# 28. Nonlinear relationships

## Purpose

Does attractiveness have a curved relationship with competence after accounting for the wider corporate-reputation model?

## Practice study

- File: [corporate-reputation.csv](../samples/corporate-reputation.csv)
- Prepared project: [corporate-reputation-nonlinear.qpls](../projects/corporate-reputation-nonlinear.qpls)
- Observations: 344 complete cases
- Data type: packaged academic teaching data
- Complexity: eight constructs, 31 indicators, multiple structural paths, and one explicitly authored quadratic relationship

## Exact procedure

1. Start QuickPLS and choose **Open Project**. Select [corporate-reputation-nonlinear.qpls](../projects/corporate-reputation-nonlinear.qpls). This qualified project contains the exact data, authored quadratic relationship, saved result, and arranged model used for this tutorial.

2. Open **Data** and confirm the Corporate Reputation dataset contains 344 observations and 31 indicators. Return to **Model**. The linked CSV remains available separately for inspection and re-import practice.

   ![Nonlinear relationships sample data](../screenshots/nonlinear-relationships/01-data-ready.png)

3. Confirm that the prepared model contains Attractiveness, Competence, Corporate social responsibility, Customer satisfaction, Customer loyalty, Likeability, Performance, and Quality. The model deliberately retains its reflective, formative, and single-indicator specifications.

   Confirm that the saved model includes the authored quadratic relationship **Attractiveness² → Competence**. Do not add a second quadratic relationship.

4. The prepared project already contains a saved, neatly arranged model layout. Do not choose **Arrange** or otherwise change the canvas before this tutorial calculation. If you later edit the model, arrange it once and save the edited project before calculating.

   ![Nonlinear relationships prepared model or variable roles](../screenshots/nonlinear-relationships/02-arranged-model.png)

5. Choose **Validate** and confirm there are no blockers. Do not save the unchanged prepared project; save only after you intentionally edit it.

6. Use **Calculate → Quadratic Nonlinear Effects**.

   ![Nonlinear relationships calculation setup](../screenshots/nonlinear-relationships/03-calculation-setup.png)

7. Complete the method-specific settings:

- Confirm **Attractiveness → Competence** is the selected authored quadratic relationship
- Use percentile bootstrap inference with 999 refits and the documented fixed seed

8. Read **Readiness**, leave **Open Results when finished** selected, and choose **Start calculation** once. Wait for **Completed**; do not close the project while the result is being saved.

9. In **Results**, confirm **Nonlinear relationships** is selected and inspect these outputs in order:

1. Joint equation coefficients
2. Derivative probes and simple slopes
3. Conditional curve values
4. Turning points

   ![Nonlinear relationships primary result](../screenshots/nonlinear-relationships/04-results-primary.png)

   ![Nonlinear relationships secondary result](../screenshots/nonlinear-relationships/05-results-secondary.png)

10. Choose **Save Report** to preserve the exact result. Use **Export** for the needed table/report format. Close and reopen the project once and confirm the saved result remains selectable.

## Reading guidance

- The data are deterministic synthetic teaching data. They are suitable for reproducing the workflow, not for substantive publication claims.
- The installed 2.62.8 qualification used 999 complete-case bootstrap refits and verified persistence, formatted copy, Saved Report, reopen, and canonical export.