- as.matrix(sigma_hat_saturated)
rownames(sigma_hat_saturated) <- colnames(sigma_hat_saturated)
## Model-implied indicator cor (estimated)
sigma_hat_estimated <- read.xlsx(path_to_results,
sheetName = "Impl_Cor Estimated Model",
startRow = 2, endRow = 29, colIndex = c(3:29))
sigma_hat_estimated <- as.matrix(sigma_hat_estimated)
rownames(sigma_hat_estimated) <- colnames(sigma_hat_estimated)
### Load data and define model =================================================
# Model cSEM
model <- "
# Structural model
EXPE ~ IMAG
QUAL ~ EXPE
VAL ~ EXPE + QUAL
SAT ~ IMAG + EXPE + QUAL + VAL
LOY ~ IMAG + SAT
# Measurement model
IMAG =~ imag1 + imag2 + imag3 + imag4 + imag5
EXPE =~ expe1 + expe2 + expe3 + expe4 + expe5
QUAL =~ qual1 + qual2 + qual3 + qual4 + qual5
VAL =~ val1 + val2 + val3 + val4
SAT =~ sat1 + sat2 + sat3 + sat4
LOY =~ loy1 + loy2 + loy3 + loy4
"
### cSEM -----------------------------------------------------------------------
a1 <- csem(
.data = satisfaction,
.model = model,
.approach_weights = "PLS-PM",
.tolerance = 1e-06,
.PLS_modes = NULL,
.PLS_ignore_structural_model = FALSE,
.PLS_weight_scheme_inner = "centroid"
)
suma1 <- cSEM:::summarize(a1)
assa1 <- assess(a1)
### Matrixpls ------------------------------------------------------------------
a2 <- matrixpls(S = cor(satisfaction),
model = model,
standardize = TRUE,
parametersReflective = estimator.plscLoadings,
disattenuate = TRUE,
innerEstim = innerEstim.centroid,
ignoreInnerModel = FALSE,
outerEstim = outerEstim.modeA,
tol = 1e-06
)
suma2 <- summary(a2)
resid_matpls <- matrixpls:::residuals.matrixpls(a2, observed = FALSE)
W_matpls <- attr(a2, "W")
Lambda_matpls <- attr(a2, "reflective")
path_matpls <- attr(a2, "inner")
S_matpls <- attr(a2, "S")
vcv_proxy_matpls <- W_matpls %*% S_matpls %*% t(W_matpls)
vcv_construct_matpls <- attr(a2, "C")
Theta_matpls <- diag(1 - diag(Lambda_matpls %*% t(Lambda_matpls)))
sigma_hat_saturated_matpls <- Lambda_matpls %*% vcv_construct_matpls %*% t(Lambda_matpls) + Theta_matpls
sigma_hat_estimated_matpls <- matrixpls:::fitted.matrixpls(a2)
### Compare ====================================================================
# Note (19.12.2019): Apparently ADANCO has a bug. If you change the weighting scheme
# from Factor to Centroid nothing changes, i.e., the ADANCO always uses the
# factor scheme.
# Note (19.07.2021): This issue has been fixed in version 2.2.1. Now centroid and
# factorial scheme yield different results
## Compare weights
a1$Estimates$Weight_estimates - t(weights_ADANCO) # identical at the 8th sig digit
a1$Estimates$Weight_estimates - W_matpls # identical
## Compare loadings
a1$Estimates$Loading_estimates - t(loadings_ADANCO) # identical at the 8th sig digit
a1$Estimates$Loading_estimates - t(Lambda_matpls) # identical
## Compare path
a1$Estimates$Path_estimates[-1, -6] - t(path_ADANCO) # identical at the 8th sig digit
a1$Estimates$Path_estimates - path_matpls # identical
## Compare proxy/composite correlation matrix (C in cSEM)
a1$Estimates$Proxy_VCV - cor(scores_ADANCO) # identical at the 8th sig digit
a1$Estimates$Proxy_VCV - vcv_proxy_matpls # identical
## Compare construct correlation matrix (P in cSEM)
a1$Estimates$Construct_VCV - construct_cor_ADANCO # identical at the 8th sig digit
a1$Estimates$Construct_VCV - vcv_construct_matpls # identical
## Compare model_implied indicator cor (saturated)
round(fit(a1, .saturated = TRUE) - sigma_hat_saturated, 8) # identical at the 8th sig digit
fit(a1, .saturated = TRUE) - sigma_hat_saturated_matpls # identical
## Compare model_implied indicator cor (estimated)
round(fit(a1) - sigma_hat_estimated, 6) # Identical
round(fit(a1) - sigma_hat_estimated_matpls, 6) # Differences for blocks of SAT and LOY
