Invariance Test: Detecting Difference Between Latent Variables Structure in Partial Least Squares Path Modeling

Abstract

In the context of heterogeneity, almost all partial least squares path modeling (PLS-PM) approaches focus on differences in the causal relationships between the latent variables. The principal goal is to detect segments that have different path coefficients in the structural model, yet inadequate attention is generally given to the measurement model. Thus, anytime that we define specific sub-models for different groups of individuals, we may wonder if the latent variables are the same in all detected sub-models. Taking this into consideration, the problem of invariance arises, meaning that if the estimation of latent variables are specific in each sub-model, there is reasonable doubt regarding whether we can compare the distinct behavior of individuals who belong to two different segments. In this paper, we present an invariance test as a possible solution, whereby the goal is to verify whether or not the measurement models of each sub-model may be assumed equal among themselves.

The Pathmox approach for PLS path modeling: Discovering which constructs differentiate segments

“…In this situation, it becomes difficult to guarantee that each construct in each segment is measuring the same latent concept, and it is not reliable to compare the latent variables for individuals belonging to different segments. This is an important issue that we shall continue to investigate, and which deserves further research.…”