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

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.