Nevill's explanation of kleiber's 0.75 mass exponent: a fortuitous
artifact of collinearity problems in least squares models.
Batterham, Alan M., Keith Tolfrey, and Keith P. George.
Department of Exercise and Sport Sciences, the Manchester
Metropolitan University, Crewe and Alsager Faculty, Hassall Road,
Alsager, ST7 2HL, ENGLAND
APStracts 3:0464A, 1996.
Intraspecific allometric modeling (Y = a . massb) of peak VO2, 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(. 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 modeling peak VO2 in prepubertal, teenage, and adult males.
A mean exponent of 0.81 (95% CI, 0.65-0.97) was found when scaling by
mass alone. Nevill's method reduced the mean mass exponent to 0.67
(95% CI, 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 Indices > 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.
Received 26 April 1996; accepted in final form 4 October 1996.
APS Manuscript Number A403-6.
Article publication pending Journal of Applied Physiology.
ISSN 1080-4757 Copyright 1996 The American Physiological Society.
Published in APStracts on 5 November 1996