Key message Fitting allometric biomass models using ln-ln transformation approach can produce biased estimates, as in certain conditions correction factors were shown to overcompensate the back transformation bias. However, weighted nonlinear regression approach consistently provided unbiased estimates. Given the difficulty of correctly identifying error distributions, especially with unreliable normality tests, cautious method selection is essential to avoid biased biomass predictions. Context When fitting allometric biomass models, it is generally recommended to use logarithmic transformation for sample data from populations with lognormal distributions of aboveground biomass (AGB) errors and weighted nonlinear models for sample data from populations with normal AGB errors. However, when the type of AGB error distribution in the population is not accurately identified, an inappropriate fitting method may be adopted, potentially yielding biased AGB estimates. Aims The study aimed to compare the two fitting approaches (weighted nonlinear regression and logarithmic transformation with different correction factors) with respect to tree AGB prediction bias they produce. Methods Simulated finite populations of trees with normal and lognormal distributions of AGB errors were defined for three tree species. A Monte-Carlo procedure was used to assess the effects of fitting approaches on tree AGB prediction bias. Results Weighted nonlinear approach was an unbiased estimator of population mean tree AGB, unlike the logarithmic transformation, which, in certain conditions, was a biased estimator. The logarithmic transformation correction factors overcompensated the back transformation bias, creating a positive “overcompensation bias” of up to 2% when using logarithmic transformation for populations with a normal distribution of AGB errors. A commonly used correction factor overcompensated the bias even for populations with a lognormal distribution of AGB errors when sample size was small. Determining the appropriate fitting method proved challenging because of large Type II error rates (up to 73%) in the Shapiro–Wilk test of model residuals, suggesting that logarithmic transformation might erroneously appear appropriate for populations with normally distributed AGB errors, potentially leading to significant AGB prediction biases. The results were consistent across species, supporting their generalization. Conclusions To reduce tree AGB prediction bias, careful consideration should be given to the selection of the fitting approach in developing allometric biomass models.

Correction factors can overcompensate log-transformation bias in allometric biomass models

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2026年5月14日

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Ioan Dutcă

摘要

Key message

Fitting allometric biomass models using ln-ln transformation approach can produce biased estimates, as in certain conditions correction factors were shown to overcompensate the back transformation bias. However, weighted nonlinear regression approach consistently provided unbiased estimates. Given the difficulty of correctly identifying error distributions, especially with unreliable normality tests, cautious method selection is essential to avoid biased biomass predictions.

Context

When fitting allometric biomass models, it is generally recommended to use logarithmic transformation for sample data from populations with lognormal distributions of aboveground biomass (AGB) errors and weighted nonlinear models for sample data from populations with normal AGB errors. However, when the type of AGB error distribution in the population is not accurately identified, an inappropriate fitting method may be adopted, potentially yielding biased AGB estimates.

Aims

The study aimed to compare the two fitting approaches (weighted nonlinear regression and logarithmic transformation with different correction factors) with respect to tree AGB prediction bias they produce.

Methods

Simulated finite populations of trees with normal and lognormal distributions of AGB errors were defined for three tree species. A Monte-Carlo procedure was used to assess the effects of fitting approaches on tree AGB prediction bias.

Results

Weighted nonlinear approach was an unbiased estimator of population mean tree AGB, unlike the logarithmic transformation, which, in certain conditions, was a biased estimator. The logarithmic transformation correction factors overcompensated the back transformation bias, creating a positive “overcompensation bias” of up to 2% when using logarithmic transformation for populations with a normal distribution of AGB errors. A commonly used correction factor overcompensated the bias even for populations with a lognormal distribution of AGB errors when sample size was small. Determining the appropriate fitting method proved challenging because of large Type II error rates (up to 73%) in the Shapiro–Wilk test of model residuals, suggesting that logarithmic transformation might erroneously appear appropriate for populations with normally distributed AGB errors, potentially leading to significant AGB prediction biases. The results were consistent across species, supporting their generalization.

Conclusions

To reduce tree AGB prediction bias, careful consideration should be given to the selection of the fitting approach in developing allometric biomass models.