Calculating the variance and prediction intervals for estimates obtained from allometric relationships

Abstract

Often researchers are interested in obtaining estimates of variables which are quite difficult or expensive to measure. To obtain these estimates, relationships between those variables of interest and more easily measured variables are used. These relationships are referred to as allometric equations. In science it is important to quantify the error associated with an estimate in order to determine the reliability of the estimate. Therefore, prediction intervals or standard errors are usually quoted with estimated values. In the case of allometric equations, information about the original fitting of the allometric relationship is needed in order to put a prediction interval around an estimated value. However, often all the information required to calculate this prediction interval is not provided with published allometric equations, forcing the users of these equations to use alternative, less rigorous methods of obtaining error estimates. This paper will explain the method behind obtaining prediction intervals for allometric estimates, and what information is required from the original fitting of the allometric relationships. This information seeks to provide researchers with the necessary parameters which should be published with allometric relationships. In addition, a method is explained for how to deal with relationships which are in the power function form – a common form for allometric relationships