Permutation
Permutation is a nonparametric test that lets researchers check whether pre-defined data groups (e.g., customers from different countries) have statistically significant differences in their group-specific PLS-SEM parameter estimates, such as outer weights, outer loadings, and path coefficients. It also supports the MICOM procedure for assessing measurement invariance, which is a prerequisite for meaningful group comparisons. Researchers use permutation when they want to conduct a multigroup analysis (MGA) or test whether a construct is measured equivalently across groups.
What Permutation Is Used For
The purpose of the permutation routine in SmartPLS is twofold:
- It allows conducting a PLS-SEM multigroup analysis (Hair et al., 2024; Sarstedt, Henseler, & Ringle, 2011) as suggested by Dibbern and Chin (2005) and Chin and Dibbern (2010). This lets you decide if group-specific PLS-SEM results have statistically significant differences.
- It allows conducting the PLS-SEM measurement invariance assessment as suggested by Henseler, Ringle, and Sarstedt's (2015) MICOM routine. This lets you substantiate that significant differences in group-specific PLS-SEM results do not stem from differences in how constructs (e.g., customer loyalty) are measured across groups.
The permutation results report in SmartPLS includes both the outcomes of the PLS-SEM multigroup analysis (using the permutation test) and the MICOM results for assessing measurement invariance.
Permutation Settings in SmartPLS
| Setting | Default | Description |
|---|---|---|
| Select groups | — | The data group selected under Group A is compared against the data group selected under Group B; both are assessed for significant differences in parameter estimates and for measurement invariance (MICOM). If the group selection combo box is empty, double-click the data set in the SmartPLS project window and use the available options to generate data groups for the multigroup analysis. |
| Permutations | 1,000 | Number of permutation runs, each created by randomly drawing (without replacement) n observations for Group A, where n equals Group A's size in the original data set; all remaining observations are assigned to Group B. Group-specific sample sizes therefore stay constant across runs. For a quick initial assessment, a smaller number (e.g., 500–1,000) may suffice; for final results, use a large number (e.g., 5,000). Larger numbers increase computation time. |
| Test type | Two-tailed | Specifies whether a one-tailed (one-sided) or two-tailed (two-sided) significance test is conducted; this also affects the p value computation. |
| Significance level | 0.05 | Specifies the significance level used for the confidence interval computations. |
| Do parallel processing | Enabled | Runs the permutation procedure on multiple processors, if available, considerably reducing computation time. |
Frequently Asked Questions
What does the permutation procedure test in PLS-SEM?
It tests whether pre-defined data groups have statistically significant differences in their group-specific parameter estimates, such as outer weights, outer loadings, and path coefficients (a multigroup analysis), and it supports the MICOM procedure for assessing measurement invariance across groups.
Why do I need MICOM before comparing groups?
MICOM substantiates that significant differences in group-specific PLS-SEM results stem from genuine differences between groups rather than from the constructs being measured differently across groups. It is a prerequisite for meaningful multigroup comparisons.
How many permutations should I use?
For a quick initial assessment, a smaller number such as 500 or 1,000 permutations may be sufficient. For final results preparation, use a larger number, such as 5,000, since more permutations increase the stability of the results at the cost of additional computation time. SmartPLS defaults to 1,000.
Should I use a one-tailed or two-tailed test?
SmartPLS defaults to a two-tailed test. The choice between a one-tailed and two-tailed test depends on whether your hypothesis predicts the direction of the group difference, and it affects how the p value is computed.
Why is Group A always compared against Group B with fixed sample sizes?
In each permutation run, n observations equal to Group A's original size are drawn without replacement and assigned to Group A, and the rest are assigned to Group B. This keeps the group-specific sample sizes constant across all runs and equal to the sizes observed in the original data set.
Related SmartPLS Methods
References
- Chin, W. W., & Dibbern, J. (2010). A permutation based procedure for multi-group PLS analysis: Results of tests of differences on simulated data and a cross cultural analysis of the sourcing of information system services between Germany and the USA. In V. Esposito Vinzi, W. W. Chin, J. Henseler, & H. Wang (Eds.), Handbook of partial least squares: Concepts, methods and applications (pp. 171–193). Springer.
- Hair, J. F., Sarstedt, M., Ringle, C. M., & Gudergan, S. P. (2024). Advanced issues in partial least squares structural equation modeling (PLS-SEM) (2nd ed.). Sage.
- Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). Testing measurement invariance of composites using partial least squares. International Marketing Review, 33(3), 405–431.
- Sarstedt, M., Henseler, J., & Ringle, C. M. (2011). Multi-group analysis in partial least squares (PLS) path modeling: Alternative methods and empirical results. Advances in International Marketing, 22, 195–218.
- Edgington, E., & Onghena, P. (2007). Randomization tests (4th ed.). Chapman & Hall.
- More literature ...
Cite correctly
Please always cite the use of SmartPLS!
Ringle, Christian M., Wende, Sven, & Becker, Jan-Michael. (2024). SmartPLS 4. Bönningstedt: SmartPLS. Retrieved from https://www.smartpls.com
