Robust Inference for Multivariate Growth Curve Models and High-Dimensional Extensions

多元增长曲线模型和高维扩展的稳健推理

• 批准号: RGPIN-2018-06693
• 负责人: Hamid, Jemila
• 金额: $ 2.62万
• 依托单位: University of Ottawa
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=749536
• 关键词: Robust; Inference; Multivariate; Growth; Curve

Background: Multivariate Growth Curve Model (GCM), also known as the Generalized Analysis of Variance (GMANOVA) model, is useful in the analysis of longitudinal data, growth curves as well as other response curves (eg. dose-response curves). The model arises when the mean is structured due to, for instance, time or dose dependency of the outcome of interest, which is often the case in applications involving longitudinal or dose-response data. Traditional methods for the GCM are developed under the assumption of normality. In practice, however, it is common to encounter outcomes with skewed distributions. A recent simulation study reveals that estimators derived under the normality assumption are sensitive to departure from normality, where the results show that the estimators are associated with increased bias and mean squared error (MSE), when used in the analysis of skewed data. Inference for the GCM is also based on the assumption of larger sample size (n) than the number of time points (p), where the covariance matrix is assumed to be positive definite. In high-dimensional data, however, p is often larger than n, leading to singularity of the sample covariance matrix, and hence traditional approaches do not work. Methods for handling high-dimensional data have been developed in recent years. Although these methods account for correlations among measurements taken across the different time points, the methods fail to account for time dependency, which often motivates longitudinal studies, where researchers are interested to determine the change over time. In previous work, we considered two approaches. The first approach involves a transformation to the MANOVA model followed by an empirical Bayes approach. The second method involves use of the Moore-Penrose generalized inverse. Although the approach using a transformation provided a framework for incorporating time dependency in the model, the method lacks statistical power and lead to estimators with increased bias and MSE. On the other hand, the method based on Moore-Penrose inverse provided increased power and precision; and the estimators are in general associated with a bias randomly distributed around zero. Nevertheless, the simulation results show that the optimallity of the estimators and the performance of the test declines near singularity (when np). This proposal attempts to address the limitations of the previous method and provides improved inference for high-dimensional longitudinal data.The overall objective of this proposal is to provide robust estimators for the parameters of the GCM and provide high-dimensional extensionsSpecific Objectives are to 1) drive estimators for the model parameters of the GCM under multivariate skewed normal distribution 2) derive estimators for the extended GCM under multivariate skewed normal distribution 3) provide an optimal inference for the GCM under high-dimensional scenarios

背景：多元增长曲线模型（GCM），也称为广义方差分析（Gmanova）模型，在纵向数据，生长曲线以及其他响应曲线的分析中很有用（例如，剂量反应曲线）。 当均值由于感兴趣结果的时间或剂量依赖性而导致的平均值时，该模型就会出现，这在涉及纵向或剂量反应数据的应用中通常是这种情况。 GCM的传统方法是在正态性的假设下开发的。但是，在实践中，通常会遇到偏斜分布的结果。最近的一项仿真研究表明，在正态性假设下得出的估计量对偏离正态性很敏感，在这种情况下，结果表明，当用于分析偏斜数据时，估计器与偏置和平方误差（MSE）的增加相关。 GCM的推论还基于比时间点（P）的数量（p）的假设，其中认为协方差矩阵是正定的。但是，在高维数据中，P通常大于n，导致样品协方差矩阵的奇异性，因此传统方法不起作用。近年来已经开发了处理高维数据的方法。尽管这些方法解释了跨不同时间点进行的测量之间的相关性，但该方法无法解释时间依赖性，这通常会激发纵向研究，研究人员有兴趣确定随着时间的推移的变化。在以前的工作中，我们考虑了两种方法。第一种方法涉及对Manova模型的转换，然后是经验贝叶斯方法。第二种方法涉及使用Moore-Penrose概括性逆。 尽管使用转换的方法为在模型中纳入时间依赖性提供了一个框架，但该方法缺乏统计能力，导致估计器具有增加的偏差和MSE。 另一方面，基于摩尔 - 芬罗逆的方法提供了提高的功率和精度。并且估计器通常与随机分布的偏差相关。然而，仿真结果表明，估计器的最佳性和测试的性能在奇异性接近（NP时）。该提案试图解决先前方法的局限性并为高维纵向数据提供改进的推断。该提案的总体目标是为GCM的参数提供可靠的估计器，并为超维扩展目标提供了高维扩展目标，以驱动器估算值的驱动器估算值，以下是GCM的驱动器估算值，以下是GCM的驱动器2）。偏斜的正态分布3）在高维情况下为GCM提供了最佳推断