What does multi-group analysis tell you?

Whether a relationship in your model is significantly stronger in one group than another. It tests moderation by a categorical grouping variable at the level of individual structural paths.

Do I need measurement invariance before MGA?

Yes. You should establish at least partial measurement invariance (the MICOM procedure) first. Otherwise a difference in path coefficients could come from the groups measuring the constructs differently rather than from a real structural difference.

Which MGA test should I use?

The permutation test is the recommended default because it makes no distributional assumptions. The parametric and Welch-Satterthwaite tests are alternatives; for more than two groups, start with an omnibus test.

PLS-SEM METHOD

Multi-group analysis (MGA): comparing paths across groups

Multi-group analysis (MGA) tests whether the relationships in your PLS-SEM model differ significantly between predefined groups, such as men and women, two countries, or customers and non-customers. This page explains what it tests, how to read the result, the test variants, the measurement-invariance step most people skip, and the common pitfalls.

What multi-group analysis tests

A standard PLS-SEM model estimates one path coefficient per structural relationship, pooled across the whole sample. MGA asks a more specific question: is that relationship the same for everyone, or does it depend on which group a respondent belongs to? It is a form of moderation, where the moderator is a categorical grouping variable.

MGA estimates the model separately for each group and then tests whether the difference between the groups’ path coefficients is larger than you would expect by chance. A significant difference means the grouping variable moderates that relationship: the effect is genuinely stronger in one group than in the other.

A worked example

The path from perceived usefulness to adoption is estimated separately for two groups. In Group A the coefficient is 0.45 and in Group B it is 0.18. The permutation test gives a p-value of 0.02 for the difference, so the path differs significantly across the groups.

You would report the two group-specific coefficients and conclude that the grouping variable moderates this relationship.

The usefulness-to-adoption path is 0.45 in Group A versus 0.18 in Group B; the difference is significant (p = 0.02).

How to read the result

For each structural path, MGA reports the difference between the two groups’ coefficients and a p-value for that difference.

p(diff) < 0.05: The path differs significantly between the two groups. The grouping variable moderates this relationship; report and interpret the two group-specific coefficients separately.
p(diff) ≥ 0.05: No evidence that the path differs across groups. You can report the pooled coefficient from the full-sample model for this relationship.
Mixed results: It is normal for some paths to differ across groups and others not. Interpret each structural path on its own, rather than declaring the whole model invariant from a single path.

A non-significant difference is not proof that the groups are identical, only that your data does not show a difference. Groups that are too small make real differences hard to detect.

MGA test variants

Permutation test

The recommended non-parametric approach (Henseler 2007). Group labels are repeatedly shuffled to build the distribution of the coefficient difference under the null hypothesis. It makes no distributional assumptions, which is why OpenPLS uses it.

Parametric test

A two-sample t-test on the bootstrap coefficients (Keil et al. 2000). Simple, but it assumes equal variances across groups.

Welch-Satterthwaite

A variant of the parametric test that does not assume equal variances. More robust when group sizes or variances differ.

Omnibus test (OTG)

For more than two groups, the omnibus test of group differences checks whether a path differs across all groups at once, before any pairwise comparison.

Running MGA step by step

Define the groups from a categorical column (for example gender, region, or a split of a continuous variable).
Check measurement invariance first (the MICOM procedure). You must establish at least partial invariance, or group differences could reflect how the constructs are measured rather than real structural differences.
Estimate the model within each group and confirm each group has enough cases for stable estimates.
Run the MGA to obtain the coefficient difference and p-value for every structural path.
Report the group-specific coefficients for paths that differ significantly, and the pooled coefficient for those that do not.

Common pitfalls

Skipping the measurement-invariance (MICOM) check. Without it, a significant path difference may simply mean the two groups interpret the items differently.
Groups that are too small. MGA needs a reasonable sample within each group; tiny groups produce unstable coefficients and low power.
Comparing more than two groups with pairwise tests only, without an omnibus test, which inflates the false-positive rate.
Reading a non-significant difference as proof of equality. It is only an absence of evidence.
Splitting a continuous moderator into groups when a continuous moderation analysis would keep more information.

MGA in OpenPLS

OpenPLS includes a Multi-Group Analysis panel that runs Henseler’s permutation test. Define your groups from any column, choose the number of permutations, and get, for each structural path, the difference in coefficients and a two-sided p-value. It handles two groups directly and reports pairwise comparisons for more. Free and runs in the browser.

Compare groups in your own model

Build your model in the visual editor, define your groups, and run a permutation-based MGA in one click. Free, no install.

Open OpenPLS What is PLS-SEM?

Frequently asked questions

What does multi-group analysis tell you?: Whether a relationship in your model is significantly stronger in one group than another. It tests moderation by a categorical grouping variable at the level of individual structural paths.
Do I need measurement invariance before MGA?: Yes. You should establish at least partial measurement invariance (the MICOM procedure) first. Otherwise a difference in path coefficients could come from the groups measuring the constructs differently rather than from a real structural difference.
Which MGA test should I use?: The permutation test is the recommended default because it makes no distributional assumptions. The parametric and Welch-Satterthwaite tests are alternatives; for more than two groups, start with an omnibus test.