Gaussian Copula Regression Models
We offer two regression analysis examples for SmartPLS 4 that use the Gaussian copula approach to identify and deal with endogeneity issues in regression models. The Gaussian copula approach was introduced by
Park, S., & Gupta, S. (2012). Handling Endogenous Regressors by Joint Estimation Using Copulas. Marketing Science, 31(4), 567-586.
In its Gaussian copula implementation for regression models, but also for PLS-SEM, path models and other algorithms, SmartPLS uses the extended Gaussian copula framework presented in
Liengaard, B. D., Becker, J.-M., Bennedsen, M., Heiler, P., Taylor, L. N., & Ringle, C. M. (2025). Dealing with Regression Models’ Endogeneity by Means of an Adjusted Estimator for the Gaussian Copula Approach. Journal of the Academy of Marketing Science, 53, pp. 279–299.
The following two sample projects illustrate the use of the Gaussian copula approach for regression models in SmartPLS.
(1) Regression model with endogeneity issues based on simulated data to illustrate the Gaussian copula approach.
This sample SmartPLS 4 project uses a custom data set of 500 observations. The project includes examples for two models. Model 1 considers a single endogenous regressor, while Model 2 considers multiple endogenous regressors simultaneously. In addition to the regression models with Gaussian copula terms to identify and deal with endogeneity issues, we also show the regression model without the copula term. This illustrates the bias that can occur in regression models when researchers do not address endogeneity issues.
Simply download the project and import it into SmartPLS 4.
(2) Regression model example from Park and Gupta (2012)
We also provide the regression model example presented by Park and Gupta (2012). These authors use this example to illustrate the use of the Gaussian copula approach to identify and deal with endogeneity problems in this linear regression model. The data in this journal article example includes 260 observations for two different stores. Following Park and Gupta, we use a modified version of their dataset for our example. The project consists of two models. Model 1 considers a single endogenous regressor, while Model 2 considers multiple endogenous regressors simultaneously.
Simply download the project and import it into SmartPLS 4.
