High-throughput phenomics data are being collected in both the laboratory and the field. The data are often collected at many time points and there may be spatial variation in the laboratory or field that impacts on the growth of the plants, and that may influence the traits of interest. Modelling the genetic effects is of primary interest in such studies, but these effects might be biased if non-genetic effects present in the experiment are ignored. With data that are collected both in time and space, there may be a need to jointly model these multi-dimensional non-genetic effects. Thus both modelling of genetic effects over time and non-genetic effects over time and space in a one-stage analysis is considered. An experiment that involves field phenomics data with four dimensions, two in space and two in time, provides the vehicle to examine the models. Factor analytic (FA) models are often used for genetic effects for different environments to provide reliable estimates of genetic variances and correlations. As the time dimension defines the environments, FA models are examined for the phenomics data. Reduced rank tensor smoothing splines are presented as a possible approach for modelling the spatio-temporal effects, although an additional term is included for heterogeneity over the two time dimensions. This approach is feasible, although very time-consuming. The process of model selection for the genetic effects is presented including tests, information criteria and diagnostics. Comparisons of more simplistic models are made with the reduced rank tensor spline. This also shows the interplay between the genetic and residual models in model selection.

中文翻译：

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模拟高通量表型数据的时间遗传和时空残留效应*

实验室和现场都在收集高通量表型组学数据。数据通常在许多时间点收集，实验室或田间可能存在影响植物生长的空间变化，并可能影响感兴趣的性状。对遗传效应建模是此类研究的主要兴趣，但如果忽略实验中存在的非遗传效应，这些效应可能会产生偏差。通过在时间和空间上收集的数据，可能需要对这些多维非遗传效应进行联合建模。因此，在一个阶段分析中，既考虑了遗传效应随时间的建模，又考虑了非遗传效应随时间和空间的变化。一个涉及四个维度的现场表型组数据的实验，两个维度，两个时间维度，提供车辆来检查模型。因子分析 (FA) 模型通常用于不同环境的遗传效应，以提供对遗传方差和相关性的可靠估计。由于时间维度定义了环境，因此会检查 FA 模型的表型组数据。降阶张量平滑样条被提出作为对时空效应进行建模的一种可能方法，尽管在两个时间维度上包含了一个额外的术语来表示异质性。这种方法是可行的，虽然非常耗时。介绍了遗传效应的模型选择过程，包括测试、信息标准和诊断。使用降阶张量样条对更简单的模型进行比较。这也显示了模型选择中遗传模型和残差模型之间的相互作用。