Latent health factor index: A statistical modeling approach for ecological health assessment

Multimetric indices (MMIs) are appealing scalar-valued tools for policy makers when rating ecosystems with respect to biological conditions that are not directly measurable. For conventional assessment of ecological health using MMIs, the quantitative calibration of health qualities can be specific to the investigator, and to the geographical region and time frame of interest. We propose a statistical-model-based approach that provides a systematic mechanism to construct MMIs; our approach aims to address some common issues of conventional practices, including the loss of information from data, spatio-temporal restrictions, and concerns over arbitrariness and costs. Our latent health factor index (LHFI) is obtained via statistical inference for an unobservable health factor term in a mixed-effects analysis-of-covariance regression that directly models the relationship among metrics, a very general notion of health, and factors that can influence health. We illustrate the approach by constructing an LHFI for a freshwater system using benthic taxonomic data in various Bayesian hierarchical formulations of generalized linear mixed models, implemented by Markov chain Monte Carlo techniques. The concept of the LHFI is also applicable to medical and other contexts.