PLS-MGA and MICOM in SmartPLS 4: Evidence-Based Group Comparisons

1. What Should You Be Able to Do After This Article?

Readers should be able to distinguish MGA from continuous moderation, create groups without distorting the data’s meaning, assess the three MICOM steps, run permutation and PLS-MGA in SmartPLS 4, and correctly interpret each procedure’s p-values. Report the software version and cite it in the methods section (Ringle et al., 2024).

Inputs include a predefined grouping variable, a hypothesis identifying which parameters are expected to differ, a common PLS-SEM model for all groups, a coding codebook, and sufficient observations in each group. Total sample size does not replace assessment of power and stability in the smallest group.

• Groups must have theoretical or design-based meaning and must not be created after examining results.
• A hypothesis or question must identify the parameters to be compared.
• Each observation must belong to exactly one group, with no missing group codes.
• Use the same model, indicators, coding, and algorithm settings across groups.
• Check sample size and data quality separately for each group.
• Decide between PLS-SEM and PLSc-SEM before selecting the corresponding permutation procedure.

2. What Does MGA Test?

MGA directly tests whether the same parameter, such as a path coefficient, outer loading, or outer weight, differs across predefined groups. Sarstedt et al. (2011) show that MGA procedures differ in assumptions and construction of their test distributions, so reports must identify the method used.

MGA cannot be performed by comparing two separate p-values. A coefficient with p = 0,03 in group A and p = 0,12 in group B may still show no significant between-group difference because the standard error and distribution of the difference have not been tested.

3. Defining Groups and Checking Data Before Analysis

Natural or design-based groups, such as countries, intervention groups, or customer types, suit MGA when clearly defined and coded. Splitting continuous variables at the mean or median loses information, reduces power, and makes results dependent on the cutoff. If the hypothesis concerns a continuous variable changing a slope, an interaction term is usually more appropriate.

Before comparison, tabulate observation counts, missing data, the grouping-variable distribution, sample characteristics, and indicator quality for each group. Each group’s model must converge without serious problems; good full-sample results do not guarantee adequacy in a small group.

4. Why MICOM precedes MGA

A path difference may reflect different score composition rather than a different structural mechanism. MICOM assesses PLS-SEM composites; it does not replace within-group measurement evaluation and is not a copy of multigroup CFA (Henseler et al., 2016).

Configural and compositional evidence supports partial invariance. A model-wide comparability claim requires examining all relevant composites. Step 3 additionally examines mean and variance equality; full invariance does not establish equal paths or automatically justify replacing group analyses with pooled results (Hair et al., 2018, Chapter 4).

5. Reading MICOM in SmartPLS 4

SmartPLS (n.d.-a) includes MICOM in the permutation report; Step 1 requires configuration records. At Step 2 and alpha = .05, compare c with the fifth percentile of its permutation distribution, retaining enough precision for the decision. A single-item c of 1 is not evidence of reliability (Hair et al., 2018, Chapter 4).

At Step 3, compare the observed mean difference and log variance ratio with their corresponding permutation intervals. An interval may contain zero while excluding the observed difference. Check this distinction when reconciling a book, output and older interpretations (Hair et al., 2018, Chapter 4; SmartPLS, n.d.-a).

Prepare a construct-level table before reading paths. If composition is unsupported for a construct, comparisons involving it lack the necessary invariance evidence. Increasing permutations cannot repair coding or specification errors; justify corrections and rerun the sequence (Hair et al., 2018, Chapter 4).

6. Workflow in SmartPLS 4

Permutation and PLS-MGA both use groups created within the dataset. For standard PLS-SEM, use standard permutation; for a PLSc-SEM model, use consistent permutation so comparisons rely on the same algorithm (SmartPLS, n.d.-b).

7. Distinguish permutation and PLS-MGA

Permutation exchanges observations between groups, preserves group sizes and refits the model to form a reference distribution of differences. Specify a one- or two-sided test from the planned hypothesis, rather than changing direction after inspecting coefficient signs. Hair et al. (2018, Chapter 4) distinguish this procedure from the bootstrap-distribution comparisons used in PLS-MGA.

Under the SmartPLS PLS-MGA reporting convention, p < .05 or p > .95 is flagged at the 5% level (SmartPLS, n.d.-c). These tails concern the procedure's directional representation, not a rule for every p-value column. Do not call p = .98 an ordinary two-sided p-value. For a nondirectional difference hypothesis, prespecifying a two-sided permutation test gives a clearer interpretation (Hair et al., 2018, Chapter 4).

