csem: Composite-based SEM
In cSEM: Composite-Based Structural Equation Modeling
csem R Documentation
Composite-based SEM
Description
\lifecyclestable
Usage
csem(
.data = NULL,
.model = NULL,
.approach_2ndorder = c("2stage", "mixed"),
.approach_cor_robust = c("none", "mcd", "spearman"),
.approach_nl = c("sequential", "replace"),
.approach_paths = c("OLS", "2SLS"),
.approach_weights = c("PLS-PM", "SUMCORR", "MAXVAR", "SSQCORR",
"MINVAR", "GENVAR","GSCA", "PCA",
"unit", "bartlett", "regression"),
.conv_criterion = c("diff_absolute", "diff_squared", "diff_relative"),
.disattenuate = TRUE,
.dominant_indicators = NULL,
.estimate_structural = TRUE,
.id = NULL,
.instruments = NULL,
.iter_max = 100,
.normality = FALSE,
.PLS_approach_cf = c("dist_squared_euclid", "dist_euclid_weighted",
"fisher_transformed", "mean_arithmetic",
"mean_geometric", "mean_harmonic",
"geo_of_harmonic"),
.PLS_ignore_structural_model = FALSE,
.PLS_modes = NULL,
.PLS_weight_scheme_inner = c("path", "centroid", "factorial"),
.reliabilities = NULL,
.starting_values = NULL,
.resample_method = c("none", "bootstrap", "jackknife"),
.resample_method2 = c("none", "bootstrap", "jackknife"),
.R = 499,
.R2 = 199,
.handle_inadmissibles = c("drop", "ignore", "replace"),
.user_funs = NULL,
.eval_plan = c("sequential", "multicore", "multisession"),
.seed = NULL,
.sign_change_option = c("none", "individual", "individual_reestimate",
"construct_reestimate"),
.tolerance = 1e-05
)
Arguments
.data
A data.frame or a matrix of standardized or unstandardized
data (indicators/items/manifest variables).
Additionally, a list of data sets (data frames or matrices) is accepted in which
case estimation is repeated for each data set. Possible column types or classes
of the data provided are: "logical", "numeric" ("double" or "integer"),
"factor" ("ordered" and/or "unordered"), "character" (will be converted to factor),
or a mix of several types.
.model
A model in lavaan model syntax
or a cSEMModel list.
.approach_2ndorder
Character string. Approach used for models containing
second-order constructs. One of: "2stage", or "mixed". Defaults to "2stage".
.approach_cor_robust
Character string. Approach used to obtain a robust
indicator correlation matrix. One of: "none" in which case the standard
Bravais-Pearson correlation is used,
"spearman" for the Spearman rank correlation, or
"mcd" via MASS::cov.rob() for a robust correlation matrix.
Defaults to "none". Note that many postestimation procedures (such as
testOMF() or fit() implicitly assume a continuous
indicator correlation matrix (e.g. Bravais-Pearson correlation matrix).
Only use if you know what you are doing.
.approach_nl
Character string. Approach used to estimate nonlinear
structural relationships. One of: "sequential" or "replace".
Defaults to "sequential".
.approach_paths
Character string. Approach used to estimate the
structural coefficients. One of: "OLS" or "2SLS". If "2SLS", instruments
need to be supplied to .instruments. Defaults to "OLS".
.approach_weights
Character string. Approach used to
obtain composite weights. One of: "PLS-PM", "SUMCORR", "MAXVAR",
"SSQCORR", "MINVAR", "GENVAR", "GSCA", "PCA", "unit", "bartlett",
or "regression". Defaults to "PLS-PM".
.conv_criterion
Character string. The criterion to use for the convergence check.
One of: "diff_absolute", "diff_squared", or "diff_relative". Defaults
to "diff_absolute".
.disattenuate
Logical. Should composite/proxy correlations
be disattenuated to yield consistent loadings and path estimates if at least
one of the construct is modeled as a common factor? Defaults to TRUE.
.dominant_indicators
A character vector of "construct_name" = "indicator_name" pairs,
where "indicator_name" is a character string giving the name of the dominant indicator
and "construct_name" a character string of the corresponding construct name.
Dominant indicators may be specified for a subset of the constructs.
Default to NULL.
.estimate_structural
Logical. Should the structural coefficients
be estimated? Defaults to TRUE.
.id
Character string or integer. A character string giving the name or
an integer of the position of the column of .data whose levels are used
to split .data into groups. Defaults to NULL.
.instruments
A named list of vectors of instruments. The names
of the list elements are the names of the dependent (LHS) constructs of the structural
equation whose explanatory variables are endogenous. The vectors
contain the names of the instruments corresponding to each equation. Note
that exogenous variables of a given equation must be supplied as
instruments for themselves. Defaults to NULL.
.iter_max
Integer. The maximum number of iterations allowed.
If iter_max = 1 and .approach_weights = "PLS-PM" one-step weights are returned.
If the algorithm exceeds the specified number, weights of iteration step
.iter_max - 1 will be returned with a warning. Defaults to 100.
.normality
Logical. Should joint normality of
[η_(1:p); ζ; ε]
be assumed in the nonlinear model? See \insertCiteDijkstra2014cSEM for details.
Defaults to FALSE. Ignored if the model is not nonlinear.
.PLS_approach_cf
Character string. Approach used to obtain the correction
factors for PLSc. One of: "dist_squared_euclid", "dist_euclid_weighted",
"fisher_transformed", "mean_arithmetic", "mean_geometric", "mean_harmonic",
"geo_of_harmonic". Defaults to "dist_squared_euclid".
Ignored if .disattenuate = FALSE or if .approach_weights is not PLS-PM.
.PLS_ignore_structural_model
Logical. Should the structural model be ignored
when calculating the inner weights of the PLS-PM algorithm? Defaults to FALSE.
Ignored if .approach_weights is not PLS-PM.
.PLS_modes
Either a named list specifying the mode that should be used for
each construct in the form "construct_name" = mode, a single character
string giving the mode that should be used for all constructs, or NULL.
