Consequences of metabolic scaling and log-scale allometry on means and variances and parameter estimates from Type I and Type II linear regression models

The slope bias when the predictor variable suffers from measurement errors is investigated. The presence of measurement errors can undermine the least squares linear regression parameter estimates, which in turn will have consequences if slope-based meaningful functions are calculated and used. Methods to determine suitable regression model choice are outlined. Also, the consequences of data size shrinkage due to scaling by metabolic weight in energy balance studies are illustrated. A problem arises when the assumed value of the metabolic index (b) changes. In the literature, this index varies from 0.62 to 0.75 for calculation of metabolic weight (MW) from live weight (LW) i.e. MW=LWb. The estimates of regression parameters vary according to the assumed value of the metabolic index b and that will impact further on intercept and slope based calculations. Similar problems occur when allometry functions are linearized using logarithmic transformation. Disproportional shrinkage of data size introduces scale bias which can introduce inaccuracies in further use of the regression parameters. Both of these issues have potential difficulties when using databases where data size is unevenly distributed