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14 - Case study 3: Separating the effects of explanatory variables

Published online by Cambridge University Press:  05 May 2014

Petr Šmilauer
Affiliation:
University of South Bohemia, Czech Republic
Jan Lepš
Affiliation:
University of South Bohemia, Czech Republic
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Summary

Introduction

In many cases, the effects of several explanatory variables need to be separated, even when the explanatory variables are correlated. The example below comes from a field fertilisation experiment (Pyšek & Lepš 1991). A barley field was fertilised with three types of nitrogen fertiliser (ammonium sulphate, calcium-ammonium nitrate, and liquid urea) and two different total nitrogen doses. For practical reasons, the experiment was not established in a correct experimental design, the plots are pseudoreplicates, which limits correct statistical inference (see Section 3.4). The experiment was designed by hydrologists to assess nutrient runoff and, consequently, smaller plots were not practical. In 122 plots, the species composition of weed community was recorded as classical Braun-Blanquet relevés (for the calculations, the ordinal transformation was used, i.e. numbers 1–7 were used for grades of the Braun-Blanquet scale: r, +, 1, .…, 5). The percentage cover of barley was estimated in all relevés.

The authors expected the weed community to be influenced both directly by fertilisers and indirectly through the effect of crop competition. Based on the experimental manipulations, the overall fertiliser effect can be assessed. However, barley cover is highly correlated with fertiliser dose. As the cover of barley was not manipulated, there is no direct evidence of the effect of barley cover on the weed assemblages. But the data enable us to partially separate the direct effects of fertilisation from the indirect effects of barley competition. This is done in a way similar to the separation of the effects of correlated predictors on the univariate response in multiple regression. The separation can be done using the variable of interest as an explanatory variable and the other one as a covariate.

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Publisher: Cambridge University Press
Print publication year: 2014

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