# 20. PLS-MGA

## Purpose and applicability

PLS-MGA evaluates whether a selected PLS estimate differs across observed groups. This tutorial compares the Organizational Identification → Affective Commitment (Joy) path across the two recorded gender groups.

Use PLS-MGA only when the grouping variable is meaningful, group sizes are adequate, the same model is estimated in both groups, and the relevant MICOM evidence has been reviewed. A significant difference identifies group heterogeneity in the selected estimate; it does not explain why the difference exists.

## Practice study

- Dataset: [organizational-identification-model-comparison.csv](../samples/organizational-identification-model-comparison.csv)
- Prepared project: [organizational-identification-multimod.qpls](../projects/organizational-identification-multimod.qpls)
- Observations: 305 complete cases
- Groups: `gender = 1` (157 cases) and `gender = 2` (148 cases)
- Data type: deterministic synthetic instructional data
- Selected parameter: Organizational Identification → Affective Commitment (Joy)

The four reflective constructs are Organizational Prestige (8 indicators), Organizational Identification (6), Affective Commitment (Joy) (4), and Affective Commitment (Love) (3). The saved model contains Organizational Prestige → Organizational Identification and Organizational Identification → both commitment dimensions.

## Preparation

1. Open the prepared project, then open **Data** and confirm the 305 observations and `gender` grouping column.

   ![Organizational-identification data prepared for PLS-MGA](../screenshots/pls-mga/01-data-ready.png)

2. Return to **Model**. Confirm the saved four-construct model and its already arranged coordinates; do not press **Arrange**.

   ![Saved arranged model for PLS-MGA](../screenshots/pls-mga/02-arranged-model.png)

3. Choose **Validate** and confirm no blocker. Review the qualified [MICOM](19-micom.md) result before interpreting a structural difference.

## Calculation

4. Choose **Calculate → MICOM and Multigroup Analysis (PLS / PLSc)**.
5. Select the ordinary PLS profile, `gender`, groups 1 and 2, and the authored Organizational Identification → Affective Commitment (Joy) path. Retain the saved configural checklist.
6. Use the two-tailed pairwise permutation procedure, deterministic seed, and 5,000 resamples. Leave multiplicity handling at the saved qualified setting.

   ![PLS-MGA setup with the authored structural path](../screenshots/pls-mga/03-calculation-setup.png)

7. Leave **Open Results when finished** selected and choose **Start calculation** once. Wait for **Completed**; the qualified run takes several minutes because all 5,000 draws are retained and accounted for.

## Results and interpretation

8. In **Pairwise group comparisons**, read the signed left-minus-right difference, raw permutation p value, adjusted p value, and measurement-comparability decision. The qualified teaching run retained a difference of about 0.2315 with raw and adjusted p values about 0.0028.

   ![PLS-MGA pairwise comparison statistics](../screenshots/pls-mga/04-results-primary.png)

9. Scroll the same table horizontally to confirm measurement comparability and whether interpretation is blocked.

   ![PLS-MGA comparability and interpretation columns](../screenshots/pls-mga/05-results-secondary.png)

The sign depends on the left/right group order. Report the group definitions and group-specific estimates with the difference; do not report only the p value.

## QuickPLS 2.62.8 display note

The canonical result retains the exact authored parameter identity, but QuickPLS 2.62.8 displays the selected target in this table as a technical parameter token. The screenshots therefore keep the target column hidden. Identify the tested relationship from the calculation-setup screen above and retain the full identity in technical export/provenance. This is a presentation limitation, not a change to the calculated statistic.

## Reporting and reproducibility

Use **Copy** for the visible table or **Export** for complete output. Record the procedure, group order and sizes, resample count, seed, signed difference, raw and adjusted p values, and MICOM basis. Save a report when needed, then close and reopen the project to confirm the result remains selectable.

Common mistakes include reversing the group order without updating the interpretation, selecting loadings when the research question concerns paths, reporting a directional probability as an ordinary two-sided p value, and ignoring failed resamples or MICOM evidence.

## Limitations and related methods

The deterministic teaching data illustrate the workflow only. PLS-MGA evaluates selected group differences rather than latent, unobserved segments. For latent heterogeneity, see [FIMIX-PLS](24-fimix-pls.md) or [PLS-POS](23-pls-pos.md). For consistent-PLS group estimates, see [PLSc-MGA](21-plsc-mga.md).

Last verified with QuickPLS 2.62.8.