Batterham A M, Tolfrey K, George K P
Department of Exercise and Sport Science, Crew and Alsager Faculty, Manchester Metropolitan University, United Kingdom.
J Appl Physiol (1985). 1997 Feb;82(2):693-7. doi: 10.1152/jappl.1997.82.2.693.
Intraspecific allometric modeling (Y = a.mass(b), where Y is the physiological dependent variable and a is the proportionality coefficient) of peak oxygen uptake (VO2peak) 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: 2,870-2,873, 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 aggression model: ln Y = 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 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 VO2peak 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.
种内异速生长模型（Y = a·质量^b，其中Y是生理因变量，a是比例系数）用于最大摄氧量（VO2peak）时，常常显示质量指数（b）大于从量纲理论预测的值，接近基础代谢率的克莱伯3/4指数。内维尔（《应用生理学杂志》77: 2870 - 2873, 1994）提出了一种解释和方法，可将膨胀的指数恢复到预期的2/3。在人类受试者中，该方法涉及在多元对数线性回归模型中添加“身高”作为连续预测变量：ln Y = a + c·ln身高 + b·ln质量 + ln ε，其中c是总体体型指数，ε是误差项。很可能严重的共线性混淆因素会对模型的可靠性和有效性产生不利影响。本研究的目的是严格检验内维尔的方法在青春期前、青少年和成年男性VO2peak建模中的应用。仅按质量进行标度时，发现平均指数为0.81（95%置信区间，0.65 - 0.97）。内维尔的方法将平均质量指数降至0.67（95%置信区间，0.44 - 0.9）。然而，对数变换后的身高和质量变量的方差膨胀因子和容忍度超过了已发表的严重共线性标准。主成分分析也诊断出两个主成分存在严重共线性，条件指数> 30，两个回归系数的方差分解比例超过50%。因此，得出的指数在数值上可能不准确且不稳定。总之，将平均质量指数恢复到预期的2/3可能是一个偶然的统计假象。