Possible choices for mode are: "modeA", "modeB", "modeBNNLS",
"unit", "PCA", a single integer or
a vector of fixed weights of the same length as there are indicators for the
construct given by "construct_name". If only a single number is provided this is identical to
using unit weights, as weights are rescaled such that the related composite
has unit variance. Defaults to NULL.
If NULL the appropriate mode according to the type
of construct used is chosen. Ignored if .approach_weight is not PLS-PM.
.PLS_weight_scheme_inner
Character string. The inner weighting scheme
used by PLS-PM. One of: "centroid", "factorial", or "path".
Defaults to "path". Ignored if .approach_weight is not PLS-PM.
.reliabilities
A character vector of "name" = value pairs,
where value is a number between 0 and 1 and "name" a character string
of the corresponding construct name, or NULL. Reliabilities
may be given for a subset of the constructs. Defaults to NULL in which case
reliabilities are estimated by csem(). Currently, only supported for
.approach_weights = "PLS-PM".
.starting_values
A named list of vectors where the
list names are the construct names whose indicator weights the user
wishes to set. The vectors must be named vectors of "indicator_name" = value
pairs, where value is the (scaled or unscaled) starting weight. Defaults to NULL.
.resample_method
Character string. The resampling method to use. One of:
"none", "bootstrap" or "jackknife". Defaults to "none".
.resample_method2
Character string. The resampling method to use when resampling
from a resample. One of: "none", "bootstrap" or "jackknife". For
"bootstrap" the number of draws is provided via .R2. Currently,
resampling from each resample is only required for the studentized confidence
interval ("CI_t_interval") computed by the infer() function. Defaults to "none".
.R
Integer. The number of bootstrap replications. Defaults to 499.
.R2
Integer. The number of bootstrap replications to use when
resampling from a resample. Defaults to 199.
.handle_inadmissibles
Character string. How should inadmissible results
be treated? One of "drop", "ignore", or "replace". If "drop", all
replications/resamples yielding an inadmissible result will be dropped
(i.e. the number of results returned will potentially be less than .R).
For "ignore" all results are returned even if all or some of the replications
yielded inadmissible results (i.e. number of results returned is equal to .R).
For "replace" resampling continues until there are exactly .R admissible solutions.
Depending on the frequency of inadmissible solutions this may significantly increase
computing time. Defaults to "drop".
.user_funs
A function or a (named) list of functions to apply to every
resample. The functions must take .object as its first argument (e.g.,
myFun <- function(.object, ...) {body-of-the-function}).
Function output should preferably be a (named)
vector but matrices are also accepted. However, the output will be
vectorized (columnwise) in this case. See the examples section for details.
.eval_plan
Character string. The evaluation plan to use. One of
"sequential", "multicore", or "multisession". In the two latter cases
all available cores will be used. Defaults to "sequential".
.seed
Integer or NULL. The random seed to use. Defaults to NULL in which
case an arbitrary seed is chosen. Note that the scope of the seed is limited
to the body of the function it is used in. Hence, the global seed will
not be altered!
.sign_change_option
Character string. Which sign change option should
be used to handle flipping signs when resampling? One of "none","individual",
"individual_reestimate", "construct_reestimate". Defaults to "none".
.tolerance
Double. The tolerance criterion for convergence.
Defaults to 1e-05.
Details
Estimate linear, nonlinear, hierarchical or multigroup structural equation
models using a composite-based approach. In cSEM
any method or approach that involves linear compounds (scores/proxies/composites)
of observables (indicators/items/manifest variables) is defined as composite-based.
See the Get started
section of the cSEM website
for a general introduction to composite-based SEM and cSEM.
csem() estimates linear, nonlinear, hierarchical or multigroup structural
equation models using a composite-based approach.
Data and model:
The .data and .model arguments are required. .data must be given
a matrix or a data.frame with column names matching
the indicator names used in the model description. Alternatively,
a list of data sets (matrices or data frames) may be provided
in which case estimation is repeated for each data set.
Possible column types/classes of the data provided are: "logical",
"numeric" ("double" or "integer"), "factor" ("ordered" and/or "unordered"),
"character", or a mix of several types. Character columns will be treated
as (unordered) factors.
Depending on the type/class of the indicator data provided cSEM computes the indicator
correlation matrix in different ways. See calculateIndicatorCor() for details.
In the current version .data must not contain missing values. Future versions
are likely to handle missing values as well.
To provide a model use the lavaan model syntax.
Note, however, that cSEM currently only supports the "standard" lavaan
model syntax (Types 1, 2, 3, and 7 as described on the help page).
Therefore, specifying e.g., a threshold or scaling factors is ignored.
Alternatively, a standardized (possibly incomplete) cSEMModel-list may be supplied.
See parseModel() for details.
Weights and path coefficients:
By default weights are estimated using the partial least squares path modeling
algorithm ("PLS-PM").
A range of alternative weighting algorithms may be supplied to
.approach_weights. Currently, the following approaches are implemented
(Default) Partial least squares path modeling ("PLS-PM"). The algorithm
can be customized. See calculateWeightsPLS() for details.
Generalized structured component analysis ("GSCA") and generalized
structured component analysis with uniqueness terms (GSCAm). The algorithms
can be customized. See calculateWeightsGSCA() and calculateWeightsGSCAm() for details.
Note that GSCAm is called indirectly when the model contains constructs
modeled as common factors only and .disattenuate = TRUE. See below.
Generalized canonical correlation analysis (GCCA), including
"SUMCORR", "MAXVAR", "SSQCORR", "MINVAR", "GENVAR".
Principal component analysis ("PCA")
Factor score regression using sum scores ("unit"),
regression ("regression") or bartlett scores ("bartlett")
It is possible to supply starting values for the weighting algorithm
via .starting_values. The argument accepts a named list of vectors where the
list names are the construct names whose indicator weights the user
wishes to set. The vectors must be named vectors of "indicator_name" = value
pairs, where value is the starting weight. See the examples section below for details.
Composite-indicator and composite-composite correlations are properly
disattenuated by default to yield consistent loadings, construct correlations,
and path coefficients if any of the concepts are modeled as a
common factor.
