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Department of Exercise and Sport Science, Crewe and Alsager Faculty, Manchester Metropolitan University, Alsager ST7 2HL, United Kingdom
Received 26 April 1996; accepted in final form 4 October 1996.
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 · massb,
where Y is the physiological dependent
variable and a is the proportionality
coefficient) of peak oxygen uptake
(
O2 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
, where c is the general body size
exponent and 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 modeling
O2 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.
allometry; multiple regression; log-linear models
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