Multi-group invariance testing: An illustrative comparison of PLS permutation and covariance-based SEM invariance analysis

Abstract

This paper provides a didactic example of how to conduct multigroup invariance testing distribution-free multi-group permutation procedure used in conjunction with Partial Least Squares (PLS).To address the likelihood that methods such as covariance-based SEM (CBSEM) with chi-square difference testing can enable group effects that mask noninvariance at lower levels of analysis problem, a variant of CBSEM invariance testing that focuses the evaluation on one parameter at a time (i.e. single parameter invariance testing) is proposed. Using a theoretical model from the field of Information Systems, with three exogenous constructs (routinization, infusion, and faithfulness of appropriation) predicting the endogenous construct of deep usage, the results show both techniques yield similar outcomes for the measurement and structural paths. The results enable greater confidence in the permutation-based procedure with PLS. The pros and cons of both techniques are also discussed.