Amanda M. Little | USGS Science

USGS2013

An algorithmic and information-theoretic approach to multimetric index construction

The use of multimetric indices (MMIs), such as the widely used index of biological integrity (IBI), to measure, track, summarize and infer the overall impact of human disturbance on biological communities has been steadily growing in recent years. Initially, MMIs were developed for aquatic communities using pre-selected biological metrics as indicators of system integrity. As interest in these bioassessment tools has grown, so have the types of biological systems to which they are applied. For many ecosystem types the appropriate biological metrics to use as measures of biological integrity are not known a priori. As a result, a variety of ad hoc protocols for selecting metrics empirically has developed. However, the assumptions made by proposed protocols have not be explicitly described or justified, causing many investigators to call for a clear, repeatable methodology for developing empirically derived metrics and indices that can be applied to any biological system. An issue of particular importance that has not been sufficiently addressed is the way that individual metrics combine to produce an MMI that is a sensitive composite indicator of human disturbance. In this paper, we present and demonstrate an algorithm for constructing MMIs given a set of candidate metrics and a measure of human disturbance. The algorithm uses each metric to inform a candidate MMI, and then uses information-theoretic principles to select MMIs that capture the information in the multidimensional system response from among possible MMIs. Such an approach can be used to create purely empirical (data-based) MMIs or can, optionally, be influenced by expert opinion or biological theory through the use of a weighting vector to create value-weighted MMIs. We demonstrate the algorithm with simulated data to demonstrate the predictive capacity of the final MMIs and with real data from wetlands from Acadia and Rocky Mountain National Parks. For the Acadia wetland data, the algorithm identified 4 metrics that combined to produce a -0.88 correlation with the human disturbance index. When compared to other methods, we find this algorithmic approach resulted in MMIs that were more predictive and comprise fewer metrics.

Ecological Indicators↗

USGS2012

Guidelines for a graph-theoretic implementation of structural equation modeling

Structural equation modeling (SEM) is increasingly being chosen by researchers as a framework for gaining scientific insights from the quantitative analyses of data. New ideas and methods emerging from the study of causality, influences from the field of graphical modeling, and advances in statistics are expanding the rigor, capability, and even purpose of SEM. Guidelines for implementing the expanded capabilities of SEM are currently lacking. In this paper we describe new developments in SEM that we believe constitute a third-generation of the methodology. Most characteristic of this new approach is the generalization of the structural equation model as a causal graph. In this generalization, analyses are based on graph theoretic principles rather than analyses of matrices. Also, new devices such as metamodels and causal diagrams, as well as an increased emphasis on queries and probabilistic reasoning, are now included. Estimation under a graph theory framework permits the use of Bayesian or likelihood methods. The guidelines presented start from a declaration of the goals of the analysis. We then discuss how theory frames the modeling process, requirements for causal interpretation, model specification choices, selection of estimation method, model evaluation options, and use of queries, both to summarize retrospective results and for prospective analyses. The illustrative example presented involves monitoring data from wetlands on Mount Desert Island, home of Acadia National Park. Our presentation walks through the decision process involved in developing and evaluating models, as well as drawing inferences from the resulting prediction equations. In addition to evaluating hypotheses about the connections between human activities and biotic responses, we illustrate how the structural equation (SE) model can be queried to understand how interventions might take advantage of an environmental threshold to limit Typha invasions. The guidelines presented provide for an updated definition of the SEM process that subsumes the historical matrix approach under a graph-theory implementation. The implementation is also designed to permit complex specifications and to be compatible with various estimation methods. Finally, they are meant to foster the use of probabilistic reasoning in both retrospective and prospective considerations of the quantitative implications of the results.

Ecosphere↗