Testing mediating effects directly with WarpPLS

Since version 3.0, WarpPLS allows users to test mediating effects directly through inspection of coefficients generated for indirect and total effects, which include P values.

This allows for the direct test, without having to resort to intermediate calculations (e.g., Baron & Kenny; Preacher & Hayes), of mediation of various levels of complexity (e.g., multiple mediation).

WarpPLS also calculates total effects and respective P values, in addition to indirect effects. All of these are calculated whether linear or nonlinear analyses are conducted.

The two video clips below explain how to interpret indirect and total effects, and how to isolate complex mediating effects:

- View Indirect and Total Effects in WarpPLS

http://youtu.be/D9m4K_fv2vI

- Isolate Mediating Effects in WarpPLS

http://youtu.be/1wk5eedKupI

If you still want to use the Baron & Kenny and/or Preacher & Hayes approaches, please see the following blog posts:

http://warppls.blogspot.com/2010/07/testing-significance-of-mediating.html

http://warppls.blogspot.com/2011/06/testing-significance-of-mediating.html

Hands-On Workshop on WarpPLS; 31 May - 1 June 2013; San Antonio, Texas

*** Two-Day Hands-On Workshop on WarpPLS: SEM Fundamentals with Linear and Nonlinear Applications ***

Structural equation modeling (SEM), or path analysis with latent variables, is one of the most general and comprehensive statistical analysis methods. Path analysis, multiple regression, ANCOVA, ANOVA and other widely used statistical analysis methods can be seen as special cases of SEM.

WarpPLS is a very user-friendly and powerful SEM software tool, arguably the first of its kind to implement linear and nonlinear algorithms. It provides one of the most extensive sets of SEM outputs. Among other things it automatically calculates indirect and total effects and respective P values, as well as full collinearity estimates.

This SEM fundamentals workshop (details below) is aimed at beginner and intermediate SEM practitioners. Among possible participants are those who are interested in: (a) being productive co-authors or research collaborators, even if not doing SEM analyses themselves; (b) conducting basic SEM analyses occasionally in the future; (c) conducting SEM analyses of intermediate complexity on a regular basis.

*** Registration and additional details ***

http://bit.ly/VWTRlL

or

http://scriptwarp.com/warppls/prjs/2013_WarpPLSwkshp_Jun_SanAntonio

*** Instructor ***

Ned Kock, Ph.D.
WarpPLS Developer
http://nedkock.com

Easily calculating the GoF fit index with WarpPLS outputs

Note: The post below applies to version 3.0 of WarpPLS. In version 4.0 and newer versions of WarpPLS, the GoF index is calculated automatically, using the procedure outlined below. This index is referred to in WarpPLS as “Tenenhaus GoF”, in honor of Michel Tenenhaus.

***

This post is in response to a question I received late last year: How can one easily calculate the GoF index discussed by Tenenhaus et al. (2005) with WarpPLS outputs? Before getting into that, I would like to thank the participants in last week’s WarpPLS workshop in San Antonio, Texas – for attending, participating in the discussions, and asking very good questions. That was a knowledgeable group!

Tenenhaus et al. (2005) defined the GoF as the square root of the product between what they refer to as the average communality index and the average R-squared for the model. The communality index for a given latent variable is defined as the sum of the squared loadings for that latent variable, each loading associated with an indicator, divided by the number of indicators. The average communality index for a model is defined similarly, and takes all latent variables into account in its calculation.

I should note that the loadings we refer to above are the unrotated loadings, which are available from the structure loadings and cross-loadings table generated by WarpPLS. I should also note that the definition of the communality index above does not match the typical definition of communality, at least as it is normally stated in the context of factor analysis.

Here is the main point of this post: you do NOT need the average communality index to calculate the GoF using WarpPLS. Instead, you can use the average variances extracted (AVEs). As noted by Wetzels et al. (2009), the AVE for each latent variable equals the corresponding communality index. So the average AVE for the model can be used instead of the average communality index for the model. The formula for calculating the GoF proposed by Wetzels et al. (2009) then becomes:

GoF = square root of: (average AVE) x (average R-squared).

The average R-squared (ARS) is already provided by WarpPLS, as one of its three model fit indices in version 3.0 (there will be more fit indices in future versions of WarpPLS). The average AVE can be easily calculated based on the AVEs reported on the latent variable coefficients table. The figure below shows these outputs and the calculation of the corresponding GoF using Excel. The numbers are from a specific model that includes a formative variable, which is the reason for the low AVE of 0.244. There is some debate as to whether formative latent variables should be included in the calculation of the GoF. In this example, the formative latent variable was included.

The ARS, already provided by WarpPLS, is in my opinion a more conservative and robust measure of model fit than the GoF. The reason is that the AVE tends to go up as one removes indicators from a latent variable, going up to 1 for a latent variable with one single indicator. Therefore, a model where all latent variables are measured through single indicators (i.e., a path model, without “true” latent variables) will have a higher GoF than an equivalent model where the latent variables are measured through multiple indicators. The same will not happen with the ARS, which will also tend to be lower than the GoF for any model – and thus a more conservative measure of fit between the model and the data.

On a final note, Wetzels et al. (2009) also proposed the following thresholds for the GoF: small=0.1, medium=0.25, and large=0.36. They did so by assuming a minimum average AVE of 0.5, and using Cohen’s thresholds for small, medium and large effect sizes; the latter are discussed in the WarpPLS 3.0 User Manual (Kock, 2012).

References:

Kock, N. (2012). WarpPLS 3.0 User Manual. Laredo, Texas: ScriptWarp Systems.

