Allometric modeling does not determine a dimensionless power function ratio for maximal muscular function

Batterham, Alan M., and Keith P. George. Allometricmodeling does not determine a dimensionless power function ratio formaximal muscular function. J. Appl.Physiol. 83(6): 2158-2166, 1997.In the exercise sciences, simple allometry(y = ax^b) israpidly becoming the method of choice for scaling physiological andhuman performance data for differences in body size. The purpose ofthis study is to detail the specific regression diagnostics required tovalidate such models. The sum (T, in kg) of the "snatch" and"clean-and-jerk" lifts of the medalists from the 1995 Men's andWomen's World Weightlifting Championships was modeled as a function ofbody mass (M, in kg). A log-linearized allometric model (ln T = lna + bln M) yielded a common mass exponent(b) of 0.47 (95% confidenceinterval = 0.43-0.51, P < 0.01). However, size-related patterned deviations in the residuals wereevident, indicating that the allometric model was poorly specified and that the mass exponent was not size independent. Model respecification revealed that second-order polynomials provided the best fit, supporting previous modeling of weightlifting data (R. G. Sinclair. Can. J. Appl. Sport Sci. 10:94-98, 1985). The model parameters (means ± SE) were T = (21.48 ± 16.55) + (6.119 ± 0.359)M  (0.022 ± 0.002)M²(R² = 0.97) for men and T = (20.73 ± 24.14) + (5.662 ± 0.722)M  (0.031 ± 0.005)M²(R² = 0.92) for women. We conclude that allometric scaling should beapplied only when all underlying model assumptions have been rigorouslyevaluated.