The expected value of the solution of the differential equation arising from the allometric hypothesis when the variables are random is found. This solution differs from the deterministic solution, so that predictions using the allometric equation which ignore the stochastic nature of the differential equation are biased. When lease squares estimation is carried out using the deterministic solution, ignoring the stochastic nature of the size variable, the estimate of the constant coefficient of the allometric equation may be severely biased. An example shows mild bias in estimates of the maturity parameter, but large bias in the estimate of the constant coefficient. To obtain unbiased estimates of the parameters in the allometric equation a factor equal to the reciprocal of the square of the size variable must be added to the usual log-log regression used to calculate estimates of the parameters. These results have application to models based on the allometric hypothesis, in particular models which are used in studies of carcass composition and the description of maintenance requirements in animal nutrition. When these models are used for prediction they need to be modified to account for any random variation occurring in the size variable.
Proceedings of the New Zealand Society of Animal Production, Volume 53, , 327-330, 1993
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