# 30. Gaussian-copula endogeneity

## Purpose

Is the Trust → Renewal effect sensitive to potential endogeneity detected with a Gaussian copula?

## Practice study

- File: [trust-endogeneity.csv](../samples/trust-endogeneity.csv)
- Prepared project: [trust-endogeneity.qpls](../projects/trust-endogeneity.qpls)
- Observations: 420
- Data type: deterministic synthetic instructional data
- Complexity: a realistic multi-construct model with multi-item measurement blocks

**Prerequisites**

- Run PLS-SEM Algorithm first

## Exact procedure

1. Start QuickPLS and choose **Open Project**. Select [trust-endogeneity.qpls](../projects/trust-endogeneity.qpls). This prepared teaching project contains the exact dataset, analysis-ready base model, bindings, and a saved layout. Complete any method-specific term, group, or higher-order instruction stated below before calculation.

2. Open **Data** and confirm **trust-endogeneity.csv** contains 420 observations. Return to **Model**. The linked CSV remains available separately for inspection and re-import practice.

   ![Gaussian-copula endogeneity sample data](../screenshots/gaussian-copula-endogeneity/01-data-ready.png)

3. Confirm that the prepared model contains these constructs and measurement blocks: Price Fairness (price_fairness_1–price_fairness_3), Service Quality (service_quality_1–service_quality_4), Trust (trust_1–trust_4), and Renewal (renewal_1–renewal_3), all reflective.

   Confirm these saved structural paths: Price Fairness → Trust; Service Quality → Trust; Service Quality → Renewal; Trust → Renewal.

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.

   ![Gaussian-copula endogeneity prepared model or variable roles](../screenshots/gaussian-copula-endogeneity/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 → Gaussian-Copula Endogeneity Diagnostics**.

   ![Gaussian-copula endogeneity calculation setup](../screenshots/gaussian-copula-endogeneity/03-calculation-setup.png)

7. In the dedicated **Gaussian-Copula Endogeneity** workspace, complete the method-specific setting:

- Select Trust → Renewal as the focal path
- Leave other paths unselected for the exact tutorial result

8. Confirm that the status reports **1 focal path selected**, leave **Open results when finished** selected, and choose **Start Gaussian-copula diagnostic** once. Wait for **Completed**; do not close the project while the result is being saved.

9. In **Results**, confirm **Gaussian-copula endogeneity** is selected and inspect these outputs in order:

1. Joint equation coefficients
2. Source-normality diagnostics
3. Equation fit and sensitivity tables

   ![Gaussian-copula endogeneity primary result](../screenshots/gaussian-copula-endogeneity/04-results-primary.png)

   ![Gaussian-copula endogeneity secondary result](../screenshots/gaussian-copula-endogeneity/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.