Skip to Main Content
U.S. Forest Service
Caring for the land and serving people

United States Department of Agriculture

Home > Search > Publication Information

  1. Share via EmailShare on FacebookShare on LinkedInShare on Twitter
    Dislike this pubLike this pub
    Author(s): Sean M. McMahon; Jeffrey M. Diez
    Date: 2007
    Source: Ecology letters, Vol. 10: 1-16
    Publication Series: Miscellaneous Publication
    PDF: Download Publication  (3.07 MB)


    A fundamental challenge to understanding patterns in ecological systems lies in employing methods that can analyse, test and draw inference from measured associations between variables across scales. Hierarchical linear models (HLM) use advanced estimation algorithms to measure regression relationships and variance-covariance parameters in hierarchically structured data. Although hierarchical models have occasionally been used in the analysis of ecological data, their full potential to describe scales of association, diagnose variance explained, and to partition uncertainty has not been employed. In this paper we argue that the use of the HLM framework can enable significantly improved inference about ecological processes across levels of organization. After briefly describing the principals behind HLM, we give two examples that demonstrate a protocol for building hierarchical models and answering questions about the relationships between variables at multiple scales. The first example employs maximum likelihood methods to construct a two-level linear model predicting herbivore damage to a perennial plant at the individual- and patch-scale; the second example uses Bayesian estimation techniques to develop a three-level logistic model of plant flowering probability across individual plants, microsites and populations. HLM model development and diagnostics illustrate the importance of incorporating scale when modelling associations in ecological systems and offer a sophisticated yet accessible method for studies of populations, communities and ecosystems. We suggest that a greater coupling of hierarchical study designs and hierarchical analysis will yield significant insights on how ecological processes operate across scales.

    Publication Notes

    • You may send email to to request a hard copy of this publication.
    • (Please specify exactly which publication you are requesting and your mailing address.)
    • We recommend that you also print this page and attach it to the printout of the article, to retain the full citation information.
    • This article was written and prepared by U.S. Government employees on official time, and is therefore in the public domain.


    McMahon, Sean M.; Diez, Jeffrey M. 2007. Scale of association: hierarchical linear models and the measurement of ecological systems. Ecology letters, Vol. 10: 1-16


    bayesian statistics, hierarchical linear models, inference, maximum liklihood, multilevel models, regression, scale, variance components

    Related Search

    XML: View XML
Show More
Show Fewer
Jump to Top of Page