8 - From biological hypotheses to structural equation models: the imperfection of causal translation

Summary

Abstract

It is possible to test a multivariate biological hypothesis concerning cause–effect relationships using structural equation modeling (SEM) applied to observational data. However, to do this we must translate from the language of causality to the language of probability distributions and this process of translation is almost always imperfect. One consequence of this imperfection of causal translation is the existence of equivalent SEM models; that is, different causal models that produce exactly equivalent statistical structural equation models. In this chapter I describe how such equivalent models arise, how to find equivalent models based on path diagrams, and why their existence complicates our interpretation of standard statistical tests in SEM. I illustrate these concepts using two actual path models taken from plant ecology.