Beyond linearity - a new Partial Least Squares - Path Modelling (PLS-PM) inner weighting scheme for detecting and...

Area of Science:

• Statistics
• Econometrics
• Marketing Analytics

Background:

• Partial Least Squares - Path Modelling (PLS-PM) is a key method for Structural Equation Models (SEM).
• Traditional PLS-PM struggles with estimating nonlinear structural relationships between latent variables.
• Existing inner weighting schemes (centroid, factor, path) have limitations in capturing nonlinearity.

Purpose of the Study:

• To introduce a novel inner weighting scheme for PLS-PM.
• To enhance the detection and approximation of nonlinear structural relationships in SEM.
• To provide an alternative to existing weighting schemes for improved nonlinear analysis.

Main Methods:

• Proposed a new 'smooth weighting' inner weighting scheme for PLS-PM.
• Utilized a real marketing dataset to demonstrate practical application.
• Employed a simulated dataset to rigorously assess approximation capabilities for nonlinear forms.

Main Results:

• The smooth weighting scheme successfully recovers various nonlinear functional forms.
• Demonstrated superior performance compared to traditional schemes for sample sizes >75.
• Performance remained robust despite varying levels of error contamination in manifest variables.

Conclusions:

• The proposed smooth weighting scheme offers a significant advancement for PLS-PM in SEM.
• It provides a valuable tool for researchers needing to model complex, nonlinear associations.
• This method enhances the accuracy and applicability of SEM in fields like marketing and econometrics.