Multilevel statistical models and the analysis of experimental data

Authors

  • Jocelyn E. Behm,

    Corresponding author
    1. Animal Ecology, Department of Ecological Science, Vrije Universitiet, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands
    2. Department of Zoology, University of Wisconsin, 430 Lincoln Drive, Madison, Wisconsin 53706 USA
    3. Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences, 88 Xuefu Road, Kunming 650223 People's Republic of China
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  • Devin A. Edmonds,

    1. Department of Zoology, University of Wisconsin, 430 Lincoln Drive, Madison, Wisconsin 53706 USA
    2. Xishuangbanna Tropical Botanical Garden, Chinese Academy of Sciences, 88 Xuefu Road, Kunming 650223 People's Republic of China
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  • Jason P. Harmon,

    1. Department of Entomology, North Dakota State University, P.O. Box 6050, Fargo, North Dakota 58108 USA
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  • Anthony R. Ives

    1. Department of Zoology, University of Wisconsin, 430 Lincoln Drive, Madison, Wisconsin 53706 USA
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  • Corresponding Editor: J. M. Levine.

Abstract

Data sets from ecological experiments can be difficult to analyze, due to lack of independence of experimental units and complex variance structures. In addition, information of interest may lie in complicated contrasts among treatments, rather than direct output from statistical tests. Here, we present a statistical framework for analyzing data sets containing non-independent experimental units and differences in variance among treatments (heteroscedasticity) and apply this framework to experimental data on interspecific competition among three tadpole species. Our framework involves three steps: (1) use a multilevel regression model to calculate coefficients of treatment effects on response variables; (2) combine coefficients to quantify the strength of competition (the target information of our experiment); and (3) use parametric bootstrapping to calculate significance of competition strengths. We repeated this framework using three multilevel regression models to analyze data at the level of individual tadpoles, at the replicate level, and at the replicate level accounting for heteroscedasticity. Comparing results shows the need to correctly specify the statistical model, with the model that accurately accounts for heteroscedasticity leading to different conclusions from the other two models. This approach gives a single, comprehensive analysis of experimental data that can be used to extract informative biological parameters in a statistically rigorous way.

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