For PLS-PM disattenuation is done using PLSc \insertCiteDijkstra2015cSEM.
For GSCA disattenuation is done implicitly by using GSCAm \insertCiteHwang2017cSEM.
Weights obtained by GCCA, unit, regression, bartlett or PCA are
disattenuated using Croon's approach \insertCiteCroon2002cSEM.
Disattenuation my be suppressed by setting .disattenuate = FALSE.
Note, however, that quantities in this case are inconsistent
estimates for their construct level counterparts if any of the constructs in
the structural model are modeled as a common factor!
By default path coefficients are estimated using ordinary least squares (.approach_path = "OLS").
For linear models, two-stage least squares ("2SLS") is available, however, only if
instruments are internal, i.e., part of the structural model. Future versions
will add support for external instruments if possible. Instruments must be supplied to
.instruments as a named list where the names
of the list elements are the names of the dependent constructs of the structural
equations whose explanatory variables are believed to be endogenous.
The list consists of vectors of names of instruments corresponding to each equation.
Note that exogenous variables of a given equation must be supplied as
instruments for themselves.
If reliabilities are known they can be supplied as "name" = value pairs to
.reliabilities, where value is a numeric value between 0 and 1.
Currently, only supported for "PLS-PM".
Nonlinear models:
If the model contains nonlinear terms csem() estimates a polynomial structural equation model
using a non-iterative method of moments approach described in
\insertCiteDijkstra2014;textualcSEM. Nonlinear terms include interactions and
exponential terms. The latter is described in model syntax as an
"interaction with itself", e.g., xi^3 = xi.xi.xi. Currently only exponential
terms up to a power of three (e.g., three-way interactions or cubic terms) are allowed:
- Single, e.g., eta1
- Quadratic, e.g., eta1.eta1
- Cubic, e.g., eta1.eta1.eta1
- Two-way interaction, e.g., eta1.eta2
- Three-way interaction, e.g., eta1.eta2.eta3
- Quadratic and two-way interaction, e.g., eta1.eta1.eta3
The current version of the package allows two kinds of estimation:
estimation of the reduced form equation (.approach_nl = "replace") and
sequential estimation (.approach_nl = "sequential", the default). The latter does not
allow for multivariate normality of all exogenous variables, i.e.,
the latent variables and the error terms.
Distributional assumptions are kept to a minimum (an i.i.d. sample from a
population with finite moments for the relevant order); for higher order models,
that go beyond interaction, we work in this version with the assumption that
as far as the relevant moments are concerned certain combinations of
measurement errors behave as if they were Gaussian.
For details see: \insertCiteDijkstra2014;textualcSEM.
Models containing second-order constructs
Second-order constructs are specified using the operators =~ and <~. These
operators are usually used with indicators on their right-hand side. For
second-order constructs the right-hand side variables are constructs instead.
If c1, and c2 are constructs forming or measuring a higher-order
construct, a model would look like this:
my_model <- "
# Structural model
SAT ~ QUAL
VAL ~ SAT
# Measurement/composite model
QUAL =~ qual1 + qual2
SAT =~ sat1 + sat2
c1 =~ x11 + x12
c2 =~ x21 + x22
# Second-order construct (in this case a second-order composite build by common
# factors)
VAL <~ c1 + c2
"
Currently, two approaches are explicitly implemented:
(Default) "2stage". The (disjoint) two-stage approach as proposed by \insertCiteAgarwal2000;textualcSEM.
Note that by default a correction for attenuation is applied if common factors are
involved in modeling second-order constructs. For instance, the three-stage approach
proposed by \insertCiteVanRiel2017;textualcSEM is applied in case of a second-order construct specified as a
composite of common factors. On the other hand, if no common factors are involved the two-stage approach
is applied as proposed by \insertCiteSchuberth2020;textualcSEM.
"mixed". The mixed repeated indicators/two-stage approach as proposed by \insertCiteRingle2012;textualcSEM.
The repeated indicators approach as proposed by \insertCiteJoereskog1982b;textualcSEM
and the extension proposed by \insertCiteBecker2012;textualcSEM are
not directly implemented as they simply require a respecification of the model.
In the above example the repeated indicators approach
would require to change the model and to append the repeated indicators to
the data supplied to .data. Note that the indicators need to be renamed in this case as
csem() does not allow for one indicator to be attached to multiple constructs.
my_model <- "
# Structural model
SAT ~ QUAL
VAL ~ SAT
VAL ~ c1 + c2
# Measurement/composite model
QUAL =~ qual1 + qual2
SAT =~ sat1 + sat2
VAL =~ x11_temp + x12_temp + x21_temp + x22_temp
c1 =~ x11 + x12
c2 =~ x21 + x22
"
According to the extended approach indirect effects of QUAL on VAL via c1
and c2 would have to be specified as well.
Multigroup analysis
To perform a multigroup analysis provide either a list of data sets or one
data set containing a group-identifier-column whose column
name must be provided to .id. Values of this column are taken as levels of a
factor and are interpreted as group
identifiers. csem() will split the data by levels of that column and run
the estimation for each level separately. Note, the more levels
the group-identifier-column has, the more estimation runs are required.
This can considerably slow down estimation, especially if resampling is
requested. For the latter it will generally be faster to use
.eval_plan = "multisession" or .eval_plan = "multicore".
Inference:
Inference is done via resampling. See resamplecSEMResults() and infer() for details.
Value
An object of class cSEMResults with methods for all postestimation generics.
Technically, a call to csem() results in an object with at least
two class attributes. The first class attribute is always cSEMResults.
The second is one of cSEMResults_default, cSEMResults_multi, or
cSEMResults_2ndorder and depends on the estimated model and/or the type of
data provided to the .model and .data arguments. The third class attribute
cSEMResults_resampled is only added if resampling was conducted.
For a details see the cSEMResults helpfile .
Postestimation
assess()Assess results using common quality criteria, e.g., reliability,
fit measures, HTMT, R2 etc.
infer()Calculate common inferential quantities, e.g., standard errors,
confidence intervals.
predict()Predict endogenous indicator scores and compute common prediction metrics.
summarize()Summarize the results. Mainly called for its side-effect the print method.
verify()Verify/Check admissibility of the estimates.
