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

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 suggeste...

Full description

Saved in:
Bibliographic Details
Published in:Ecology (Durham) 2011-10, Vol.92 (10), p.1887-1894
Main Authors: Xiao, Xiao, White, Ethan P, Hooten, Mevin B, Durham, Susan L
Format: Article
Language:English
Subjects:
allometry
Animal and plant ecology
Animal, plant and microbial ecology
Biological and medical sciences
Conservation biology
Datasets
Ecological genetics
Ecophysiology
Ecosystem
Environmental Monitoring - methods
Experimental data
Fundamental and applied biological sciences. Psychology
General aspects
Linear regression
log-transformation
model averaging
model comparison
Modeling
Models, Biological
Nonlinear Dynamics
nonlinear regression
parameter estimation
Parametric models
Point estimators
power law
Power laws
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0012-9658
1939-9170
DOI:10.1890/11-0538.1