A flexible way to study composites in ecology using structural equation modeling

Composites, which refer to weighted linear combinations of variables, are receiving increasing attention in the field of ecology. In practice, however, researchers relying on the common approaches to study composites encounter limitations in flexibly specifying composites with structural equation modeling (SEM). To enrich the researchers' statistical toolbox and to flexibly model composites in structural equation models, we introduce the Henseler-Ogasawara (H-O) specification to the field of ecology. As we show in this paper, this approach can not only mimic the common approaches such as the one-step and two-step approaches, but also offers improvements. Compared to the two-step approach, the H-O specification explicitly models composites, i.e., it takes into account the formation of the composites and it allows modeling composites with free weights and with fixed weights, i.e., unknown-weight and fixed weight composites. Consequently, this specification allows for a more in-depth model assessment. Compared to the one-step approach, the H-O specification offers more modeling flexibility. For example, it allows researchers to specify the effects of other variables on a composite. Consequently, conceptual models can be more adequately represented by the statistical model using this specification. To demonstrate these advantages, we provide an ecological illustrative example including the R code to reproduce our results. Specifically, we present different H-O specifications and compare them statistically. Our analysis also shows that the specified model, closest to the conceptual model of the illustrative example does not adequately describe the data. Instead, a model that does not assume that all covariances between the components of the composites are accounted for by the composites fits the data well.