Tests are performed using the test-family of functions. Currently the following
tests are implemented:
testOMF()Bootstrap-based test for overall model fit based on
\insertCiteBeran1985;textualcSEM
testMICOM()Permutation-based test for measurement invariance of composites
proposed by \insertCiteHenseler2016;textualcSEM
testMGD()Several (mainly) permutation-based tests for multi-group comparisons.
testHausman()Regression-based Hausman test to test for endogeneity.
Other miscellaneous postestimation functions belong do the do-family of functions.
Currently three do functions are implemented:
doIPMA()Performs an importance-performance matrix analyis (IPMA).
doNonlinearEffectsAnalysis()Perform a nonlinear effects analysis as
described in e.g.,
\insertCiteSpiller2013;textualcSEM
doRedundancyAnalysis()Perform a redundancy analysis (RA) as proposed by
\insertCiteHair2016;textualcSEM with reference to \insertCiteChin1998;textualcSEM
References
\insertAllCited
See Also
args_default(), cSEMArguments, cSEMResults, foreman(), resamplecSEMResults(),
assess(), infer(), predict(), summarize(), verify(), testOMF(),
testMGD(), testMICOM(), testHausman()
Examples
# ===========================================================================
# Basic usage
# ===========================================================================
### Linear model ------------------------------------------------------------
# Most basic usage requires a dataset and a model. We use the
# `threecommonfactors` dataset.
## Take a look at the dataset
#?threecommonfactors
## Specify the (correct) model
model <- "
# Structural model
eta2 ~ eta1
eta3 ~ eta1 + eta2
# (Reflective) measurement model
eta1 =~ y11 + y12 + y13
eta2 =~ y21 + y22 + y23
eta3 =~ y31 + y32 + y33
"
## Estimate
res <- csem(threecommonfactors, model)
## Postestimation
verify(res)
summarize(res)
assess(res)
# Notes:
# 1. By default no inferential quantities (e.g. Std. errors, p-values, or
# confidence intervals) are calculated. Use resampling to obtain
# inferential quantities. See "Resampling" in the "Extended usage"
# section below.
# 2. `summarize()` prints the full output by default. For a more condensed
# output use:
print(summarize(res), .full_output = FALSE)
## Dealing with endogeneity -------------------------------------------------
# See: ?testHausman()
### Models containing second constructs--------------------------------------
## Take a look at the dataset
#?dgp_2ndorder_cf_of_c
model <- "
# Path model / Regressions
c4 ~ eta1
eta2 ~ eta1 + c4
# Reflective measurement model
c1 <~ y11 + y12
c2 <~ y21 + y22 + y23 + y24
c3 <~ y31 + y32 + y33 + y34 + y35 + y36 + y37 + y38
eta1 =~ y41 + y42 + y43
eta2 =~ y51 + y52 + y53
# Composite model (second order)
c4 =~ c1 + c2 + c3
"
res_2stage <- csem(dgp_2ndorder_cf_of_c, model, .approach_2ndorder = "2stage")
res_mixed <- csem(dgp_2ndorder_cf_of_c, model, .approach_2ndorder = "mixed")
# The standard repeated indicators approach is done by 1.) respecifying the model
# and 2.) adding the repeated indicators to the data set
# 1.) Respecify the model
model_RI <- "
# Path model / Regressions
c4 ~ eta1
eta2 ~ eta1 + c4
c4 ~ c1 + c2 + c3
# Reflective measurement model
c1 <~ y11 + y12
c2 <~ y21 + y22 + y23 + y24
c3 <~ y31 + y32 + y33 + y34 + y35 + y36 + y37 + y38
eta1 =~ y41 + y42 + y43
eta2 =~ y51 + y52 + y53
# c4 is a common factor measured by composites
c4 =~ y11_temp + y12_temp + y21_temp + y22_temp + y23_temp + y24_temp +
y31_temp + y32_temp + y33_temp + y34_temp + y35_temp + y36_temp +
y37_temp + y38_temp
"
# 2.) Update data set
data_RI <- dgp_2ndorder_cf_of_c
coln <- c(colnames(data_RI), paste0(colnames(data_RI), "_temp"))
data_RI <- data_RI[, c(1:ncol(data_RI), 1:ncol(data_RI))]
colnames(data_RI) <- coln
# Estimate
res_RI <- csem(data_RI, model_RI)
summarize(res_RI)
### Multigroup analysis -----------------------------------------------------
# See: ?testMGD()
# ===========================================================================
# Extended usage
# ===========================================================================
# `csem()` provides defaults for all arguments except `.data` and `.model`.
# Below some common options/tasks that users are likely to be interested in.
# We use the threecommonfactors data set again:
model <- "
# Structural model
eta2 ~ eta1
eta3 ~ eta1 + eta2
# (Reflective) measurement model
eta1 =~ y11 + y12 + y13
eta2 =~ y21 + y22 + y23
eta3 =~ y31 + y32 + y33
"
