Ordinary least squares regression is indicated for studies of allometry |
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| Authors: | J T Kilmer R L Rodríguez |
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| Affiliation: | Behavioral and Molecular Ecology Group, Department of Biological Sciences, University of Wisconsin–Milwaukee, Milwaukee, WI, USA |
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| Abstract: | When it comes to fitting simple allometric slopes through measurement data, evolutionary biologists have been torn between regression methods. On the one hand, there is the ordinary least squares (OLS) regression, which is commonly used across many disciplines of biology to fit lines through data, but which has a reputation for underestimating slopes when measurement error is present. On the other hand, there is the reduced major axis (RMA) regression, which is often recommended as a substitute for OLS regression in studies of allometry, but which has several weaknesses of its own. Here, we review statistical theory as it applies to evolutionary biology and studies of allometry. We point out that the concerns that arise from measurement error for OLS regression are small and straightforward to deal with, whereas RMA has several key properties that make it unfit for use in the field of allometry. The recommended approach for researchers interested in allometry is to use OLS regression on measurements taken with low (but realistically achievable) measurement error. If measurement error is unavoidable and relatively large, it is preferable to correct for slope attenuation rather than to turn to RMA regression, or to take the expected amount of attenuation into account when interpreting the data. |
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| Keywords: | linear regression measurement error scaling relationships slope underestimation |
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