On the use of log-transformation vs. nonlinear regression for analyzing biological power laws

Ecology
By: , and 

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Abstract

Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power laws using linear regression (LR) on log-transformed data has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations, we demonstrate that the error distribution determines which method performs better, with NLR better characterizing data with additive, homoscedastic, normal error and LR better characterizing data with multiplicative, heteroscedastic, lognormal error. Analysis of 471 biological power laws shows that both forms of error occur in nature. While previous analyses based on log-transformation appear to be generally valid, future analyses should choose methods based on a combination of biological plausibility and analysis of the error distribution. We provide detailed guidelines and associated computer code for doing so, including a model averaging approach for cases where the error structure is uncertain. ?? 2011 by the Ecological Society of America.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title On the use of log-transformation vs. nonlinear regression for analyzing biological power laws
Series title Ecology
DOI 10.1890/11-0538.1
Volume 92
Issue 10
Year Published 2011
Language English
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Ecology
First page 1887
Last page 1894