Bias in equations used to estimate fossil primate body mass

Abstract

Abstract The body mass of a fossil primate is often estimated from a regression equation in which both variables are transformed to logarithms. During this procedure, a bias is introduced when the body mass estimate derived in logarithmic units is detransformed back to arithmetic units. Detransformed estimates represent the geometric mean of the conditional distribution of the dependent variable at the selected value of the independent variable. This value is always less than the arithmetic mean; the difference between the geometric and arithmetic means being the magnitude of the bias. Several formulas have been proposed for correction factors that can be applied to predicted values to correct for this underestimation. The quasi-maximum likelihood estimate (QMLE), smearing estimate (SE), and ratio estimate (RE) are calculated for 12 equations that have been used to predict fossil primate body mass. A few of the equations have biases of 18-19%, but most are under 8%, and a few have 0-2% bias. The three estimators are compared and recommendations are made for their use. The magnitude of detransformation bias and the consistency of correction factors for an equation are criteria to be considered when selecting equations for paleontological inference.