Using relative brain size as predictor variable: Serious pitfalls and solutions

There is a long-standing interest in the effect of relative brain size on other life history variables in a comparative context. Historically, residuals have been used to calculate these effects, but more recently it has been recognized that regression on residuals is not good practice. Instead, absolute brain size and body size are included in a multiple regression, with the idea that this controls for allometry. I use a simple simulation to illustrate how a case in which brain size is a response variable differs from a case in which relative brain size is a predictor variable. I use the simulated data to test which modeling approach can estimate the underlying causal effects for each case. The results show that a multiple regression model with both body size and another variable as predictor variable and brain size as response variable work well. However, if relative brain size is a predictor variable, a multiple regression fails to correctly estimate the effect of body size. I propose the use of structural equation models to simultaneously estimate relative brain size and its effect on the third variable and discuss other potential methods.