# See: fit function for explanation why.
## Compare model_implied indicator cor of constructs
# We have:
# Sigma = Lambda V_eta Lambda' + Theta
# Lambda' (Sigma - Theta ) Lambda = (Lambda'Lambda) V_eta (Lambda' Lambda)
# V_eta = (Lambda' Lambda)^-1 Lambda' (Sigma - Theta ) Lambda (Lambda' Lambda)^-1
#
# V_eta matrixpls
V_eta_matpls <- solve(t(Lambda_matpls) %*% Lambda_matpls) %*% t(Lambda_matpls) %*%
(sigma_hat_estimated_matpls - Theta_matpls) %*% Lambda_matpls %*%
solve(t(Lambda_matpls) %*% Lambda_matpls)
round(fit(a1, .type_vcv = "construct") - V_eta_matpls, 8)
# main diagonal elements differ, i.e., model-implied construct variances are not
# 1 (which they should be). This causes the blocks of those constructs that
# dont have a variance of 1 to be wrong in "sigma_hat_estimated_matpls".
## V_eta for ADANCO
V_eta_ADANCO <- solve(t(Lambda_matpls) %*% Lambda_matpls) %*% t(Lambda_matpls) %*%
(sigma_hat_estimated - Theta_matpls) %*% Lambda_matpls %*%
solve(t(Lambda_matpls) %*% Lambda_matpls)
round(fit(a1, .type_vcv = "construct") - V_eta_ADANCO, 8) # identical to the 8th digit
### Quality criteria -------------------------------------------------------------
## Overall model fit
# SRMR, dG dL
# Note : the fitted function in ADANCO is not correct. Reason: the model-implied
# construct correlation matrix does not always have ones on its main diagonal,
# i.e. the variance of some constructs (those deeper down the nomologial net).
# Note (19.07.2021): fixed in ADANCO version 2.2.1
## Distance measures for saturated model
cSEM:::calculateSRMR(a1, .saturated = TRUE) - gof_s_ADANCO["SRMR"] # identical at the 8th sig digit
cSEM:::calculateDL(a1, .saturated = TRUE) - gof_s_ADANCO["dULS"] # identical at the 8th sig digit
cSEM:::calculateDG(a1, .saturated = TRUE) - gof_s_ADANCO["dG"] # identical at the 8th sig digit
# no measures for matrixpls
## Distance measures for estimated model
cSEM:::calculateSRMR(a1) - gof_e_ADANCO["SRMR"] # identical at the 8th sig digit
cSEM:::calculateDL(a1) - gof_e_ADANCO["dULS"] # identical at the 8th sig digit
cSEM:::calculateDG(a1) - gof_e_ADANCO["dG"] # identical at the 8th sig digit
cSEM:::calculateSRMR(a1) - resid_matpls$indices[1] # different, since model-implied vcv is different
# for dg and DL no measure for matrixpls
## R2
assa1$R2 - r2_ADANCO$Coefficient.of.determination..R2. # identical at the 8th sig digit
assa1$R2 - suma2$r2[-1] # identical to matrixpls
## R2 adjusted
assa1$R2_adj - r2_ADANCO$Adjusted.R2 # identical at the 8th sig digit
# no measures for matrixpls
## AVE
assa1$AVE - ave_ADANCO # identical at the 8th sig digit
assa1$AVE - suma2$ave$ave # identical to matrixpls
## HTMT
assa1$HTMT$values - htmt_ADANCO # identical to ADANCO
assa1$HTMT$values - suma2$htmt # identical to matrixpls
## Fornell-Larcker
assa1$`Fornell-Larcker` - fl_ADANCO # identical to ADANCO
# no measure for matrixpls
## Cohens f^2
f2_ADANCO
assa1$F2 # identical to ADANCO
# no measure for matrixpls
## Reliability
assa1$Reliability$`Dijkstra-Henselers_rho_A` - reliability_ADANCO$Dijkstra.Henseler.s.rho...U.03C1.A. # identical to ADNACO
assa1$Reliability$Joereskogs_rho - reliability_ADANCO$Jรถreskog.s.rho...U.03C1.c. # identical to ADANCO
assa1$Reliability$Cronbachs_alpha - reliability_ADANCO$Cronbach.s.alpha.a. # identical ADANCO
assa1$Reliability$Joereskogs_rho - suma2$cr # identical to matrixpls
## GoF
assa1$GoF - suma2$gof # identical to matrixpls
# no measure for ADANCO
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