用分层自相关分析比较数据
Analysis of comparative data with hierarchical autocorrelation
摘要：
在分层相关抽样单元下，研究了线性模型中估计和信息准则的渐近性态。这项工作的动机是收集的物种的生物数据，其中自相关是基于物种的系谱树。分层自相关也存在于许多其他类型的数据中，例如来自微阵列实验或人类语言的数据。在具有嵌套效应的ANOVA模型中也会出现类似的相关性。我表明，最好的线性无偏估计几乎肯定是收敛的，但可能不一致的一些参数，如截距和血统的影响，在布朗运动进化的背景下的系谱树。为了模型选择的目的，我表明，通常的BIC不提供一个适当的近似模型的后验概率。为了纠正这一点，有效的样本量是不一致的估计参数。对于生物学研究，这项工作意味着树感知的采样设计是可取的，增加更多的采样单位可能无助于祖先重建，只有强大的谱系效应可以检测到高功率。
英文摘要：
The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is based on the species' genealogical tree. Hierarchical autocorrelation is also found in many other kinds of data, such as from microarray experiments or human languages. Similar correlation also arises in ANOVA models with nested effects. I show that the best linear unbiased estimators are almost surely convergent but may not be consistent for some parameters such as the intercept and lineage effects, in the context of Brownian motion evolution on the genealogical tree. For the purpose of model selection I show that the usual BIC does not provide an appropriate approximation to the posterior probability of a model. To correct for this, an effective sample size is introduced for parameters that are inconsistently estimated. For biological studies, this work implies that tree-aware sampling design is desirable; adding more sampling units may not help ancestral reconstruction and only strong lineage effects may be detected with high power.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
