Thursday Links: Structural equation modeling resources for ecologists

I've recently jumped into the world of structural equation models (SEM) as I try to model direct and indirect drivers of fish habitat in the Columbia and Missouri River basins. While I have tried to stay current on the analytical methods being used in ecology and environmental science, I have only recently found myself saying, "there's a statistically measurable effect of B on A and A on C, but we intuitively know that variable A is only correlated to variable B, and C is the actual process driving the system..." What do I do, build some models and then use AIC to pull out the best model, accepting correlations as surrogate causes? Or do I try to decouple those direct and indirect effects? Fortunately for me and others who have response variables that are driven by seemingly direct and indirect effects, SEM provides the framework for testing composite hypotheses in theoretical models.

A case for SEMs in ecology: decoupling multiple lines of evidence can be difficult
SEM has been made popular by numerous books on the topic, but only recently have SEM methods become somewhat common in the statistical literature. Within R there are numerous packages to implement structural equation models. I have found lavaan, which has very thorough documentation and teaching materials, to be quite user-friendly. The SEM package is less well-documented and somewhat less convenient to implement, but has a nice, freely available book chapter by John Fox to accompany the SEM R package documentation

There are numerous free resources that explain how SEM can be used, include those works listed in James Graces', a recent paper in Ecosphere by Grace et al., Grace's website which includes a link to his 2006 book (not free), and the SEM website and SEM GitHub of Jarrett Byrnes. From these links, you can start to develop a library of code, example models, and documentation on how SEMs work both theoretically and technically. Oh, and Bill Shipley has a book on SEMs and path analysis.

I would be excluding a serious portion of the literature on SEMs were I to say that there are not prominent doubters of SEM approaches. Dynamic Ecology's Jeremy Fox is among them as he outlines in this 2012 post that received many lengthy replies akin to this piece by Jay-Z. Additionally, Andrew Gelman has worked to clarify the utility of SEMs in his recent comment on the comments that arose in NeuroImage.

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