Sanquetta Carlos Roberto, Dalla Corte Ana Paula, Behling Alexandre, de Oliveira Piva Luani Rosa, Péllico Netto Sylvio, Rodrigues Aurélio Lourenço, Sanquetta Mateus Niroh Inoue
Forest Science Department, Federal University of Paraná, Curitiba, Brazil.
Graduate Programme in Forestry, Federal University of Paraná, Curitiba, Brazil.
Carbon Balance Manag. 2018 Dec 7;13(1):25. doi: 10.1186/s13021-018-0112-6.
Biomass models are useful for several purposes, especially for quantifying carbon stocks and dynamics in forests. Selecting appropriate equations from a fitted model is a process which can involves several criteria, some widely used and others used to a lesser extent. This study analyzes six selection criteria for models fitted to six sets of individual biomass collected from woody indigenous species of the Tropical Atlantic Rain Forest in Brazil. Six models were examined and the respective fitted equations evaluated by the residual sum of squares, adjusted coefficient of determination, absolute and relative estimates of the standard error of estimate, and Akaike and Schwartz (Bayesian) information criteria. The aim of this study was to analyze the numeric behavior of these model selection criteria and discuss the ease of interpretation of them. The importance of residual analysis in model selection is stressed.
The adjusted coefficient of determination ([Formula: see text]) and the standard error of estimate in percentage (Syx%) are relative model selection criteria and are not affected by sample size and scale of the response variable. The sum of squared residuals (SSR), the absolute standard error of estimate (Syx), the Akaike information criterion and the Schwartz information criterion, in turn, depend on these quantities. The best fit model was always the same within a given data set regardless the model selection criteria considered (except for SSR in two cases), indicating they tend to converge to a common result. However, such criteria are not always closely related across different data sets. General model selection criteria are indicative of the average goodness of fit, but do not capture bias and outlier effects. Graphical residual analysis is a useful tool to this detection and must always be used in model selection.
It is concluded that the criteria for model selection tend to lead to a common result, regardless their mathematical formulation and statistical significance. Relative measures of goodness of fitting are easier to interpret than the absolute ones. Careful graphical residual analysis must always be used to confirm the performance of the models.
生物量模型在多个方面都很有用，特别是在量化森林中的碳储量和动态变化方面。从拟合模型中选择合适的方程是一个涉及多个标准的过程，有些标准被广泛使用，有些则使用较少。本研究分析了针对从巴西热带大西洋雨林的木本本土物种收集的六组个体生物量拟合的模型的六个选择标准。研究了六个模型，并通过残差平方和、调整后的决定系数、估计标准误差的绝对和相对估计值以及赤池和施瓦茨（贝叶斯）信息准则对各自的拟合方程进行了评估。本研究的目的是分析这些模型选择标准的数值行为，并讨论它们的易解释性。强调了残差分析在模型选择中的重要性。
调整后的决定系数（[公式：见正文]）和估计标准误差百分比（Syx%）是相对模型选择标准，不受样本大小和响应变量规模的影响。残差平方和（SSR）、估计标准误差的绝对值（Syx）、赤池信息准则和施瓦茨信息准则则依次取决于这些量。在给定的数据集中，无论考虑哪种模型选择标准（除了两种情况下的SSR），最佳拟合模型始终相同，这表明它们倾向于收敛到一个共同的结果。然而，不同数据集之间这些标准并不总是密切相关。一般的模型选择标准表明了平均拟合优度，但无法捕捉偏差和异常值效应。图形残差分析是检测这些问题的有用工具，在模型选择中必须始终使用。
得出的结论是，模型选择标准无论其数学公式和统计意义如何，都倾向于得出一个共同的结果。拟合优度的相对度量比绝对度量更易于解释。必须始终仔细进行图形残差分析以确认模型的性能。
