The function is essentially a wrapper around a number of internal functions
that perform an "assessment task" (called a quality criterion in cSEM
parlance) like computing reliability estimates,
the effect size (Cohen's f^2), the heterotrait-monotrait ratio of correlations (HTMT) etc.
- Average variance extracted (AVE); "ave"
An estimate of the
amount of variation in the indicators that is due to the underlying latent variable.
Practically, it is calculated as the ratio of the (indicator) true score variances
(i.e., the sum of the squared loadings)
relative to the sum of the total indicator variances. The AVE is inherently
tied to the common factor model. It is therefore unclear how to meaningfully
interpret AVE results for constructs modeled as composites.
It is possible to report the AVE for constructs modeled as composites by setting
.only_common_factors = FALSE, however, result should be interpreted with caution
as they may not have a conceptual meaning. Calculation is done
by calculateAVE().
- Congeneric reliability; "rho_C", "rho_C_mm", "rho_C_weighted", "rho_C_weighted_mm"
An estimate of the reliability assuming a congeneric measurement model (i.e., loadings are
allowed to differ) and a test score (proxy) based on unit weights.
There are four different versions implemented. See the
Methods and Formulae section
of the Postestimation: Assessing a model
article on the
cSEM website for details.
Alternative but synonemmous names for "rho_C" are:
composite reliability, construct reliablity, reliability coefficient,
Joereskog's rho, coefficient omega, or Dillon-Goldstein's rho.
For "rho_C_weighted": (Dijkstra-Henselers) rhoA. rho_C_mm and rho_C_weighted_mm
have no corresponding names. The former uses unit weights scaled by (w'Sw)^(-1/2) and
the latter weights scaled by (w'Sigma_hat w)^(-1/2) where Sigma_hat is
the model-implied indicator correlation matrix.
The Congeneric reliability is inherently
tied to the common factor model. It is therefore unclear how to meaningfully
interpret congeneric reliability estimates for constructs modeled as composites.
It is possible to report the congeneric reliability for constructs modeled as
composites by setting .only_common_factors = FALSE, however, result should be
interpreted with caution as they may not have a conceptual meaning.
Calculation is done by calculateRhoC().
- Distance measures; "dg", "dl", "dml"
Measures of the distance
between the model-implied and the empirical indicator correlation matrix.
Currently, the geodesic distance ("dg"), the squared Euclidian distance
("dl") and the the maximum likelihood-based distance function are implemented
("dml"). Calculation is done by calculateDL(), calculateDG(),
and calculateDML().
- Degrees of freedom, "df"
Returns the degrees of freedom. Calculation is done by calculateDf().
- Effects; "effects"
Total and indirect effect estimates. Additionally,
the variance accounted for (VAF) is computed. The VAF is defined as the ratio of a variables
indirect effect to its total effect. Calculation is done
by calculateEffects().
- Effect size; "f2"
An index of the effect size of an independent
variable in a structural regression equation. This measure is commonly
known as Cohen's f^2. The effect size of the k'th
independent variable in this case
is definied as the ratio (R2_included - R2_excluded)/(1 - R2_included), where
R2_included and R2_excluded are the R squares of the
original structural model regression equation (R2_included) and the
alternative specification with the k'th variable dropped (R2_excluded).
Calculation is done by calculatef2().
- Fit indices; "chi_square", "chi_square_df", "cfi", "cn", "gfi", "ifi", "nfi",
"nnfi", "rmsea", "rms_theta", "srmr"
Several absolute and incremental fit indices. Note that their suitability
for models containing constructs modeled as composites is still an
open research question. Also note that fit indices are not tests in a
hypothesis testing sense and
decisions based on common one-size-fits-all cut-offs proposed in the literature
suffer from serious statistical drawbacks. Calculation is done by calculateChiSquare(),
calculateChiSquareDf(), calculateCFI(),
calculateGFI(), calculateIFI(), calculateNFI(), calculateNNFI(),
calculateRMSEA(), calculateRMSTheta() and calculateSRMR().
- Fornell-Larcker criterion; "fl_criterion"
A rule suggested by Fornell1981;textualcSEM
to assess discriminant validity. The Fornell-Larcker
criterion is a decision rule based on a comparison between the squared
construct correlations and the average variance extracted. FL returns
a matrix with the squared construct correlations on the off-diagonal and
the AVE's on the main diagonal. Calculation is done by calculateFLCriterion().
