Simpson’s paradox, moderation, and the emergence of quadratic relationships in path models

Among the many innovative features of WarpPLS are those that deal with identification of Simpson’s paradox and modeling of nonlinear relationships. A new article discussing various issues that are important for the understanding of the usefulness of these features is now available. Its reference, abstract, and link to full text are available below.

Kock, N., & Gaskins, L. (2016). Simpson’s paradox, moderation, and the emergence of quadratic relationships in path models: An information systems illustration. International Journal of Applied Nonlinear Science, 2(3), 200-234.

While Simpson’s paradox is well-known to statisticians, it seems to have been largely neglected in many applied fields of research, including the field of information systems. This is problematic because of the strange nature of the phenomenon, the wrong conclusions and decisions to which it may lead, and its likely frequency. We discuss Simpson’s paradox and interpret it from the perspective of path models with or without latent variables. We define it mathematically and argue that it arises from incorrect model specification. We also show how models can be correctly specified so that they are free from Simpson’s paradox. In the process of doing so, we show that Simpson’s paradox may be a marker of two types of co-existing relationships that have been attracting increasing interest from information systems researchers, namely moderation and quadratic relationships.

Among other things this article shows that: (a) Simpson’s paradox may be caused by model misspecification, and thus can in some cases be fixed by proper model specification; (b) a type of model misspecification that may cause Simpson’s paradox involves missing a moderation relationship that exists at the population level; (c) Simpson’s paradox may actually be a marker of nonlinear relationships of the quadratic type, which are induced by moderation; and (d) there is a duality involving moderation and quadratic relationships, which requires separate and targeted analyses for their proper understanding.

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Interview video: Conference on Information Systems in Latin America

Recently an interview was conducted for the 3rd Conference on Information Systems in Latin America. In it, Dr. Ned Kock was interviewed by Dr. Alexandre Graeml. The topics covered include: structural equation modeling (SEM), partial least squares (PLS) and related techniques, PLS-based SEM, covariance-based SEM, factors versus composites, nonlinear analyses, and WarpPLS.

WarpPLS and its application to research in business and information systems

The link below is for the Conference’s web site.

ISLA 2016 - Information Systems in Latin America Conference

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PLS-SEM performance with non-normal data

Many claims have been made in the past about the advantages of structural equation modeling employing the partial least squares method (PLS-SEM). While some claims may have been exaggerated, we are continuously finding that others have not. One of such claims, falling in the latter category (i.e., not an exaggeration), is that PLS-SEM is robust to deviations from normality. In other words, PLS-SEM performs quite well with non-normal data.

An article illustrating this advantage of PLS-SEM is available. Its reference, abstract, and link to full text are available below.

Kock, N. (2016). Non-normality propagation among latent variables and indicators in PLS-SEM simulations. Journal of Modern Applied Statistical Methods, 15(1), 299-315.

Structural equation modeling employing the partial least squares method (PLS-SEM) has been extensively used in business research. Often the use of this method is justified based on claims about its unique performance with small samples and non-normal data, which call for performance analyses. How normal and non-normal data are created for the performance analyses are examined. A method is proposed for the generation of data for exogenous latent variables and errors directly, from which data for endogenous latent variables and indicators are subsequently obtained based on model parameters. The emphasis is on the issue of non-normality propagation among latent variables and indicators, showing that this propagation can be severely impaired if certain steps are not taken. A key step is inducing non-normality in structural and indicator errors, in addition to exogenous latent variables. Illustrations of the method and its steps are provided through simulations based on a simple model of the effect of e-collaboration technology use on job performance.

The article’s main goal is actually to discuss a method to create non-normal data where the data creator has full access to all data elements, including factor or composite scores and all error terms, and where severe non-normality is extended to error terms. In the process of achieving this goal, the article actually demonstrates that PLS-SEM is very robust to severe deviations from normality, even when these deviations apply to all error terms. This is an issue that is often glossed over in PLS-SEM performance tests with non-normal data.

Readers may also find the YouTube video linked below useful in the context of this discussion.

View Skewness and Kurtosis in WarpPLS

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A thank you note to the participants in the 2016 PLS Applications Symposium

This is just a thank you note to those who participated, either as presenters or members of the audience, in the 2016 PLS Applications Symposium:

http://plsas.net/

As in previous years, it seems that it was a good idea to run the Symposium as part of the Western Hemispheric Trade Conference. This allowed attendees to take advantage of a subsidized registration fee, and also participate in other Conference sessions and the Conference's social event.

I have been told that the proceedings will be available soon from the Western Hemispheric Trade Conference web site.

Also, the full-day workshop on PLS-SEM using the software WarpPLS was well attended. This workshop was fairly hands-on and interactive. Some participants had quite a great deal of expertise in PLS-SEM and WarpPLS. It was a joy to have conducted the workshop!

As soon as we define the dates, we will be announcing next year’s PLS Applications Symposium. Like this years’ Symposium, it will take place in Laredo, Texas, probably in mid-April as well.

Thank you and best regards to all!