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J. of the Acad. Mark. Sci. (2015) 43:115135 DOI 10.1007/s11747-014-0403-8
METHODOLOGICAL PAPER
A new criterion for assessing discriminant validity in variance-based structural equation modeling
Jrg Henseler & Christian M. Ringle & Marko Sarstedt
Received: 18 March 2014 /Accepted: 29 July 2014 /Published online: 22 August 2014 # The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract Discriminant validity assessment has become a generally accepted prerequisite for analyzing relationships between latent variables. For variance-based structural equation modeling, such as partial least squares, the Fornell-Larcker criterion and the examination of cross-loadings are the dominant approaches for evaluating discriminant validity. By means of a simulation study, we show that these approaches do not reliably detect the lack of discriminant validity in common research situations. We therefore propose an alternative approach, based on the multitrait-multimethod matrix, to assess discriminant validity: the heterotrait-monotrait ratio of correlations. We demonstrate its superior performance by means of a Monte Carlo simulation study, in which we compare the new approach to the Fornell-Larcker criterion and the assessment of (partial) cross-loadings. Finally, we provide guidelines on how to handle discriminant validity issues in variance-based structural equation modeling.
Keywords Structural equation modeling (SEM) . Partial least squares (PLS) . Results evaluation . Measurement model assessment . Discriminantvalidity .Fornell-Larckercriterion . Cross-loadings . Multitrait-multimethod (MTMM) matrix . Heterotrait-monotrait (HTMT) ratio of correlations
Introduction
Variance-based structural equation modeling (SEM) is growing in popularity, which the plethora of recent developments and discussions (e.g., Henseler et al. 2014; Hwang et al. 2010; Lu et al. 2011; Rigdon 2014; Tenenhaus and Tenenhaus 2011), as well as its frequent application across different disciplines, demonstrate (e.g., Hair et al. 2012a, b; Lee et al. 2011; Peng and Lai 2012; Ringle et al. 2012). Variance-based SEM methodssuch as partial least squares path modeling (PLS; Lohmller 1989; Wold 1982), generalized structured component analysis (GSCA; Henseler 2012; Hwang and Takane 2004), regularized generalized canonical correlation analysis (Tenenhaus and Tenenhaus 2011), and best fitting proper indices (Dijkstra and Henseler 2011)have in common that they employ linear composites of observed variables as proxies for latent variables, in order to estimate model relationships. The estimated strength of these relationships, most notably between the latent variables, can only be meaningfully interpreted if construct validity was established (Peter...