testMICOM {cSEM}R Documentation

Test measurement invariance of composites




 .object               = NULL,
 .approach_p_adjust    = "none",
 .handle_inadmissibles = c("drop", "ignore", "replace"), 
 .R                    = 499,
 .seed                 = NULL,
 .verbose              = TRUE



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


Character string or a vector of character strings. Approach used to adjust the p-value for multiple testing. See the methods argument of stats::p.adjust() for a list of choices and their description. Defaults to "none".


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".


Integer. The number of bootstrap replications. Defaults to 499.


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!


Logical. Should information (e.g., progress bar) be printed to the console? Defaults to TRUE.


The functions performs the permutation-based test for measurement invariance of composites across groups proposed by Henseler et al. (2016). According to the authors assessing measurement invariance in composite models can be assessed by a three-step procedure. The first two steps involve an assessment of configural and compositional invariance. The third steps involves mean and variance comparisons across groups. Assessment of configural invariance is qualitative in nature and hence not assessed by the testMICOM() function.

As testMICOM() requires at least two groups, .object must be of class cSEMResults_multi. As of version 0.2.0 of the package, testMICOM() does not support models containing second-order constructs.

It is possible to compare more than two groups, however, multiple-testing issues arise in this case. To adjust p-values in this case several p-value adjustments are available via the approach_p_adjust argument.

The remaining arguments set the number of permutation runs to conduct (.R), the random number seed (.seed), instructions how inadmissible results are to be handled (handle_inadmissibles), and whether the function should be verbose in a sense that progress is printed to the console.

The number of permutation runs defaults to args_default()$.R for performance reasons. According to Henseler et al. (2016) the number of permutations should be at least 5000 for assessment to be sufficiently reliable.


A named list of class cSEMTestMICOM containing the following list element:


A list containing the results of the test for compositional invariance (Step 2).


A list containing the results of the test for mean and variance equality (Step 3).


A list of additional information on the test.


Henseler J, Ringle CM, Sarstedt M (2016). “Testing Measurement Invariance of Composites Using Partial Least Squares.” International Marketing Review, 33(3), 405–431. doi:10.1108/imr-09-2014-0304.

See Also

csem(), cSEMResults, testOMF(), testMGD()


## Not run: 
# NOTE: to run the example. Download and load the newst version of cSEM.DGP
# from GitHub using devtools::install_github("M-E-Rademaker/cSEM.DGP").

# Create two data generating processes (DGPs) that only differ in how the composite
# X is build. Hence, the two groups are not compositionally invariant.
dgp1 <- "
# Structural model
Y ~ 0.6*X

# Measurement model
Y =~ 1*y1
X <~ 0.4*x1 + 0.8*x2

x1 ~~ 0.3125*x2

dgp2 <- "
# Structural model
Y ~ 0.6*X

# Measurement model
Y =~ 1*y1
X <~ 0.8*x1 + 0.4*x2

x1 ~~ 0.3125*x2

g1 <- generateData(dgp1, .N = 399, .empirical = TRUE) # requires cSEM.DGP 
g2 <- generateData(dgp2, .N = 200, .empirical = TRUE) # requires cSEM.DGP

# Model is the same for both DGPs
model <- "
# Structural model
Y ~ X

# Measurement model
Y =~ y1
X <~ x1 + x2

# Estimate
csem_results <- csem(.data = list("group1" = g1, "group2" = g2), model)

# Test
testMICOM(csem_results, .R = 50, .alpha = c(0.01, 0.05), .seed = 1987)

## End(Not run)

[Package cSEM version 0.5.0 Index]