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Parameter landscapes unveil the bias in allometric prediction
Article first published online: 18 JAN 2010
© 2010 The Authors. Journal compilation © 2010 British Ecological Society
Methods in Ecology and Evolution
Volume 1, Issue 1, pages 69–74, March 2010
How to Cite
Hui, C., Terblanche, J. S., Chown, S. L. and McGeoch, M. A. (2010), Parameter landscapes unveil the bias in allometric prediction. Methods in Ecology and Evolution, 1: 69–74. doi: 10.1111/j.2041-210X.2009.00005.x
- Issue published online: 23 FEB 2010
- Article first published online: 18 JAN 2010
- Received 2 October 2009; accepted 23 November 2009 Handling Editor: Robert P. Freckleton
- linear regression;
- log transformation;
- power law;
1. The criteria for choosing the appropriate line-fitting method (LFM) and correction estimator for determining the functional allometric relationship, and for predicting the Y-variable accurately are controversial. A widely accepted criterion for reducing bias in allometric prediction is to minimize the mean squared residual (MSR) on the antilog scale, and a series of correction estimators have been designed precisely to achieve this.
2. Here, using parameter landscapes, we examine the performance of the correction estimators and several LFMs under different data reszidual shapes, sample sizes and coefficients of determination.
3. Predictions from the nonlinear LFM were found to have minimum MSR values (minimum bias), but with obviously skewed frequency distributions of the predicted Y-variable compared with observed data. This implies that using MSR as a bias measure for allometric prediction could be misleading.
4. We introduce a new bias measure, the discrepancy of the frequency distributions of the Y-variable between predicted and observed data, and suggest that the reduced major axis method is the least biased method in most cases, both on the logarithmic and antilog scales.
5. Parameter landscapes clearly illustrate the performance of each LFM and correction estimator, as well as the best solution given specified criteria. We therefore suggest a shift in emphasis from designing more sophisticated LFM or correction estimators (equal to finding the peaks in the parameter landscape) to justifying the measure of bias and performance criterion in allometric prediction.