### PLS vs PLSc and disattenuation
# In the model all concepts are modeled as common factors. If
# .approach_weights = "PLS-PM", csem() uses PLSc to disattenuate composite-indicator
# and composite-composite correlations.
res_plsc <- csem(threecommonfactors, model, .approach_weights = "PLS-PM")
res$Information$Model$construct_type # all common factors
# To obtain "original" (inconsistent) PLS estimates use `.disattenuate = FALSE`
res_pls <- csem(threecommonfactors, model,
.approach_weights = "PLS-PM",
.disattenuate = FALSE
)
s_plsc <- summarize(res_plsc)
s_pls <- summarize(res_pls)
# Compare
data.frame(
"Path" = s_plsc$Estimates$Path_estimates$Name,
"Pop_value" = c(0.6, 0.4, 0.35), # see ?threecommonfactors
"PLSc" = s_plsc$Estimates$Path_estimates$Estimate,
"PLS" = s_pls$Estimates$Path_estimates$Estimate
)
### Resampling --------------------------------------------------------------
## Not run:
## Basic resampling
res_boot <- csem(threecommonfactors, model, .resample_method = "bootstrap")
res_jack <- csem(threecommonfactors, model, .resample_method = "jackknife")
# See ?resamplecSEMResults for more examples
### Choosing a different weightning scheme ----------------------------------
res_gscam <- csem(threecommonfactors, model, .approach_weights = "GSCA")
res_gsca <- csem(threecommonfactors, model,
.approach_weights = "GSCA",
.disattenuate = FALSE
)
s_gscam <- summarize(res_gscam)
s_gsca <- summarize(res_gsca)
# Compare
data.frame(
"Path" = s_gscam$Estimates$Path_estimates$Name,
"Pop_value" = c(0.6, 0.4, 0.35), # see ?threecommonfactors
"GSCAm" = s_gscam$Estimates$Path_estimates$Estimate,
"GSCA" = s_gsca$Estimates$Path_estimates$Estimate
)
## End(Not run)
### Fine-tuning a weighting scheme ------------------------------------------
## Setting starting values
sv <- list("eta1" = c("y12" = 10, "y13" = 4, "y11" = 1))
res <- csem(threecommonfactors, model, .starting_values = sv)
## Choosing a different inner weighting scheme
#?args_csem_dotdotdot
res <- csem(threecommonfactors, model, .PLS_weight_scheme_inner = "factorial",
.PLS_ignore_structural_model = TRUE)
## Choosing different modes for PLS
# By default, concepts modeled as common factors uses PLS Mode A weights.
modes <- list("eta1" = "unit", "eta2" = "modeB", "eta3" = "unit")
res <- csem(threecommonfactors, model, .PLS_modes = modes)
summarize(res)
cSEM documentation built on Nov. 25, 2022, 1:05 a.m.
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| csem | R Documentation |
Composite-based SEM
Description
\lifecyclestable
Usage
csem(
.data = NULL,
.model = NULL,
.approach_2ndorder = c("2stage", "mixed"),
.approach_cor_robust = c("none", "mcd", "spearman"),
.approach_nl = c("sequential", "replace"),
.approach_paths = c("OLS", "2SLS"),
.approach_weights = c("PLS-PM", "SUMCORR", "MAXVAR", "SSQCORR",
"MINVAR", "GENVAR","GSCA", "PCA",
"unit", "bartlett", "regression"),
.conv_criterion = c("diff_absolute", "diff_squared", "diff_relative"),
.disattenuate = TRUE,
.dominant_indicators = NULL,
.estimate_structural = TRUE,
.id = NULL,
.instruments = NULL,
.iter_max = 100,
.normality = FALSE,
.PLS_approach_cf = c("dist_squared_euclid", "dist_euclid_weighted",
"fisher_transformed", "mean_arithmetic",
"mean_geometric", "mean_harmonic",
"geo_of_harmonic"),
.PLS_ignore_structural_model = FALSE,
.PLS_modes = NULL,
.PLS_weight_scheme_inner = c("path", "centroid", "factorial"),
.reliabilities = NULL,
.starting_values = NULL,
.resample_method = c("none", "bootstrap", "jackknife"),
.resample_method2 = c("none", "bootstrap", "jackknife"),
.R = 499,
.R2 = 199,
.handle_inadmissibles = c("drop", "ignore", "replace"),
.user_funs = NULL,
.eval_plan = c("sequential", "multicore", "multisession"),
.seed = NULL,
.sign_change_option = c("none", "individual", "individual_reestimate",
"construct_reestimate"),
.tolerance = 1e-05
)
Arguments
.data |
A |
.model |
A model in lavaan model syntax or a cSEMModel list. |
.approach_2ndorder |
Character string. Approach used for models containing second-order constructs. One of: "2stage", or "mixed". Defaults to "2stage". |
.approach_cor_robust |
Character string. Approach used to obtain a robust
indicator correlation matrix. One of: "none" in which case the standard
Bravais-Pearson correlation is used,
"spearman" for the Spearman rank correlation, or
"mcd" via |
.approach_nl |
Character string. Approach used to estimate nonlinear structural relationships. One of: "sequential" or "replace". Defaults to "sequential". |
.approach_paths |
Character string. Approach used to estimate the
structural coefficients. One of: "OLS" or "2SLS". If "2SLS", instruments
need to be supplied to |
.approach_weights |
Character string. Approach used to obtain composite weights. One of: "PLS-PM", "SUMCORR", "MAXVAR", "SSQCORR", "MINVAR", "GENVAR", "GSCA", "PCA", "unit", "bartlett", or "regression". Defaults to "PLS-PM". |
.conv_criterion |
Character string. The criterion to use for the convergence check. One of: "diff_absolute", "diff_squared", or "diff_relative". Defaults to "diff_absolute". |
.disattenuate |
Logical. Should composite/proxy correlations
be disattenuated to yield consistent loadings and path estimates if at least
one of the construct is modeled as a common factor? Defaults to |
.dominant_indicators |
A character vector of |
.estimate_structural |
Logical. Should the structural coefficients
be estimated? Defaults to |
.id |
Character string or integer. A character string giving the name or
an integer of the position of the column of |
.instruments |
A named list of vectors of instruments. The names
of the list elements are the names of the dependent (LHS) constructs of the structural
equation whose explanatory variables are endogenous. The vectors
contain the names of the instruments corresponding to each equation. Note
that exogenous variables of a given equation must be supplied as
instruments for themselves. Defaults to |
.iter_max |
Integer. The maximum number of iterations allowed.
If |
.normality |
Logical. Should joint normality of
[η_(1:p); ζ; ε]
be assumed in the nonlinear model? See \insertCiteDijkstra2014cSEM for details.
Defaults to |
.PLS_approach_cf |
Character string. Approach used to obtain the correction
factors for PLSc. One of: "dist_squared_euclid", "dist_euclid_weighted",
"fisher_transformed", "mean_arithmetic", "mean_geometric", "mean_harmonic",
"geo_of_harmonic". Defaults to "dist_squared_euclid".
