Non-destructive high-throughput plant phenotyping is becoming increasingly used and various methods for growth analysis have been proposed. Traditional longitudinal or repeated measures analyses that model growth using statistical models are common. However, often the variation in the data is inappropriately modelled, in part because the required models are complicated and difficult to fit. We provide a novel, computationally efficient technique that is based on smoothing and extraction of traits (SET), which we compare with the alternative traditional longitudinal analysis methods. The SET-based and longitudinal analyses were applied to a tomato experiment to investigate the effects on plant growth of zinc (Zn) addition and growing plants in soil inoculated with arbuscular mycorrhizal fungi (AMF). Conclusions from the SET-based and longitudinal analyses are similar, although the former analysis results in more significant differences. They showed that added Zn had little effect on plants grown in inoculated soils, but that growth depended on the amount of added Zn for plants grown in uninoculated soils. The longitudinal analysis of the unsmoothed data fitted a mixed model that involved both fixed and random regression modelling with splines, as well as allowing for unequal variances and autocorrelation between time points. A SET-based analysis can be used in any situation in which a traditional longitudinal analysis might be applied, especially when there are many observed time points. Two reasons for deploying the SET-based method are (i) biologically relevant growth parameters are required that parsimoniously describe growth, usually focussing on a small number of intervals, and/or (ii) a computationally efficient method is required for which a valid analysis is easier to achieve, while still capturing the essential features of the exhibited growth dynamics. Also discussed are the statistical models that need to be considered for traditional longitudinal analyses and it is demonstrated that the oft-omitted unequal variances and autocorrelation may be required for a valid longitudinal analysis. With respect to the separate issue of the subjective choice of mathematical growth functions or splines to characterize growth, it is recommended that, for both SET-based and longitudinal analyses, an evidence-based procedure is adopted.

中文翻译：

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无创表型数据生长分析中性状的平滑与提取

非破坏性高通量植物表型分析越来越多地使用，并且已经提出了各种生长分析方法。使用统计模型模拟增长的传统纵向或重复测量分析很常见。然而，数据的变化经常被不恰当地建模，部分原因是所需的模型复杂且难以拟合。我们提供了一种基于平滑和特征提取 (SET) 的新颖、计算效率高的技术，我们将其与替代的传统纵向分析方法进行比较。将基于 SET 的纵向分析应用于番茄实验，以研究在接种丛枝菌根真菌 (AMF) 的土壤中添加锌 (Zn) 和植物生长对植物生长的影响。基于 SET 的分析和纵向分析得出的结论是相似的，尽管前一种分析导致更显着的差异。他们表明，添加的锌对在接种土壤中生长的植物几乎没有影响，但对于在未接种土壤中生长的植物，生长取决于添加的锌量。未平滑数据的纵向分析拟合了一个混合模型，该模型涉及使用样条曲线的固定和随机回归建模，以及允许时间点之间的不等方差和自相关。基于 SET 的分析可用于任何可能应用传统纵向分析的情况，尤其是当有许多观察到的时间点时。部署基于 SET 的方法的两个原因是 (i) 需要简单描述生长的生物学相关生长参数，通常专注于少数间隔，和/或（ii）需要一种计算有效的方法，更容易实现有效的分析，同时仍能捕捉到所展示的增长动态的基本特征。还讨论了传统纵向分析需要考虑的统计模型，并且证明了有效的纵向分析可能需要经常忽略的不等方差和自相关。关于主观选择数学增长函数或样条来表征增长的单独问题，建议对于基于 SET 的分析和纵向分析，都采用基于证据的程序。同时仍然捕捉到所展示的增长动态的基本特征。还讨论了传统纵向分析需要考虑的统计模型，并且证明了有效的纵向分析可能需要经常忽略的不等方差和自相关。关于主观选择数学增长函数或样条来表征增长的单独问题，建议对于基于 SET 的分析和纵向分析，都采用基于证据的程序。同时仍然捕捉到所展示的增长动态的基本特征。还讨论了传统纵向分析需要考虑的统计模型，并且证明了有效的纵向分析可能需要经常忽略的不等方差和自相关。关于主观选择数学增长函数或样条来表征增长的单独问题，建议对于基于 SET 的分析和纵向分析，都采用基于证据的程序。还讨论了传统纵向分析需要考虑的统计模型，并且证明了有效的纵向分析可能需要经常忽略的不等方差和自相关。关于主观选择数学增长函数或样条来表征增长的单独问题，建议对于基于 SET 的分析和纵向分析，都采用基于证据的程序。还讨论了传统纵向分析需要考虑的统计模型，并且证明了有效的纵向分析可能需要经常忽略的不等方差和自相关。关于主观选择数学增长函数或样条来表征增长的单独问题，建议对于基于 SET 的分析和纵向分析，都采用基于证据的程序。