Navigating morphometric minefields: Modelling heteroscedasticity in length-conversion models

A common problem when combining data on species' traits from multiple sources is that researchers often measure the same trait in different ways. For example, the length of a shark can be measured in a straight-line or over-the-body, and for lengths that include the tail (e.g., fork and total lengths), with the tail in 'stretched' or 'natural' position. Statistical models comparing one variant to another can be used to standardise length measurements, thus allowing data to be combined. Often, when fitting such models, little attention is paid to the patterns of residuals, trusting that log-transforming the data adequately accounts for heteroscedasticity, or whether conversion models built with data from defrosted specimens can be used on data from fresh (or live) individuals. Using a Bayesian modelling approach, we compared the out-of-sample predictive performance of linear and log-linear models, with and without a model term that explicitly modelled heteroscedasticity as a function of the predictor variable, for converting between several length variants for school shark (Galeorhinus galeus). We found that point predictions were effectively identical across all four model forms. However, models including a term for heteroscedasticity produced superior predictive performance and prediction interval coverage. Measurements recorded from fresh individuals also fell within the prediction intervals of values estimated by models built using length variants measured from defrosted animals, suggesting that such models can be used to convert between length variants measured from fresh animals. Although the simpler models may be adequate for producing point estimates of the mean, models used to convert between length variants should include a term that explicitly models heteroscedasticity wherever prediction intervals or propagated uncertainty matter.