In M-E-Rademaker/cSEM: Composite-Based Structural Equation Modeling

WARNING: this document is work in progress.

Introduction {#introduction}

The family of test function includes the following tests: - testOMF: test for overall model fit - testMGD: test for multigroup differences - testHausman2: Hausman test for endogeneity - testMICOM: test for measurement invariance of composites

Test for overall model fit (testOMF)

The test for overall model fit is used to test whether the specified model fits the dataset. In general, a bootstrap-based test suggested by @Beran1985 is employed. In the context of PLS-PM, this test was introduced by @Dijkstra2015.

Syntax & Options {#syntaxOMF}

testOMF(
  .object                = args_default()$.object, 
  .alpha                 = args_default()$.alpha, 
  .handle_inadmissibles  = args_default()$.handle_inadmissibles, 
  .R                     = args_default()$.R, 
  .saturated             = args_default()$.saturated,
  .seed                  = args_default()$.seed,
  .verbose               = args_default()$.verbose
  )

.object

: An object of class cSEMResults resulting from a call to csem().

.alpha

: An integer or a numeric vector of significance levels. Defaults to 0.05.

.handle_inadmissibles

: Character string. How should inadmissible results be treated during bootstrap/permutation? One of "drop", "ignore", or "replace". If "drop", inadmissibles estimations are dropped (i.e., the number of results returned will be likely less than .R). For "ignore" inadmissible estimations are returned even if they are inadmissible (i.e., number of results returned = .R). For "replace" inadmissible estimations are replaced, i.e., resampling continues until there are exactly .R admissible solutions (i.e., number of results returned equal .R). Defaults to "drop".

.R

: Integer. The number of bootstrap runs. Defaults to 499.

.saturated

: Logical. Whether the model-implied indicator variance-covariance matrix should be based on the a saturated structural model. Defaults to FALSE

.seed

: Integer or NULL. The random seed to use. Defaults to NULL in which case an arbitrary seed is choosen.

.verbose

:

Details

Details if there are any.

Usage & Examples {#examplesOMF}

Example 1 {#example1OMF}

Example 2 {#example2OMF}

Example 3 {#example3OMF}

Methods & Formulae {#methodsOMF}

Definition

Formula

Implementation

See also

Test for multi-group differences (testMGD)

The test for multigroup differences is generally used to compare groups. In doing so, various suggested test are implemented: - Approach suggested by @Chin2010 to compare a single parameter between two groups. - Approach suggested by @Sarstedt2011 to compare a single parameter across several groups. - Approach suggested by @Klesel2019 to compare the model-implied indicator/construct correlation matrix across several groups.

Syntax & Options {#syntaxMGD}

testMGD(
  .object                = args_default()$.object,
  .alpha                 = args_default()$.alpha,
  .approach_p_adjust     = args_default()$.approach_p_adjust,
  .approach_mgd          = args_default()$.approach_mgd,
  .model                 = args_default()$.model,
  .handle_inadmissibles  = args_default()$.handle_inadmissibles,
  .R_permutation         = args_default()$.R_permutation,
  .R_bootstrap           = args_default()$.R_bootstrap,
  .saturated             = args_default()$.saturated,
  .seed                  = args_default()$.seed,
  .type_vcv              = args_default()$.type_vcv,
  .verbose               = args_default()$.verbose
  ) 

.object

: An object of class cSEMResults_multi resulting from a call to csem().

.alpha

: An integer or a numeric vector of significance levels. Defaults to 0.05.

.approach_p_adjust

: Character string. Approach used for the correction of the p-value in case of multiple comparisons. One of "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", and "none". Defaults to "none".

.approach_mgd

: Character string. Approach used for multi-group comparison. One of "Chin", "Sarstedt", and "Klesel". Defaults to "none".

.model

: A model in lavaan model syntax or NULL. The specified model determines which parameters are compared across groups. If set to NULL all model parameters are comapred across groups. Defaults to NULL.

.handle_inadmissibles

: Character string. How should inadmissible results be treated during bootstrap/permutation? One of "drop", "ignore", or "replace". If "drop", inadmissibles estimations are dropped (i.e., the number of results returned will be likely less than .R). For "ignore" inadmissible estimations are returned even if they are inadmissible (i.e., number of results returned = .R). For "replace" inadmissible estimations are replaced, i.e., resampling continues until there are exactly .R admissible solutions (i.e., number of results returned equal .R). Defaults to "drop".

.R_permutation

: Integer. The number of permutation runs. Defaults to 499.

