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I am trying to understand the graph topology of the structural equation model (SEM) given in Figure 1 of Bisset et al 2023. It is stated in the paper that it reflects an a priori causal structure.

I am trying to understand why the SEM assumes that climate variables do not affect the vegetation coverage variables. It seems like basic plant biology that they are affected by precipitation, humidity and temperature. Did I miss something about the nature of the coverage estimates?

Why would vegetation coverage not be assumed to be caused (in part at least) by climate these climate variables?

  • EC: electric conductivity
  • OC: organic carbon
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    $\begingroup$ Probably mostly because people misuse these sorts of models all the time. $\endgroup$
    – Bryan Krause ♦
    Commented Aug 26, 2023 at 15:27

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The title of the article is (my emphasis):

Linking niche size and phylogenetic signals to predict future soil microbial relative abundances.

To look at bacterial abundance, they generated models that look at factors that affect bacterial abundance. In this case, this is a mathematical model that is used to describe the effect (emphasis mine):

Whereas a number of multivariate methods are largely descriptive and more appropriate for exploratory analyses, SEM is able to test a network of causal hypotheses and is recommended for evaluation of multivariate hypotheses (Grace, 2006; Grace et al., 2012). Specifically, we used SEM because it allows the evaluation of simultaneous influences...

...The method is thus appropriate for establishing probable causality at the system (for example, climate-vegetation-soil-bacteria), rather than the individual level (for example, climate–bacteria).

So, they are generating a model that looks specifically at establishing a causal model for bacterial abundance only. This model does not seek to establish causality for other factors, such as vegetation cover, even though this might be related to some of the factors being investigated. In fact the models explain mathematically only the significant factors for bacterial abundance, and factors that are left out of the model have no effect in the system being described - basically Occam's razor being applied.

You could indeed examine vegetation cover using a variables used in this system, but you would need to establish a whole new mathematical model to do so, and you might well find that the variables are different or need other factors not shown in this model.

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  • $\begingroup$ I disagree with you and the authors on how to proceed with causal inference (see Pearl 2009 for an introduction), but your answer clarifies why the authors might have thought to exclude this relation between climate and vegetation. $\endgroup$
    – Galen
    Commented Aug 27, 2023 at 15:00
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    $\begingroup$ @Galen I agree, it doesn't make sense to a me either, but this is how the mathematical models work, for better or worse. The factors that they show in the model are explicitly the ones that affect the thing being looked at and explicitly exclude those that don't, even though from a logical sense it might make sense to include them. Basically aiming for a minimal component model. $\endgroup$
    – bob1
    Commented Aug 27, 2023 at 20:54
  • $\begingroup$ I have substantial disagreements with you, but I don't think it will be productive to clarify and argue here. It just isn't a great venue for it. There is a rigorous approach to thinking about statistical models in conjunction with causality. The book I cited is a detailed account, but if you don't have the time/money for it you might find Science Before Statistics: Causal Inference to be a feasible investment at least to get the general idea. $\endgroup$
    – Galen
    Commented Aug 27, 2023 at 21:32
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    $\begingroup$ @Galen I'm not a modeler or anything of the sort, but thanks for the link. I agree this isn't the right place for discussion of your point. I've had similar arguments with modelers in the past, with me in your position, so I totally understand where you are coming from. $\endgroup$
    – bob1
    Commented Aug 27, 2023 at 21:44

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