Ignored if |
.PLS_ignore_structural_model |
Logical. Should the structural model be ignored
when calculating the inner weights of the PLS-PM algorithm? Defaults to |
.PLS_modes |
Either a named list specifying the mode that should be used for
each construct in the form |
.PLS_weight_scheme_inner |
Character string. The inner weighting scheme
used by PLS-PM. One of: "centroid", "factorial", or "path".
Defaults to "path". Ignored if |
.reliabilities |
A character vector of |
.starting_values |
A named list of vectors where the
list names are the construct names whose indicator weights the user
wishes to set. The vectors must be named vectors of |
.resample_method |
Character string. The resampling method to use. One of: "none", "bootstrap" or "jackknife". Defaults to "none". |
.resample_method2 |
Character string. The resampling method to use when resampling
from a resample. One of: "none", "bootstrap" or "jackknife". For
"bootstrap" the number of draws is provided via |
.R |
Integer. The number of bootstrap replications. Defaults to |
.R2 |
Integer. The number of bootstrap replications to use when
resampling from a resample. Defaults to |
.handle_inadmissibles |
Character string. How should inadmissible results
be treated? One of "drop", "ignore", or "replace". If "drop", all
replications/resamples yielding an inadmissible result will be dropped
(i.e. the number of results returned will potentially be less than |
.user_funs |
A function or a (named) list of functions to apply to every
resample. The functions must take |
.eval_plan |
Character string. The evaluation plan to use. One of "sequential", "multicore", or "multisession". In the two latter cases all available cores will be used. Defaults to "sequential". |
.seed |
Integer or |
.sign_change_option |
Character string. Which sign change option should be used to handle flipping signs when resampling? One of "none","individual", "individual_reestimate", "construct_reestimate". Defaults to "none". |
.tolerance |
Double. The tolerance criterion for convergence.
Defaults to |
Details
Estimate linear, nonlinear, hierarchical or multigroup structural equation models using a composite-based approach. In cSEM any method or approach that involves linear compounds (scores/proxies/composites) of observables (indicators/items/manifest variables) is defined as composite-based. See the Get started section of the cSEM website for a general introduction to composite-based SEM and cSEM.
csem() estimates linear, nonlinear, hierarchical or multigroup structural
equation models using a composite-based approach.
Data and model:
The .data and .model arguments are required. .data must be given
a matrix or a data.frame with column names matching
the indicator names used in the model description. Alternatively,
a list of data sets (matrices or data frames) may be provided
in which case estimation is repeated for each data set.
Possible column types/classes of the data provided are: "logical",
"numeric" ("double" or "integer"), "factor" ("ordered" and/or "unordered"),
"character", or a mix of several types. Character columns will be treated
as (unordered) factors.
Depending on the type/class of the indicator data provided cSEM computes the indicator
correlation matrix in different ways. See calculateIndicatorCor() for details.
In the current version .data must not contain missing values. Future versions
are likely to handle missing values as well.
To provide a model use the lavaan model syntax.
Note, however, that cSEM currently only supports the "standard" lavaan
model syntax (Types 1, 2, 3, and 7 as described on the help page).
Therefore, specifying e.g., a threshold or scaling factors is ignored.
Alternatively, a standardized (possibly incomplete) cSEMModel-list may be supplied.
See parseModel() for details.
Weights and path coefficients:
By default weights are estimated using the partial least squares path modeling
algorithm ("PLS-PM").
A range of alternative weighting algorithms may be supplied to
.approach_weights. Currently, the following approaches are implemented
(Default) Partial least squares path modeling (
"PLS-PM"). The algorithm can be customized. SeecalculateWeightsPLS()for details.Generalized structured component analysis (
"GSCA") and generalized structured component analysis with uniqueness terms (GSCAm). The algorithms can be customized. SeecalculateWeightsGSCA()andcalculateWeightsGSCAm()for details. Note that GSCAm is called indirectly when the model contains constructs modeled as common factors only and.disattenuate = TRUE. See below.Generalized canonical correlation analysis (GCCA), including
"SUMCORR","MAXVAR","SSQCORR","MINVAR","GENVAR".Principal component analysis (
"PCA")Factor score regression using sum scores (
"unit"), regression ("regression") or bartlett scores ("bartlett")
It is possible to supply starting values for the weighting algorithm
via .starting_values. The argument accepts a named list of vectors where the
list names are the construct names whose indicator weights the user
wishes to set. The vectors must be named vectors of "indicator_name" = value
pairs, where value is the starting weight. See the examples section below for details.
Composite-indicator and composite-composite correlations are properly disattenuated by default to yield consistent loadings, construct correlations, and path coefficients if any of the concepts are modeled as a common factor.
For PLS-PM disattenuation is done using PLSc \insertCiteDijkstra2015cSEM.
For GSCA disattenuation is done implicitly by using GSCAm \insertCiteHwang2017cSEM.
Weights obtained by GCCA, unit, regression, bartlett or PCA are
disattenuated using Croon's approach \insertCiteCroon2002cSEM.
Disattenuation my be suppressed by setting .disattenuate = FALSE.
Note, however, that quantities in this case are inconsistent
estimates for their construct level counterparts if any of the constructs in
the structural model are modeled as a common factor!
By default path coefficients are estimated using ordinary least squares (.approach_path = "OLS").
For linear models, two-stage least squares ("2SLS") is available, however, only if
instruments are internal, i.e., part of the structural model. Future versions
will add support for external instruments if possible. Instruments must be supplied to
.instruments as a named list where the names
of the list elements are the names of the dependent constructs of the structural
equations whose explanatory variables are believed to be endogenous.
The list consists of vectors of names of instruments corresponding to each equation.
Note that exogenous variables of a given equation must be supplied as
instruments for themselves.
If reliabilities are known they can be supplied as "name" = value pairs to
.reliabilities, where value is a numeric value between 0 and 1.
Currently, only supported for "PLS-PM".
