Multi-group Invariance Testing: An Illustrative Comparison of PLS Permutation and Covariance-Based SEM Invariance Analys
This paper provides a didactic example of how to conduct multi-group 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-base
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Multi-group Invariance Testing: An Illustrative Comparison of PLS Permutation and Covariance-Based SEM Invariance Analysis Wynne W. Chin, Annette M. Mills, Douglas J. Steel, and Andrew Schwarz
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. Keywords Multi-group Invariance Testing • Permutation Analysis • PLS • Covariance Based SEM
W.W. Chin () Department of Decision and Information Systems, C. T. Bauer College of Business, University of Houston, Houston, TX 77204–6021, USA e-mail: [email protected] A.M. Mills Department of Accounting and Information Systems, College of Business and Economics, University of Canterbury, Ilam Christchurch 8140, New Zealand e-mail: [email protected] D.J. Steel Department of Management Information Systems, School of Business, University of Houston-Clear Lake, Houston, TX 77058, USA e-mail: [email protected] A. Schwarz Louisiana State University, Baton Rouge LA, USA e-mail: [email protected] © Springer International Publishing Switzerland 2016 H. Abdi et al. (eds.), The Multiple Facets of Partial Least Squares and Related Methods, Springer Proceedings in Mathematics & Statistics 173, DOI 10.1007/978-3-319-40643-5_20
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20.1 Introduction Multi-group invariance (MGI) testing is a technique that allows researchers to determine whether parameters of a measurement model and/or the structural model are equivalent (i.e. invariant) across two or more groups (Breckler 1990; Byrne 2010). For the measurement model, invariance testing indicates whether the items used mean the same thing to respondents from different groups or populations (Cheung and Rensvold 2002). If invariance cannot be established, it would be difficult to determine if the differences observed are due to true differences or to different psychometric responses to the items. For the structural model, MGI testing indicates whether the structural paths are equivalent across groups. MGI testing also provides a particularly strong test of the validity of the measurement model and replicability of the structural model across settings. Covariance-based SEM (CBSEM) using chi-sq
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