Individual paths can be set as linear or nonlinear in PLS-SEM analyses

In WarpPLS, the “View or change individual inner model analysis algorithm settings” option allows you to set inner model algorithms for individual paths in PLS-SEM analyses; whether these analyses are composite-based or factor-based. That is, for each path a user can select a different algorithm from among the following choices: “Linear”, “Warp2”, “Warp2 Basic”, “Warp3”, and “Warp3 Basic”.

This option is particularly useful in empirical investigations where researchers have solid theoretical reasons to expect certain paths to be associated with nonlinear relationships of particular types. Those researchers may also have solid theoretical reasons to expect certain paths to be associated with linear relationships. Given that one of the main goals of SEM is to test theory, theoretical considerations should be given a very high priority in the selection of algorithms to be used for each path in a model.

There is a short video that illustrates this ().

On a related note - since classic moderating effects analyses already capture nonlinearity, it is usually advisable for users to set moderating paths as linear. They can do this even as they set direct paths as nonlinear. This leads to 2D graphs that are easier to interpret. If users set moderating paths as nonlinear, their interpretation becomes more difficult, as more complex types of moderating relationships are captured.

How to theorize nonlinear relationships and test them: A journal article example

How can a researcher theorize nonlinear relationships and test them? This question is addressed through the publication below, which provides an example of nonlinear theorizing and related empirical analysis. To the best of our knowledge, this is one of the first articles that exemplifies how nonlinear theorizing can be incorporated into a casual model and tested with WarpPLS.

Kock, N., Mayfield, M., Mayfield, J., Sexton, S., & De La Garza, L. (2019). Empathetic leadership: How leader emotional support and understanding influences follower performance. Journal of Leadership and Organizational Studies, 26(2), 217-236.

A link to a PDF file is available ().

Abstract:

This article presents a theory of empathetic leadership and its initial test. Empathetic leadership provides a model of how leader understanding and support improves follower behaviors and affective states. For this article, we explored the link between empathetic leadership and follower performance. Specifically, we tested the causal processes by which empathetic language influences follower performance. These processes include follower job satisfaction and innovation. Findings support model hypotheses and provide preliminary causal support for the model.