Date of Award
2011
Degree Type
Report
Degree Name
Master of Science (MS)
Department
Mathematics and Statistics
Committee Chair(s)
Mevin Hooten
Committee
Mevin Hooten
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 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 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 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.
Recommended Citation
Xiao, Xiao, "On the Use of Log-Transformation vs. Nonlinear Regression for Analyzing Biological Power-Laws" (2011). All Graduate Plan B and other Reports, Spring 1920 to Spring 2023. 1219.
https://digitalcommons.usu.edu/gradreports/1219
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