Nonlinear models:
If the model contains nonlinear terms csem() estimates a polynomial structural equation model
using a non-iterative method of moments approach described in
\insertCiteDijkstra2014;textualcSEM. Nonlinear terms include interactions and
exponential terms. The latter is described in model syntax as an
"interaction with itself", e.g., xi^3 = xi.xi.xi. Currently only exponential
terms up to a power of three (e.g., three-way interactions or cubic terms) are allowed:
- Single, e.g.,
eta1- Quadratic, e.g.,
eta1.eta1- Cubic, e.g.,
eta1.eta1.eta1- Two-way interaction, e.g.,
eta1.eta2- Three-way interaction, e.g.,
eta1.eta2.eta3- Quadratic and two-way interaction, e.g.,
eta1.eta1.eta3
The current version of the package allows two kinds of estimation:
estimation of the reduced form equation (.approach_nl = "replace") and
sequential estimation (.approach_nl = "sequential", the default). The latter does not
allow for multivariate normality of all exogenous variables, i.e.,
the latent variables and the error terms.
Distributional assumptions are kept to a minimum (an i.i.d. sample from a population with finite moments for the relevant order); for higher order models, that go beyond interaction, we work in this version with the assumption that as far as the relevant moments are concerned certain combinations of measurement errors behave as if they were Gaussian. For details see: \insertCiteDijkstra2014;textualcSEM.
Models containing second-order constructs
Second-order constructs are specified using the operators =~ and <~. These
operators are usually used with indicators on their right-hand side. For
second-order constructs the right-hand side variables are constructs instead.
If c1, and c2 are constructs forming or measuring a higher-order
construct, a model would look like this:
my_model <- " # Structural model SAT ~ QUAL VAL ~ SAT # Measurement/composite model QUAL =~ qual1 + qual2 SAT =~ sat1 + sat2 c1 =~ x11 + x12 c2 =~ x21 + x22 # Second-order construct (in this case a second-order composite build by common # factors) VAL <~ c1 + c2 "
Currently, two approaches are explicitly implemented:
(Default)
"2stage". The (disjoint) two-stage approach as proposed by \insertCiteAgarwal2000;textualcSEM. Note that by default a correction for attenuation is applied if common factors are involved in modeling second-order constructs. For instance, the three-stage approach proposed by \insertCiteVanRiel2017;textualcSEM is applied in case of a second-order construct specified as a composite of common factors. On the other hand, if no common factors are involved the two-stage approach is applied as proposed by \insertCiteSchuberth2020;textualcSEM."mixed". The mixed repeated indicators/two-stage approach as proposed by \insertCiteRingle2012;textualcSEM.
The repeated indicators approach as proposed by \insertCiteJoereskog1982b;textualcSEM
and the extension proposed by \insertCiteBecker2012;textualcSEM are
not directly implemented as they simply require a respecification of the model.
In the above example the repeated indicators approach
would require to change the model and to append the repeated indicators to
the data supplied to .data. Note that the indicators need to be renamed in this case as
csem() does not allow for one indicator to be attached to multiple constructs.
my_model <- " # Structural model SAT ~ QUAL VAL ~ SAT VAL ~ c1 + c2 # Measurement/composite model QUAL =~ qual1 + qual2 SAT =~ sat1 + sat2 VAL =~ x11_temp + x12_temp + x21_temp + x22_temp c1 =~ x11 + x12 c2 =~ x21 + x22 "
According to the extended approach indirect effects of QUAL on VAL via c1
and c2 would have to be specified as well.
Multigroup analysis
To perform a multigroup analysis provide either a list of data sets or one
data set containing a group-identifier-column whose column
name must be provided to .id. Values of this column are taken as levels of a
factor and are interpreted as group
identifiers. csem() will split the data by levels of that column and run
the estimation for each level separately. Note, the more levels
the group-identifier-column has, the more estimation runs are required.
This can considerably slow down estimation, especially if resampling is
requested. For the latter it will generally be faster to use
.eval_plan = "multisession" or .eval_plan = "multicore".
Inference:
Inference is done via resampling. See resamplecSEMResults() and infer() for details.
Value
An object of class cSEMResults with methods for all postestimation generics.
Technically, a call to csem() results in an object with at least
two class attributes. The first class attribute is always cSEMResults.
The second is one of cSEMResults_default, cSEMResults_multi, or
cSEMResults_2ndorder and depends on the estimated model and/or the type of
data provided to the .model and .data arguments. The third class attribute
cSEMResults_resampled is only added if resampling was conducted.
For a details see the cSEMResults helpfile .
Postestimation
assess()Assess results using common quality criteria, e.g., reliability, fit measures, HTMT, R2 etc.
infer()Calculate common inferential quantities, e.g., standard errors, confidence intervals.
predict()Predict endogenous indicator scores and compute common prediction metrics.
summarize()Summarize the results. Mainly called for its side-effect the print method.
verify()Verify/Check admissibility of the estimates.
Tests are performed using the test-family of functions. Currently the following tests are implemented:
testOMF()Bootstrap-based test for overall model fit based on \insertCiteBeran1985;textualcSEM
testMICOM()Permutation-based test for measurement invariance of composites proposed by \insertCiteHenseler2016;textualcSEM
testMGD()Several (mainly) permutation-based tests for multi-group comparisons.
testHausman()Regression-based Hausman test to test for endogeneity.
Other miscellaneous postestimation functions belong do the do-family of functions. Currently three do functions are implemented:
doIPMA()Performs an importance-performance matrix analyis (IPMA).
doNonlinearEffectsAnalysis()Perform a nonlinear effects analysis as described in e.g., \insertCiteSpiller2013;textualcSEM
doRedundancyAnalysis()Perform a redundancy analysis (RA) as proposed by \insertCiteHair2016;textualcSEM with reference to \insertCiteChin1998;textualcSEM
References
\insertAllCitedSee Also
args_default(), cSEMArguments, cSEMResults, foreman(), resamplecSEMResults(),
assess(), infer(), predict(), summarize(), verify(), testOMF(),
testMGD(), testMICOM(), testHausman()
