Ecological Society of America
Power-law relationships are among the most well-studied functional relationships in biology. Recently the common practice of fitting power-laws using linear regression on log-transformed data (LR) 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 LR better characterizing data with multiplicative lognormal error and NLR better characterizing data with additive, homoscedastic, normal 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.
Xiao, X., White, E.P., M.B. Hooten, and S.L. Durham. 2011. On the use of logtransformation vs. nonlinear regression for analyzing biological powerlaws. Ecology 92: 18871894.