Qian Song S, Shen Zehao
Nicholas School of the Environment and Earth Sciences, Duke University, Durham, North Carolina 27708, USA.
Ecology. 2007 Oct;88(10):2489-95. doi: 10.1890/06-2041.1.
A Bayesian representation of the analysis of variance by A. Gelman is introduced with ecological examples. These examples demonstrate typical situations encountered in ecological studies. Compared to conventional methods, the multilevel approach is more flexible in model formulation, easier to set up, and easier to present. Because the emphasis is on estimation, multilevel models are more informative than the results from a significance test. The improved capacity is largely due to the changed computation methods. In our examples, we show that (1) the multilevel model is able to discern a treatment effect that is smaller than the conventional approach can detect, (2) the graphical presentation associated with the multilevel method is more informative, and (3) the multilevel model can incorporate all sources of uncertainty to accurately describe the true relationship between the outcome and potential predictors.
A. 格尔曼对方差分析的贝叶斯表示法通过生态学实例被引入。这些实例展示了生态学研究中遇到的典型情况。与传统方法相比，多层次方法在模型构建上更灵活，更易于建立，也更易于呈现。由于重点在于估计，多层次模型比显著性检验的结果更具信息量。这种改进的能力很大程度上归功于计算方法的改变。在我们的实例中，我们表明：（1）多层次模型能够识别出比传统方法所能检测到的更小的处理效应；（2）与多层次方法相关的图形展示更具信息量；（3）多层次模型能够纳入所有不确定性来源，以准确描述结果与潜在预测变量之间的真实关系。
