A parsimonious approach for modeling uncertainty within complex nonlinear relationships

Advancements in information technology led environmental scientists to the illusion that efforts should be mainly focused on developing models that reduce uncertainty rather than on models adjusted to the existing uncertainty. As a result, environmental relationships are represented by non-parsimonious and suboptimal models, which in many instances could be even wrong. The objective of this research was to provide scientists focused on modeling ecosystem processes with a procedure that supplies parsimonious correct results. The procedure transforms the response variable to achieve a linear model and the normality of the residuals. After the parameters of the transformed model are estimated, the bias induced by back-transforming is corrected. We have computed the bias corrections for 11 of the most popular functions from the power, trigonometric, and hyperbolic families by considering the truncated normal distribution, when necessary. Using generated data, we have shown that the proposed procedure supplies unbiased results. We have identified a sample size artifact of data generation such that when the variance increases the truncation of distribution starts altering the corrections of predicted values, sometimes by more than 50% from the actual values. Our results indicate that uncertainty, measured by variance, impacts the analysis in a non-intuitive way when the defining domain of the response variable is restricted. The subtle way of influencing the development of complex nonlinear models by uncertainty advocates the usage of parsimonious linear models, which are less sensitive to the method of processing data. Finally, ecosystem processes should be modeled with strategies that consider not only processes and computation aspects, but also uncertainty, in particularly reducing variance to levels with no significant impact on the results.