Fitting statistical models in bivariate allometry: scaling metabolic rate to body mass in mustelid carnivores

The ongoing debate about methods for fitting the two-parameter allometric equation y=ax(b) to bivariate data seemed to be resolved recently when three groups of investigators independently reported that statistical models fitted by the traditional allometric method (i.e., by back-transforming a linear model fitted to log-log transformations) typically are superior to models fitted by standard nonlinear regression. However, the narrow focus for the statistical analyses in these investigations compromised the most important of the ensuing conclusions. All the investigations focused on two-parameter power functions and excluded from consideration other simple functions that might better describe pattern in the data; and all relied on Akaike's Information Criterion instead of graphical validation to identify the better statistical model. My re-analysis of data from one of the studies (BMR vs. body mass in mustelid carnivores) revealed (1) that the best descriptor for pattern in the dataset is a straight line and not a two-parameter power function; (2) that a model with additive, normal, heteroscedastic error is superior to one with multiplicative, lognormal, heteroscedastic error; and (3) that Akaike's Information Criterion is not a generally reliable metric for discriminating between models fitted to different distributions. These findings have apparent implications for interpreting the outcomes of all three of the aforementioned studies. Future investigations of allometric variation should adopt a more holistic approach to analysis and not be wedded to the traditional allometric method.