Repeated measures refer to multiple observations obtained in the same sampling plot or experimental unit. Such observations can be taken in a particular period and the same local space in many cases. In either case, repeated measures lead to correlated data. Statistical analysis using correlated data without an appropriate covariance structure would lead to Type I or Type II errors. This study used rainfall interception data from a coniferous forest in Mexico, May to September 2010, to develop a multi-level linear model by assessing different covariance structures. Our main objectives were to evaluate the implications of these covariance structures in tests of fixed effects over categories of basal area and estimate differences between means and standard errors of each test. Based on the numerical inspection of the estimated correlations, their graphic representation, values of the statistics of fit (AICC and BIC) and considering that it is desirable to model a covariance structure in a parsimonious way, we concluded that the best selection for the structure of covariance was “heterogeneous Toeplitz.” Therefore, $F$-values of fixed effects and the estimates of differences between means and standard errors of each test based on the “heterogeneous Toeplitz” covariance structure were considered the most appropriate among the analyzed covariance models.

中文翻译：

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多层次模型中的协方差结构评估用于重复测量的森林降雨截取数据分析

重复测量是指在同一采样区或实验单元中获得的多个观测值。在许多情况下，可以在特定时期和相同的局部空间中进行此类观察。在任何一种情况下，重复测量都会导致相关数据。使用没有适当协方差结构的相关数据进行统计分析会导致 I 型或 II 型错误。本研究使用 2010 年 5 月至 2010 年 9 月墨西哥针叶林的降雨截取数据，通过评估不同的协方差结构来开发多层次线性模型。我们的主要目标是评估这些协方差结构在对基底区域类别的固定效应测试中的影响，并估计每个测试的均值和标准误差之间的差异。基于估计相关性的数值检查，他们的图形表示、拟合统计值（AICC 和 BIC），并考虑到需要以简约的方式对协方差结构进行建模，我们得出结论，协方差结构的最佳选择是“异构 Toeplitz”。所以，$F$- 基于“异质 Toeplitz”协方差结构的固定效应值以及每个检验的平均值和标准误差之间的差异估计值被认为是分析的协方差模型中最合适的。