Tenenhaus, M., Vinzi, V.E., Chatelin, Y.-M., & Lauro, C. (2005). PLS path modeling. Computational Statistics & Data Analysis, 48(1), 159-205.

Wetzels, M., Odekerken-Schroder, G., & van Oppen, C. (2009). Using PLS path modeling for assessing hierarchical construct models: Guidelines and empirical illustration. MIS Quarterly, 33(1), 177-196.

Hands-On Workshop on WarpPLS; 11-12 January 2013; San Antonio, Texas

*** Two-Day Hands-On Workshop on WarpPLS: SEM Fundamentals with Linear and Nonlinear Applications ***

Structural equation modeling (SEM), or path analysis with latent variables, is one of the most general and comprehensive statistical analysis methods. Path analysis, multiple regression, ANCOVA, ANOVA and other widely used statistical analysis methods can be seen as special cases of SEM.

WarpPLS is a very user-friendly and powerful software tool that can be used for SEM, arguably being the first of its kind to implement linear and nonlinear algorithms. This software provides one of the most extensive sets of SEM outputs; among other things it is the first of its kind to automatically calculate indirect and total effects and respective P values, as well as to calculate full collinearity estimates.

This SEM fundamentals workshop (details below) is designed to be useful to beginners and intermediate SEM practitioners. Among possible participants are those who are interested in: (a) being productive co-authors or research collaborators, even if not doing SEM analyses themselves; (b) conducting basic SEM analyses occasionally in the future; (c) conducting SEM analyses of intermediate complexity on a regular basis.

*** Registration and additional details ***

http://bit.ly/X0IHMP

or

http://scriptwarp.com/warppls/prjs/2013_WarpPLSwkshp_Jan_SanAntonio

*** Instructor ***

Ned Kock, Ph.D.
WarpPLS Developer
http://nedkock.com

*** Location and dates ***

Our Lady of the Lake University
San Antonio, Texas
11-12 January 2013 (Fri-Sat), 8 am–5 pm

*** Workshop program at a glance ***

The main goal of this workshop is to give participants a practical understanding of how to use the software WarpPLS to conduct variance-based SEM. The workshop is very hands-on and covers linear and nonlinear applications.

Day 1 of workshop
• Overview of workshop and formation of teams
• Overview of web resources: Video clips, blog, publications, spreadsheets, and templates
• Overview of steps 1 to 5 of a complete SEM analysis
• Hands-on exercise: Complete SEM analysis
• Resampling as shuffling multiple decks of cards
• Choosing the right resampling method
• Hands-on exercise: Resampling options
• Choosing the right warping (i.e., nonlinear) algorithm
• Viewing and interpreting plots of linear and nonlinear relationships
• Hands-on exercise: Linear and nonlinear relationships
• Charting non-standardized data
• Reporting results in non-standardized terms
• Hands-on exercise: Standardized to non-standardized results
• Reading discussion: WarpPLS User Manual

Day 2 of workshop
• Classical tests of mediating effects – Baron & Kenny and Preacher & Hayes
• Using indirect and total effect outputs to test mediating effects
• Hands-on exercise: Indirect/mediating and total effects
• Reading discussion: Kock & Verville’s free questionnaire data article
• Testing a moderating effect
• Double, triple etc. moderation
• Hands-on exercise: Moderating effects
• Adding control variables into an analysis
• Using second-, third- etc. order latent variables
• Conducting a multi-group analysis
• Hands-on exercise: Multi-group analysis
• Reading discussion: Kock & Lynn’s lateral collinearity article
• Conducting a full collinearity test
• Hands-on exercise: Team project using participant’s own data
• Presentation of results from team project

Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations

A new article discussing methodological issues based on WarpPLS is available. The article is titled “Lateral collinearity and misleading results in variance-based SEM: An illustration and recommendations”. It has been recently published in the Journal of the Association for Information Systems. A full text version of the article is available here as a PDF file. Below is the abstract of the article.

Variance-based structural equation modeling is extensively used in information systems research, and many related findings may have been distorted by hidden collinearity. This is a problem that may extend to multivariate analyses, in general, in the field of information systems as well as in many other fields. In multivariate analyses, collinearity is usually assessed as a predictor-predictor relationship phenomenon, where two or more predictors are checked for redundancy. This type of assessment addresses vertical, or “classic”, collinearity. However, another type of collinearity may also exist, here called “lateral” collinearity. It refers to predictor-criterion collinearity. Lateral collinearity problems are exemplified based on an illustrative variance-based structural equation modeling analysis. The analysis employs WarpPLS 2.0, with the results double-checked with other statistical analysis software tools. It is shown that standard validity and reliability tests do not properly capture lateral collinearity. A new approach for the assessment of both vertical and lateral collinearity in variance-based structural equation modeling is proposed and demonstrated in the context of the illustrative analysis.

View indirect and total effects in WarpPLS: YouTube video

A new YouTube video for WarpPLS is available; please see link below.

http://youtu.be/D9m4K_fv2vI

The video shows how to view and interpret indirect and total effects, as well as various related coefficients s (e.g., P values), calculated through a structural equation modeling (SEM) analysis using the software WarpPLS.

Enjoy!

Create and use second order latent variables in WarpPLS: YouTube video

A new YouTube video for WarpPLS is available; please see link below.

http://youtu.be/bkO6YoRK8Zg

The video shows how to create and use second (and higher) order latent variables with the structural equation modeling (SEM) analysis software WarpPLS.

Enjoy!