State the A − B ordering and verify the convention of the selected output column. The difference's magnitude and sign identify the comparison direction; p does not replace them. Parametric and Welch-Satterthwaite tests have different assumptions and should not be selected because one gives the smallest p (Sarstedt et al., 2011).

8. Hypothetical Numerical Example: Trust and Continuance Intention

The example below is illustrative rather than client data. Suppose a study compares new and long-term users. MICOM establishes partial invariance for Trust and Continuance Intention, permitting comparison of standardized paths across the two groups.

The Trust-to-Continuance Intention coefficient is 0,42 for new users and 0,18 for long-term users. The A - B difference is 0,24. A two-sided permutation test with 5.000 permutations gives p = 0,022; PLS-MGA gives p = 0,018. Both illustrative procedures support a difference, with a stronger relationship among new users.

9. More groups and paths increase the testing family

With g groups there are g(g − 1)/2 group pairs. Testing h paths across every pair produces h × g(g − 1)/2 tests. Four groups and three paths create 18 tests, rather than one isolated question at alpha = .05. Hair et al. (2018, Chapter 4) explain why searching many pairs increases false-positive risk.

Define the hypothesis family and necessary comparisons before analysis. Asking whether any group differs requires an appropriate overall test; a set of unadjusted pairwise tests is not automatically an omnibus test. Do not run an ordinary ANOVA on bootstrap coefficients as if each resample were an independent participant (Hair et al., 2018, Chapter 4).

The chapter discusses overall tests and pairwise adjustments. Verify which procedure the available software actually supports; an old book interface does not establish a current SmartPLS menu. For pairwise reporting, retain the full testing family, raw p-values and adjustment rule, including unfavorable results.

10. Constructed example: a conclusion changes after Holm adjustment

Suppose three planned path-difference hypotheses form one testing family and use two-sided permutation. Their illustrative p-values are .012, .026 and .210. These are constructed reporting inputs, not values derived from three pairs of betas. R's p.adjust implements Holm adjustment to control familywise error (R Core Team, n.d.).

The adjusted values are .036, .052 and .210. At alpha = .05, the second hypothesis no longer meets the criterion within this family. Do not pass only p-values already below .05 to the function, since that changes the family after inspecting results. This example uses two-sided p-values, not the raw directional PLS-MGA column.

# Constructed two-sided permutation p-values for one planned family.
p <- c(path1 = 0.012, path2 = 0.026, path3 = 0.210)
result <- data.frame(raw_p = p, holm_p = p.adjust(p, method = "holm"))
print(result)
stopifnot(isTRUE(all.equal(unname(result$holm_p), c(0.036, 0.052, 0.210))))
choose(4, 2) * 3 # 18 pairwise path tests across four groups
0.42 - 0.18      # 0.24, difference in the earlier constructed example

11. Unequal group sizes and robustness

A large total sample does not remove a small group's uncertainty. Report usable observations, measurement quality, estimation diagnostics and uncertainty for each group. Hair et al. (2018, Chapter 4) note that substantial size imbalance can affect test performance; this calls for design and sensitivity assessment, not automatic deletion of large-group observations.

A nonsignificant result is not evidence of group equivalence. Inspect the difference and its uncertainty where available, and state what size of difference matters in the research context. If trying alternative specifications or sample rules, keep the question and testing family consistent and report both primary and sensitivity analyses.

Groups discovered by FIMIX/PLS-POS from the same data remain exploratory. A subsequent MGA on that dataset is not independent confirmation of stable market segments. Interpretation needs group content and evidence beyond the segmentation procedure (Hair et al., 2018, Chapter 5).

9. Common Errors in Group Comparisons

13. APA-style reporting text and completion checklist

Connect the MICOM evidence to the difference test actually used. Identify comparable composites, the A/B ordering and the hypothesis family; if reporting several procedures, keep their interpretations separate (Hair et al., 2018, Chapter 4; Sarstedt et al., 2011).

• State the grouping rationale and reference coding.
• Report group sizes, missingness and model quality.
• Document Step 1 and retain Step 2 results for each composite.
• Distinguish partial/full evidence and unsupported comparisons.
• Record permutations, bootstrap runs, test type, alpha and seed where available.
• Report each group coefficient and the A − B direction.
• Separate directional PLS-MGA p from two-sided p.
• Retain the complete testing family, raw p and adjustment rule.
• Do not infer a difference from separate group p-values.
• Discuss magnitude, uncertainty, power and robustness.