Premium
On the use of log‐transformation vs. nonlinear regression for analyzing biological power laws
Author(s) -
Xiao Xiao,
White Ethan P.,
Hooten Mevin B.,
Durham Susan L.
Publication year - 2011
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/11-0538.1
Subject(s) - homoscedasticity , multiplicative function , log normal distribution , heteroscedasticity , nonlinear regression , transformation (genetics) , regression analysis , regression , monte carlo method , mathematics , nonlinear system , statistics , linear regression , variance (accounting) , computer science , biology , mathematical analysis , biochemistry , physics , accounting , quantum mechanics , business , gene
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.