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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