- Goodness of Fit (GoF); "gof"
The GoF is defined as the square root
of the mean of the R squares of the structural model times the mean
of the variances in the indicators that are explained by their
related constructs (i.e., the average over all lambda^2_k).
For the latter, only constructs modeled as common factors are considered
as they explain their indicator variance in contrast to a composite where
indicators actually build the construct.
Note that, contrary to what the name suggests, the GoF is not a
measure of model fit in a Chi-square fit test sense. Calculation is done
by calculateGoF().
- Heterotrait-monotrait ratio of correlations (HTMT); "htmt"
An estimate of the correlation between latent variables. The HTMT is used
to assess convergent and/or discriminant validity of a construct.
The HTMT is inherently tied to the common factor model. If the model contains
less than two constructs modeled as common factors and
.only_common_factors = TRUE, NA is returned.
It is possible to report the HTMT for constructs modeled as
composites by setting .only_common_factors = FALSE, however, result should be
interpreted with caution as they may not have a conceptual meaning.
Calculation is done by calculateHTMT().
- Model selection criteria: "aic", "aicc", "aicu", "bic", "fpe", "gm",
"hq", "hqc", "mallows_cp"
Several model selection criteria as suggested by Sharma2019;textualcSEM
in the context of PLS. See: calculateModelSelectionCriteria() for details.
- Reliability: "reliability"
As described in the Methods and Formulae
section of the Postestimation: Assessing a model
article on the cSEM website
there are many different estimators for the (internal consistency) reliability.
Choosing .quality_criterion = "reliability" computes the three most common
measures, namely: "Cronbachs alpha" (identical to "rho_T"), "J<U+00F6>reskogs rho" (identical to "rho_C_mm"),
and "Dijkstra-Henselers rho A" (identical to "rho_C_weighted_mm").
Reliability is inherently
tied to the common factor model. It is therefore unclear how to meaningfully
interpret reliability estimates for constructs modeled as composites.
It is possible to report the three common reliability estimates for constructs modeled as
composites by setting .only_common_factors = FALSE, however, result should be
interpreted with caution as they may not have a conceptual meaning.
- R square and R square adjusted; "r2", "r2_adj"
The R square and the adjusted
R square for each structural regression equation.
Calculated when running csem().
- Tau-equivalent reliability; "rho_T"
An estimate of the
reliability assuming a tau-equivalent measurement model (i.e. a measurement
model with equal loadings) and a test score (proxy) based on unit weights.
Tau-equivalent reliability is the preferred name for reliability estimates
that assume a tau-equivalent measurement model such as Cronbach's alpha.
The tau-equivalent
reliability (Cronbach's alpha) is inherently
tied to the common factor model. It is therefore unclear how to meaningfully
interpret tau-equivalent
reliability estimates for constructs modeled as composites.
It is possible to report tau-equivalent
reliability estimates for constructs modeled as
composites by setting .only_common_factors = FALSE, however, result should be
interpreted with caution as they may not have a conceptual meaning.
Calculation is done by calculateRhoT().
- Variance inflation factors (VIF); "vif"
An index for the amount of (multi-)
collinearity between independent variables of a regression equation. Computed
for each structural equation. Practically, VIF_k is defined
as the ratio of 1 over (1 - R2_k) where R2_k is the R squared from a regression
of the k'th independent variable on all remaining independent variables.
Calculated when running csem().
- Variance inflation factors for PLS-PM mode B (VIF-ModeB); "vifmodeB"
An index for
the amount of (multi-) collinearity between independent variables (indicators) in
mode B regression equations. Computed only if .object was obtained using
.weight_approach = "PLS-PM" and at least one mode was mode B.
Practically, VIF-ModeB_k is defined as the ratio of 1 over (1 - R2_k) where
R2_k is the R squared from a regression of the k'th indicator of block j on
all remaining indicators of the same block.
Calculation is done by calculateVIFModeB().
Some of the quality criteria are inherently tied to the classical common
factor model and therefore only meaningfully interpreted within a common
factor model (see the
Postestimation: Assessing a model
article for details).
It is possible to force computation of all quality criteria for constructs
modeled as composites by setting .only_common_factors = FALSE, however,
we explicitly warn to interpret quality criteria in analogy to the common factor
model in this case, as the interpretation often does not carry over to composite models.
To resample a given quality criterion supply the name of the function
that calculates the desired quality criterion to csem()'s .user_funs argument.
See resamplecSEMResults() for details.