Consistent permutation applies the permutation procedure to models estimated with the consistent PLS-SEM (PLSc-SEM) algorithm rather than the standard PLS-SEM algorithm. Like standard permutation, it lets researchers test whether pre-defined data groups differ significantly in their group-specific parameter estimates, and it supports the MICOM procedure for assessing measurement invariance. Researchers use consistent permutation when their model has been estimated with PLSc-SEM and they need a multigroup comparison or a measurement invariance assessment based on PLSc-SEM results.

Consistent permutation follows the same logic as standard permutation: observations are randomly reassigned between the groups being compared (without replacement), and the model is re-estimated for each permutation to build a distribution of the group differences under the null hypothesis of no difference. The key distinction is that every permutation run is estimated using the consistent PLS-SEM (PLSc-SEM) algorithm instead of the standard PLS-SEM algorithm, so the resulting test statistics reflect the disattenuated, factor-consistent parameter estimates that PLSc-SEM produces.

In SmartPLS, consistent permutation is available whenever a multigroup comparison is run on a model that uses the PLSc-SEM algorithm. It offers the same settings as standard permutation (group selection, number of permutations, test type, significance level, and parallel processing), applied on top of the PLSc-SEM estimation, and its results report includes both the multigroup analysis and the MICOM measurement invariance results.

Standard permutation tests group differences and measurement invariance for models estimated with the standard PLS-SEM algorithm. Consistent permutation applies the same resampling logic, but each permutation run is estimated with the consistent PLS-SEM (PLSc-SEM) algorithm, so it is used for multigroup comparisons and measurement invariance testing in PLSc-SEM models.

Use consistent permutation when your model has been estimated with PLSc-SEM. Since PLSc-SEM produces different (factor-consistent) parameter estimates than standard PLS-SEM, group comparisons and measurement invariance tests for such a model should also be based on PLSc-SEM re-estimations.

Yes. Like standard permutation, consistent permutation supports the MICOM procedure, allowing researchers to substantiate that significant differences in group-specific PLSc-SEM results do not stem from differences in how constructs are measured across groups.