Advanced Mediating Effects Tests, Multi-Group Analyses, and Measurement Model Assessments in PLS-Based SEM

Advanced Mediating Effects Tests, Multi-Group Analyses, and Measurement Model Assessments in PLS-Based SEM

Ned Kock (Division of International Business and Technology Studies, Texas A&M International University, Laredo, TX, USA)
Copyright: © 2014 |Pages: 13
DOI: 10.4018/ijec.2014010101
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Abstract

Use of the partial least squares (PLS) method has been on the rise among e-collaboration researchers. It has also seen increasing use in a wide variety of fields of research. This includes most business-related disciplines, as well as the social and health sciences. The use of the PLS method has been primarily in the context of PLS-based structural equation modeling (SEM). This article discusses a variety of advanced PLS-based SEM uses of critical coefficients such as standard errors, effect sizes, loadings, cross-loadings and weights. Among these uses are advanced mediating effects tests, comprehensive multi-group analyses, and measurement model assessments.
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Introduction

The partial least squares (PLS) method has been increasingly used by e-collaboration researchers, as well as by researchers in related fields, such as information systems. It also has seen increasing use in most business-related areas of investigation, as well as in fields of research related to the social and health sciences. This is particularly the case in the context of PLS-based structural equation modeling (SEM).

This article discusses a variety of advanced tests used in PLS-based SEM, with a focus on tests that employ the following coefficients: standard errors, effect sizes, loadings, cross-loadings, and weights. The discussion presented here builds on the software WarpPLS, version 4.0 (Kock, 2013). The extensive set of outputs generated by this software makes it particularly useful in the illustration of the tests discussed (Kock, 2010; 2011a; 2011b), and allows for a straightforward discussion of the different steps involved in those tests.

As it will be clear in the following sections, the approach taken in this article is very hands-on. This article is aimed at practitioners who need to conduct multivariate analyses as part of their research, analyses that can sometimes be very complex and difficult to conduct. Hopefully this article will make their work somewhat easier, as well as less time-consuming and prone to errors, serving as a handy reference that they can go to whenever they need to conduct advanced mediating effects tests, comprehensive multi-group analyses, and measurement model assessments.

Using Standard Errors and Effect Sizes for Path Coefficients

Standard errors and effect sizes for path coefficients are provided by WarpPLS in two tables where one standard error and effect size is provided for each path coefficient (see Figure 1). The effect sizes are similar to Cohen’s (1988)f-squared coefficients, but calculated through a novel procedure (described below). Standard errors and effect sizes are provided in the same order as the path coefficients, so that users can easily visualize them; and, in certain cases, use them to perform additional analyses.

Figure 1.

Standard errors and effect sizes for path coefficients window

Standard errors and effect sizes are provided for “normal” latent variables, as well as for latent variables associated with moderating effects, which are essentially interaction latent variables. These are indicated in column and row names as products between latent variables. For example, the cell whose row is “Effe” and whose column is “Proc*Effi” refers to the moderating effect of the latent variable “Proc” on the link between “Effi” and “Effe”.

The effect sizes are calculated as the absolute values of the individual contributions of the corresponding predictor latent variables to the R-square coefficients of the criterion latent variable in each latent variable block. Unlike Cohen’s (1988) formula for estimation of effect sizes in multiple regression, which has a correction term in its denominator, WarpPLS calculates the exact values of the individual contributions of the corresponding predictor latent variables to the R-square coefficients of the criterion latent variable they point at.

With the effect sizes users can ascertain whether the effects indicated by path coefficients are small, medium, or large. The values usually recommended are 0.02, 0.15, and 0.35; respectively (Cohen, 1988). Values below 0.02 suggest effects that are too weak to be considered relevant from a practical point of view, even when the corresponding P values are statistically significant; a situation that may occur with large sample sizes.

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