NEVILL EXPLANATION OF KLEIBER 0.75 MASS EXPONENT - AN ARTIFACT OF COLLINEARITY PROBLEMS IN LEAST-SQUARES MODELS

Intraspecific allometric modeling (Y = a . mass(b), where Y is the phy siological dependent variable and a is the proportionality coefficient ) of peak oxygen uptake (Vo(2peak)) has frequently revealed a mass exp onent (b) greater than that predicted from dimensionality theory, appr oximating Kleiber's 3/4 exponent for basal metabolic rate. Nevill (J. Appl. Physiol. 77: 2870-2873, 1994) proposed an explanation and a, met hod that restores the inflated exponent to the anticipated 2/3. In hum an subjects, the method involves the addition of ''stature'' as a cont inuous predictor variable in a multiple log-linear regression model: I n Y = In a + c . ln stature + b . ln mass + ln epsilon, where c is the general body size exponent and epsilon is the error term. It is likel y that serious collinearity confounds may adversely affect the reliabi lity and validity of the model. The aim of this study was to criticall y examine Nevill's method in modeling Vo(2peak) in prepubertal, teenag e, 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). H owever, variance inflation factors and tolerance for the log-transform ed stature and mass variables exceeded published criteria for severe c ollinearity. Principal components analysis also diagnosed severe colli nearity in two principal components, with condition indexes >30 and va riance decomposition proportions exceeding 50% for two regression coef ficients. 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.