On the specification of structural equation models for ecological systems

Abstract

The use of structural equation modeling (SEM) is often motivated by its utility for investigating complex networks of relationships, but also because of its promise as a means of representing theoretical concepts using latent variables. In this paper, we discuss characteristics of ecological theory and some of the challenges for proper specification of theoretical ideas in structural equation models (SE models). In our presentation, we describe some of the requirements for classical latent variable models in which observed variables (indicators) are interpreted as the effects of underlying causes. We also describe alternative model specifications in which indicators are interpreted as having causal influences on the theoretical concepts. We suggest that this latter nonclassical specification (which involves another variable type—the composite) will often be appropriate for ecological studies because of the multifaceted nature of our theoretical concepts. In this paper, we employ the use of meta‐models to aid the translation of theory into SE models and also to facilitate our ability to relate results back to our theories. We demonstrate our approach by showing how a synthetic theory of grassland biodiversity can be evaluated using SEM and data from a coastal grassland. In this example, the theory focuses on the responses of species richness to abiotic stress and disturbance, both directly and through intervening effects on community biomass. Models examined include both those based on classical forms (where each concept is represented using a single latent variable) and also ones in which the concepts are recognized to be multifaceted and modeled as such. To address the challenge of matching SE models with the conceptual level of our theory, two approaches are illustrated, compositing and aggregation. Both approaches are shown to have merits, with the former being preferable for cases where the multiple facets of a concept have widely differing effects in the system and the latter being preferable where facets act together consistently when influencing other parts of the system. Because ecological theory characteristically deals with concepts that are multifaceted, we expect the methods presented in this paper will be useful for ecologists wishing to use SEM.

How does pedogenesis drive plant diversity?

“…hypotheses can be tested empirically using long-term (i.e., thousands to millions of years) soil chronosequences as model systems (hereafter simply referred to as 'soil chronosequences') (Box 2). Finally, we describe how our conceptual model can serve as a meta-model for quantitative evaluation using structural equation modeling [6]. In doing this, we hope to stimulate and guide research along soil chronosequences on multivariate controls over plant diversity, particularly those that operate belowground.…”

“…Recent advances in quantitative modeling provide more rigorous guidance for evaluating the multiple and simultaneous underlying mechanisms using data [6]. Furthermore, there has been an infusion of new ideas into quantitative modeling, such as the discovery that it is necessary to formalize causal reasoning for artificial intelligence systems [55].…”

“…For understanding how pedogenesis drives plant diversity, our modeling is 'mediation focused'; that is, we wish to determine the dominant mechanisms that mediate the effects of pedogenesis on diversity. The general problem then becomes one of hypothesizing alternative mediating mechanisms, identifying measures that can serve as 'indicators' for underlying mechanisms, and then testing the direct and indirect causal implications of models [6]. This sequence of operations produces both an evaluation of the strengths of hypothesized linkages and the discovery of new linkages not predicted by our initial theories.…”

“…First, theoretical ideas are often only defined at the linguistic level. General concepts must therefore be carefully specified before they meet the criterion of being theoretical 'constructs' [6]. Of particular importance is the question of whether a construct is expected to have general, unidimensional influences in the system (i.e., behave as one entity) or whether it is in fact a collection of separate processes that are weakly correlated with one another (i.e., behave as a collection of entities).…”

“…Direct measure of primary production lost to consumers [35] Herbivore exclusion approaches [36] Effects of aboveground consumers on plant diversity depend on nutrient availability [31]; in productive environments, the preferred species are generally the dominant species, thus increasing diversity [ equation modeling (SEM), are well suited to this task, because they enable explicit linkage of theory to data and can test all direct and indirect causal implications that are derived from a conceptual model [6] (Box 3). A key challenge, however, is how to translate a theoretical model into one that can be evaluated quantitatively [6].…”