Pagliari Paulo, Galindo Fernando Shintate, Strock Jeffrey, Rosen Carl
Department of Soil, Water, and Climate, Southwest Research and Outreach Center, University of Minnesota, Lamberton, MN 56152, USA.
Center for Nuclear Energy in Agriculture, University of São Paulo, Piracicaba 13416-000, SP, Brazil.
Plants (Basel). 2022 Jul 5;11(13):1783. doi: 10.3390/plants11131783.
Field studies conducted over time to collect any type of plant response to a set of treatments are often not treated as repeated measures data. The most used approaches for statistical analyses of this type of longitudinal data are based on separate analyses such as ANOVA, regression, or time contrasts. In many instances, during the review of manuscripts, reviewers have asked researchers to treat year, for example, as a random effect and ignore the interactions between year and other main effects. One drawback of this approach is that the correlation between measurements taken on the same subject over time is ignored. Here, we show that avoiding the covariance between measurements can induce erroneous (e.g., no differences reported when they exist, or differences reported when they actually do not exist) inference of treatment effects. Another issue that has received little attention for statistical inference of multi-year field experiments is the combination of fixed, random, and repeated measurement effects in the same statistical model. This type of analysis requires a more in-depth understanding of modeling error terms and how the statistical software used translates the statistical language of the given command into mathematical computations. Ignoring possible significant interactions among repeated, fixed, and random effects might lead to an erroneous interpretation of the data set. In this manuscript, we use data from two field experiments that were repeated during two and three consecutive years on the same plots to illustrate different modeling strategies and graphical tools with an emphasis on the use of mixed modeling techniques with repeated measures.
随着时间推移进行的实地研究，旨在收集任何类型植物对一组处理的反应，但这些研究通常不被视为重复测量数据。对这类纵向数据进行统计分析时，最常用的方法是基于诸如方差分析、回归或时间对比等单独分析。在许多情况下，在审阅稿件时，审稿人会要求研究人员将年份等视为随机效应，并忽略年份与其他主要效应之间的相互作用。这种方法的一个缺点是忽略了同一受试者在不同时间进行测量之间的相关性。在此，我们表明，避免测量之间的协方差会导致对处理效果的错误推断（例如，存在差异时却报告无差异，或实际无差异时却报告有差异）。对于多年实地实验的统计推断，另一个很少受到关注的问题是在同一统计模型中固定效应、随机效应和重复测量效应的组合。这种类型的分析需要更深入地理解建模误差项，以及所使用的统计软件如何将给定命令的统计语言转化为数学计算。忽略重复效应、固定效应和随机效应之间可能存在的显著相互作用，可能会导致对数据集的错误解释。在本手稿中，我们使用了在同一地块上连续两年和三年重复进行的两个实地实验的数据，以说明不同的建模策略和图形工具，重点是使用带有重复测量的混合建模技术。
