Nevill's explanation of Kleiber's 0.75 mass exponent: an artifact of collinearity problems in least squares models?

Abstract

Batterham, Alan M., Keith Tolfrey, and Keith P. George.Nevill’s explanation of Kleiber’s 0.75 mass exponent: an artifact of collinearity problems in least squares models? J. Appl. Physiol. 82(2): 693–697, 1997.—Intraspecific allometric modeling ( Y = a ⋅ mass b , where Y is the physiological dependent variable and a is the proportionality coefficient) of peak oxygen uptake (V˙o 2 peak) has frequently revealed a mass exponent ( b) greater than that predicted from dimensionality theory, approximating Kleiber’s 3/4 exponent for basal metabolic rate. Nevill ( J. Appl. Physiol. 77: 2870–2873, 1994) proposed an explanation and a method that restores the inflated exponent to the anticipated 2/3. In human subjects, the method involves the addition of “stature” as a continuous predictor variable in a multiple log-linear regression model: ln Y = ln a + c ⋅ ln stature + b ⋅ ln mass + ln ε, where c is the general body size exponent and ε is the error term. It is likely that serious collinearity confounds may adversely affect the reliability and validity of the model. The aim of this study was to critically examine Nevill’s method in modelingV˙o 2 peak in prepubertal, teenage, and adult men. A mean exponent of 0.81 (95% confidence interval, 0.65–0.97) was found when scaling by mass alone. Nevill’s method reduced the mean mass exponent to 0.67 (95% confidence interval, 0.44–0.9). However, variance inflation factors and tolerance for the log-transformed stature and mass variables exceeded published criteria for severe collinearity. Principal components analysis also diagnosed severe collinearity in two principal components, with condition indexes >30 and variance decomposition proportions exceeding 50% for two regression coefficients. The derived exponents may thus be numerically inaccurate and unstable. In conclusion, the restoration of the mean mass exponent to the anticipated 2/3 may be a fortuitous statistical artifact.