Kronecker积线性指数AR（1）多元重复测度的相关结构和可分性检验
Kronecker product linear exponent AR(1) correlation structures and separability tests for multivariate repeated measures
摘要：
纵向成像研究已经移动到医学研究的最前沿，因为它们能够表征生命周期中生物结构的时空特征。纵向成像中的相关性的可信模型需要两个或更多个图案分量。有效的推理需要相关模型具有足够的灵活性，以允许对真实模式的合理保真度。另一方面，可计算的估计的存在需要一个简约的相关结构的参数化。对于许多一维空间或时间阵列，线性指数自回归（LEAR）相关结构在一个模型中满足这两个相反的目标。LEAR结构是一种灵活的双参数相关性模型，适用于受试者内相关性在时间或空间上呈指数下降的情况。它允许由常用的连续时间AR（1）结构施加的指数衰减率的衰减或加速。在这里，我们提出了Kronecker产品LEAR相关结构的多变量重复测量数据中，测量之间的相关性为一个给定的主题是由两个因素引起的。我们还提供了一个科学的方法来评估Kronecker产品LEAR模型和一般非结构化Kronecker产品模型的充分性。该方法为高维、低样本量数据提供了有用的指导，这些数据排除了使用基于标准似然的检验。精神分裂症患者尾状核形态的纵向医学影像学数据说明了Kronecker乘积LEAR相关结构的吸引力。
英文摘要：
Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Credible models of the correlations in longitudinal imaging require two or more pattern components. Valid inference requires enough flexibility of the correlation model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the correlation structure. For many one-dimensional spatial or temporal arrays, the linear exponent autoregressive (LEAR) correlation structure meets these two opposing goals in one model. The LEAR structure is a flexible two-parameter correlation model that applies in situations in which the within-subject correlation decreases exponentially in time or space. It allows for an attenuation or acceleration of the exponential decay rate imposed by the commonly used continuous-time AR(1) structure. Here we propose the Kronecker product LEAR correlation structure for multivariate repeated measures data in which the correlation between measurements for a given subject is induced by two factors. We also provide a scientifically informed approach to assessing the adequacy of a Kronecker product LEAR model and a general unstructured Kronecker product model. The approach provides useful guidance for high dimension, low sample size data that preclude using standard likelihood based tests. Longitudinal medical imaging data of caudate morphology in schizophrenia illustrates the appeal of the Kronecker product LEAR correlation structure.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