.R_bootstrap

: Integer. The number of bootstrap runs. Defaults to 499.

.saturated

: Logical. Whether the model-implied indicator variance-covariance matrix should be based on a saturated structural model. Defaults to FALSE

.seed

: Integer or NULL. The random seed to use. Defaults to NULL in which case an arbitrary seed is choosen.

.type_vcv

: Character string. Indicates which model-implied correlation matrix is compared across groups. One of "indicator" or "construct". Defaults to "indicator".

.verbose

:

Details

Details if there are any.

Usage & Examples {#examplesMGD}

Example 1 {#example1MGD}

Example 2 {#example2MGD}

Example 3 {#example3MGD}

Methods & Formulae {#methodsMGD}

Definition

Formula

Implementation

See also

Hausman test for endogeneity (testHausman2)

Syntax & Options {#syntaxHausman}

testHausman2(
 .object               = NULL,
 .alpha                = args_default()$.alpha,
 .eval_plan            = args_default()$.eval_plan,
 .handle_inadmissibles = args_default()$.handle_inadmissibles,
 .R                    = args_default()$.R,
 .resample_method      = args_default()$.resample_method,
 .seed                 = args_default()$.seed
)

.object

: An object of class cSEMResults resulting from a call to csem().

.alpha

: An integer or a numeric vector of significance levels. Defaults to 0.05.

.eval_plan

: Character string. The evaluation plan to use. One of "sequential" or "multiprocess". In the latter case all available cores will be used. Defaults to "sequential". See resamplecSEMResults() for details.

.handle_inadmissibles

: Character string. How should inadmissible results be treated during bootstrap/permutation? One of "drop", "ignore", or "replace". If "drop", inadmissibles estimations are dropped (i.e., the number of results returned will be likely less than .R). For "ignore" inadmissible estimations are returned even if they are inadmissible (i.e., number of results returned = .R). For "replace" inadmissible estimations are replaced, i.e., resampling continues until there are exactly .R admissible solutions (i.e., number of results returned equal .R). Defaults to "drop".

.R

: Integer. The number of bootstrap/permutation runs. Defaults to 499.

.resample_method

: Character string. The resampling method to use. One of: "bootstrap" or "jackknife". Defaults to "bootstrap".

.seed

: Integer or NULL. The random seed to use. Defaults to NULL in which case an arbitrary seed is choosen.

Details

Details if there are any.

Usage & Examples {#examplesHausman}

Example 1 {#example1Hausman}

Example 2 {#example2Hausman}

Example 3 {#example3Hausman}

Methods & Formulae {#methodsHausman}

Definition

Formula

Implementation

See also

Test for measurement invariance of composites (testMICOM)

The test for measurement invariance of composites suggested by @Henseler2016 is used to test measurement of composites across groups.

Syntax & Options {#syntaxMICOM}

testMICOM(
  .object               = args_default()$.object,
  .alpha                = args_default()$.alpha,
  .approach_p_adjust    = args_default()$.approach_p_adjust, 
  .handle_inadmissibles = args_default()$.handle_inadmissibles,
  .R                    = args_default()$.R,
  .seed                 = args_default()$.seed,
  .verbose              = args_default()$.verbose
  )

.object

: An object of class cSEMResults resulting from a call to csem().

.alpha

: An integer or a numeric vector of significance levels. Defaults to 0.05.

.approach_p_adjust

: Character string. Approach used for the correction of the p-value in case of multiple comparisons. One of "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", and "none". Defaults to "none".

.handle_inadmissibles

: Character string. How should inadmissible results be treated during bootstrap/permutation? One of "drop", "ignore", or "replace". If "drop", inadmissibles estimations are dropped (i.e., the number of results returned will be likely less than .R). For "ignore" inadmissible estimations are returned even if they are inadmissible (i.e., number of results returned = .R). For "replace" inadmissible estimations are replaced, i.e., resampling continues until there are exactly .R admissible solutions (i.e., number of results returned equal .R). Defaults to "drop".

.R

: Integer. The number of bootstrap/permutation runs. Defaults to 499.

.seed

: Integer or NULL. The random seed to use. Defaults to NULL in which case an arbitrary seed is choosen.

.verbose

:

Details

Details if there are any.

Usage & Examples {#examplesMICOM}

Example 1 {#example1MICOM}

Example 2 {#example2MICOM}

Example 3 {#example3MICOM}

Methods & Formulae {#methodsMICOM}

Definition

Formula

Implementation

See also

Literature

M-E-Rademaker/cSEM documentation built on March 2, 2025, 1:04 a.m.