Examples
# ===========================================================================
# Basic usage
# ===========================================================================
### Linear model ------------------------------------------------------------
# Most basic usage requires a dataset and a model. We use the
# `threecommonfactors` dataset.
## Take a look at the dataset
#?threecommonfactors
## Specify the (correct) model
model <- "
# Structural model
eta2 ~ eta1
eta3 ~ eta1 + eta2
# (Reflective) measurement model
eta1 =~ y11 + y12 + y13
eta2 =~ y21 + y22 + y23
eta3 =~ y31 + y32 + y33
"
## Estimate
res <- csem(threecommonfactors, model)
## Postestimation
verify(res)
summarize(res)
assess(res)
# Notes:
# 1. By default no inferential quantities (e.g. Std. errors, p-values, or
# confidence intervals) are calculated. Use resampling to obtain
# inferential quantities. See "Resampling" in the "Extended usage"
# section below.
# 2. `summarize()` prints the full output by default. For a more condensed
# output use:
print(summarize(res), .full_output = FALSE)
## Dealing with endogeneity -------------------------------------------------
# See: ?testHausman()
### Models containing second constructs--------------------------------------
## Take a look at the dataset
#?dgp_2ndorder_cf_of_c
model <- "
# Path model / Regressions
c4 ~ eta1
eta2 ~ eta1 + c4
# Reflective measurement model
c1 <~ y11 + y12
c2 <~ y21 + y22 + y23 + y24
c3 <~ y31 + y32 + y33 + y34 + y35 + y36 + y37 + y38
eta1 =~ y41 + y42 + y43
eta2 =~ y51 + y52 + y53
# Composite model (second order)
c4 =~ c1 + c2 + c3
"
res_2stage <- csem(dgp_2ndorder_cf_of_c, model, .approach_2ndorder = "2stage")
res_mixed <- csem(dgp_2ndorder_cf_of_c, model, .approach_2ndorder = "mixed")
# The standard repeated indicators approach is done by 1.) respecifying the model
# and 2.) adding the repeated indicators to the data set
# 1.) Respecify the model
model_RI <- "
# Path model / Regressions
c4 ~ eta1
eta2 ~ eta1 + c4
c4 ~ c1 + c2 + c3
# Reflective measurement model
c1 <~ y11 + y12
c2 <~ y21 + y22 + y23 + y24
c3 <~ y31 + y32 + y33 + y34 + y35 + y36 + y37 + y38
eta1 =~ y41 + y42 + y43
eta2 =~ y51 + y52 + y53
# c4 is a common factor measured by composites
c4 =~ y11_temp + y12_temp + y21_temp + y22_temp + y23_temp + y24_temp +
y31_temp + y32_temp + y33_temp + y34_temp + y35_temp + y36_temp +
y37_temp + y38_temp
"
# 2.) Update data set
data_RI <- dgp_2ndorder_cf_of_c
coln <- c(colnames(data_RI), paste0(colnames(data_RI), "_temp"))
data_RI <- data_RI[, c(1:ncol(data_RI), 1:ncol(data_RI))]
colnames(data_RI) <- coln
# Estimate
res_RI <- csem(data_RI, model_RI)
summarize(res_RI)
### Multigroup analysis -----------------------------------------------------
# See: ?testMGD()
# ===========================================================================
# Extended usage
# ===========================================================================
# `csem()` provides defaults for all arguments except `.data` and `.model`.
# Below some common options/tasks that users are likely to be interested in.
# We use the threecommonfactors data set again:
model <- "
# Structural model
eta2 ~ eta1
eta3 ~ eta1 + eta2
# (Reflective) measurement model
eta1 =~ y11 + y12 + y13
eta2 =~ y21 + y22 + y23
eta3 =~ y31 + y32 + y33
"
### PLS vs PLSc and disattenuation
# In the model all concepts are modeled as common factors. If
# .approach_weights = "PLS-PM", csem() uses PLSc to disattenuate composite-indicator
# and composite-composite correlations.
res_plsc <- csem(threecommonfactors, model, .approach_weights = "PLS-PM")
res$Information$Model$construct_type # all common factors
# To obtain "original" (inconsistent) PLS estimates use `.disattenuate = FALSE`
res_pls <- csem(threecommonfactors, model,
.approach_weights = "PLS-PM",
.disattenuate = FALSE
)
s_plsc <- summarize(res_plsc)
s_pls <- summarize(res_pls)
# Compare
data.frame(
"Path" = s_plsc$Estimates$Path_estimates$Name,
"Pop_value" = c(0.6, 0.4, 0.35), # see ?threecommonfactors
"PLSc" = s_plsc$Estimates$Path_estimates$Estimate,
"PLS" = s_pls$Estimates$Path_estimates$Estimate
)
### Resampling --------------------------------------------------------------
## Not run:
## Basic resampling
res_boot <- csem(threecommonfactors, model, .resample_method = "bootstrap")
res_jack <- csem(threecommonfactors, model, .resample_method = "jackknife")
# See ?resamplecSEMResults for more examples
### Choosing a different weightning scheme ----------------------------------
res_gscam <- csem(threecommonfactors, model, .approach_weights = "GSCA")
res_gsca <- csem(threecommonfactors, model,
.approach_weights = "GSCA",
.disattenuate = FALSE
)
s_gscam <- summarize(res_gscam)
s_gsca <- summarize(res_gsca)
# Compare
data.frame(
"Path" = s_gscam$Estimates$Path_estimates$Name,
"Pop_value" = c(0.6, 0.4, 0.35), # see ?threecommonfactors
"GSCAm" = s_gscam$Estimates$Path_estimates$Estimate,
"GSCA" = s_gsca$Estimates$Path_estimates$Estimate
)
## End(Not run)
### Fine-tuning a weighting scheme ------------------------------------------
## Setting starting values
sv <- list("eta1" = c("y12" = 10, "y13" = 4, "y11" = 1))
res <- csem(threecommonfactors, model, .starting_values = sv)
## Choosing a different inner weighting scheme
#?args_csem_dotdotdot
res <- csem(threecommonfactors, model, .PLS_weight_scheme_inner = "factorial",
.PLS_ignore_structural_model = TRUE)
## Choosing different modes for PLS
# By default, concepts modeled as common factors uses PLS Mode A weights.
modes <- list("eta1" = "unit", "eta2" = "modeB", "eta3" = "unit")
res <- csem(threecommonfactors, model, .PLS_modes = modes)
summarize(res)
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