发表机构
Universidad Nacional de Colombia; Universitat de les Illes Balears（哥伦比亚国立大学; 巴利阿里群岛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文比较了线性模型中双因素方差分析（TWA）与协方差分析（Ancova）处理nuisance参数的性能，通过理论分析和模拟实验发现，在协变量异质性复杂时Ancova在精度上更优，但在假设检验准确性上无优势。
AI 中文摘要
对实验或观测数据的分析通常需要控制次要兴趣变量的影响。处理此类参数的两种常见方法是将实验或观测单位分组为同质组（分组），以及对每个单位观测定量变量（协方差分析）。通常，两种方法均可使用，因此比较它们的性能便构成一个研究问题。具体而言，在分组由定量变量定义的随机完全区组设计中，人们有兴趣比较双因素方差分析（TWA）与协方差分析（Ancova）模型。受统计咨询中实际问题的启发，我们从分析和实证的角度比较了考虑区组效应的线性模型与考虑协变量效应的线性模型的性能。模型假设高斯误差，并包含T个处理效应。形式化比较依赖于正交投影和向量空间的理论，在由实验设计或数据结构条件引起的设计矩阵列空间的包含关系下进行。我们找到了TWA至少与Ancova一样精确以及这些模型等价的新近和样本量较小的条件。就实证角度而言，模型通过受农学实验启发的模拟研究进行比较。结果表明，当协变量呈现复杂的异质性模式时，Ancova在位置参数的精度方面优于采用传统方法定义区组的TWA，但在假设检验的准确性方面则不然。
英文摘要
The analysis of experimental or observational data often requires controlling for the effects of variables of secondary interest. Two common approaches to account for such parameters are grouping experimental or observational units into homogeneous groups (blocking), and observing quantitative variables on each one of them (covariance analysis). Often, both can be used and; therefore, comparing their performance poses a research question. Specifically, under randomized complete block designs where the blocks are defined by quantitative variables, there is interest in comparing the two-way Anova (TWA) with analysis of covariance (Ancova) models. Motivated by real-life problems coming from statistical consulting, we compared the performance of linear models considering block effects and those considering covariate effects from analytical and empirical perspectives. Models assumed Gaussian errors and included the effects of T treatments. The formal comparison relied on the theory of orthogonal projections and vector spaces under containment relationships of column spaces of the design matrices induced by conditions on the experimental design or data structure. We found asymptotic and small-sample conditions for the TWA to be at least as precise as the Ancova, as well as for these models to be equivalent. As to the empirical perspective, models were compared through a simulation study motivated by agronomical experiments. The results suggested that when the covariates show complex heterogeneity patterns, the Ancova outperforms the TWA with blocks defined by traditional approaches in terms of precision of location parameters, but not in hypothesis testing accuracy.
Comments36 pages, 3 figures
