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Friday, October 25, 2013

WarpPLS 4.0 now available: 3D graphs, new fit indices, causality assessment coefficients, and more!

Dear colleagues:

Version 4.0 of WarpPLS is now available, as a beta version. You can download and install it for a free trial from:

The full User Manual is also available for download from the web site above separately from the software.

Some important notes for users of previous versions:

- There is no need to uninstall previous versions of WarpPLS to be able to install and use this new version.

- Users of previous versions can use the same license information that they already have; it will work for version 4.0 for the remainder of their license periods.

- Project files generated with previous versions are automatically converted to version 4.0 project files. Users are notified of that by the software, and given the opportunity not to convert the files if they so wish.

- The MATLAB Compiler Runtime 7.14, used in this version, is the same as the one used in versions 2.0-3.0. Therefore, if you already have one of those versions of WarpPLS installed on your computer, you should not reinstall the Runtime.

WarpPLS is a powerful PLS-based structural equation modeling (SEM) software. Since its first release in 2009, its user base has grown steadily, now comprising more than 5,000 users in over 33 countries.

Some of its most distinguishing features are the following:

- It is very easy to use, with a step-by-step user interface guide.

- It identifies nonlinear relationships, and estimates path coefficients accordingly.

- It also models linear relationships, using standard PLS algorithms.

- It models reflective and formative variables, as well as moderating effects.

- It calculates P values, model fit indices, and collinearity estimates.

At the beginning of the User Manual you will see a list of new features in this version, some of which are listed below. The User Manual has more details on how these new features can be useful in SEM analyses.

- Users can now set inner and outer model algorithms separately, and are also allowed to set inner model algorithms for individual paths.

- New causality assessment coefficients are now reported, which can be used in the assessment of the plausibility and direction of hypothesized cause-effect relationships.

- Seven new model fit and quality indices have been added to the three previously available, bringing the total number of indices to ten.

- Many new graphs and related features are now available, including 3D graphs. Both multivariate and bivariate relationship graphs are now provided, for linear and nonlinear relationships, using standardized and unstandardized scales.

- Users can now segment curves based on increments in the first derivative of the predictor latent variables on each of their criteria latent variables. This provides an alternative to data segmentation approaches such as FIMIX-PLS, without any reduction in sample size.


Wednesday, September 4, 2013

Using WarpPLS in E-Collaboration Studies: What if I Have Only One Group and One Condition?

A new article discussing methodological issues based on WarpPLS is available. The article is titled “Using WarpPLS in E-Collaboration Studies: What if I Have Only One Group and One Condition?” A full text version of the article is available here as a PDF file. Below is the abstract of the article.

What if a researcher obtains empirical data by asking questions to gauge the effect of an e-collaboration technology on task performance, but does not obtain data on the extent to which the e-collaboration technology is used? This characterizes what is referred to here as a scenario with one group and one condition, where the researcher is essentially left with only one column of data to be analyzed. When this happens, often researchers do not know how to analyze the data, or analyze the data making incorrect assumptions and using unsuitable techniques. Some of WarpPLS’s features make it particularly useful in this type of scenario, such as its support for small samples and the use of data that does not meet parametric assumptions. The main goal of this paper is to help e-collaboration researchers use WarpPLS to analyze data in this type of scenario, where only one group and one condition are available. Two other scenarios are also discussed – a typical scenario, and a scenario with one group and two before-after technology introduction conditions. While the focus here is on e-collaboration, the recommendations apply to many other fields.

Monday, June 3, 2013

Multi-group analyses with WarpPLS: The pooled standard error and Satterthwaite methods (and more)

The WarpPLS menu options “Explore multi-group analyses” and “Explore measurement invariance” allow you to conduct analyses where the data is segmented in various groups, all possible combinations of pairs of groups are generated, and each pair of groups is compared. In multi-group analyses normally path coefficients are compared, whereas in measurement invariance assessment the foci of comparison are loadings and/or weights. The grouping variables can be unstandardized indicators, standardized indicators, and labels. These types of analyzes can also be conducted via the menu option “Explore full latent growth”, which presents several advantages (as discussed in the WarpPLS User Manual).

Related YouTube videos:

Explore Multi-Group Analyses in WarpPLS

Explore Measurement Invariance in WarpPLS

I have also been asked how the standard errors reported by WarpPLS can be used in manual multi-group analyses (i.e., not automated) using the pooled standard error and Satterthwaite methods. These issues, as well as other related issues, are now addressed in one single publication:

Kock, N. (2014). Advanced mediating effects tests, multi-group analyses, and measurement model assessments in PLS-based SEM. International Journal of e-Collaboration, 10(3), 1-13.

This publication includes all of the equations used, and also addresses other tests, such as a test of mediating effects using the Sobel method. It is also a good reference for the automated approach employed in WarpPLS.

While using the WarpPLS menu options “Explore multi-group analyses” and “Explore measurement invariance” is recommended (and much less time-consuming), revised Excel spreadsheets are available from to partially automate the calculations for mediating effects tests and multi-group analyses, respectively:

Monday, April 29, 2013

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

- Isolate Mediating Effects in WarpPLS

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

Thursday, February 7, 2013

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 ***


*** Instructor ***

Ned Kock, Ph.D.
WarpPLS Developer

Friday, January 18, 2013

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).


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.