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 ( $$ R^{2}_{adj.} $$ ) 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.

中文翻译：

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用于估计巴西大西洋雨林中单个树木生物量的线性回归模型的选择标准。

生物量模型可用于多种目的，尤其是用于量化森林中的碳储量和动态。从拟合模型中选择合适的方程是一个过程，该过程可能涉及多个标准，其中一些广泛使用，而另一些则较少使用。这项研究分析了六种选择标准，这些标准适用于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。检查了六个模型，并通过残差平方和，调整后的确定系数，估计误差的绝对和相对估计值以及Akaike和Schwartz（贝叶斯）信息标准对各个拟合方程进行了评估。这项研究的目的是分析这些模型选择标准的数值行为，并讨论它们的易于解释。强调了残差分析在模型选择中的重要性。调整后的确定系数（$$ R ^ {2} _ {adj。} $$）和估计的标准误差百分比（Syx％）是相对的模型选择标准，不受样本大小和响应规模的影响变量。残差平方和（SSR），估计的绝对标准误（Syx），Akaike信息准则和Schwartz信息准则又取决于这些数量。无论考虑哪种模型选择标准（两种情况下的SSR除外），最佳拟合模型在给定的数据集中始终是相同的，这表明它们趋于收敛到相同的结果。但是，此类标准在不同数据集之间并不总是紧密相关。一般的模型选择标准指示平均拟合优度，但没有捕获偏差和离群值影响。图形残差分析是进行此检测的有用工具，必须始终在模型选择中使用。结论是，模型的选择标准往往会导致一个共同的结果，无论其数学公式和统计意义如何。相对拟合优度的度量比绝对度量的更容易解释。必须始终使用仔细的图形残差分析来确认模型的性能。但不要捕获偏差和离群值影响。图形残差分析是进行此检测的有用工具，必须始终在模型选择中使用。结论是，无论模型选择的标准是什么数学公式和统计意义如何，它都倾向于导致一个共同的结果。相对拟合优度的度量比绝对度量更容易解释。必须始终使用仔细的图形残差分析来确认模型的性能。但不要捕获偏差和离群值影响。图形残差分析是进行此检测的有用工具，必须始终在模型选择中使用。结论是，模型的选择标准往往会导致一个共同的结果，无论其数学公式和统计意义如何。相对拟合优度的度量比绝对度量更容易解释。必须始终使用仔细的图形残差分析来确认模型的性能。