Random effects modeling of longitudinal and spatial data with and without zero-inflation.

我提出的研究主要集中在医学、健康、生态、环境和生物研究中发生的纵向、空间和时空相关的倾斜数据的随机效应建模。具体地说，我们对随时间(时间序列)、在许多个体上随时间(纵向)、在空间/位置(例如空间)、在空间和时间(例如时空)上观察到的数据进行建模。我的研究兴趣主要集中在以下三个方面。首先，我将继续研究纵向倾斜数据的随机效应建模，特别是零膨胀数据。在纵向计数数据中，随着时间的推移收集的响应经常出现过多的零值。在文献中，两部分模型(也称为Delta-Gamma方法)通常用于对纵向倾斜数据进行建模，其中存在-不存在和正响应分别被建模。由于这种在零值和非零值之间中断的单独建模在密度函数中呈现不自然的不连续性，它破坏了纵向数据中常见的序列相关结构。为了克服这个问题，我建议将自由分布的随机效应结合到灵活的Twedie广义线性模型中，以模拟各种类型的零膨胀纵向偏斜响应。其次，我将把前面研究领域中提出的方法扩展到空间和时空倾斜的数据元数据。我的重点将是开发一种方法来处理在不同空间位置观察到的响应超时的数据，这些空间位置嵌套在倾斜连续、半连续和计数数据的其他空间位置中。本文提出了一种考虑两级空间随机效应的Twedie混合模型，该模型可以适应各种灵活的时空相关结构。第三，我将侧重于混合类型的时空数据的联合建模，包括计数、连续和半连续数据，其中响应与来自生态区域内嵌套的生态区的各种协变量一起被联合收集。如果不能适当考虑数据集的这种联合建模现象，可能会导致对回归参数的偏向估计。联合建模近年来受到越来越多的关注，因为它可以通过在单个模型中同时使用所有数据来提高统计效率。在文献中，很少有方法可以用来联合建模纵向数据和生存数据。就我们所知，目前还没有可用于联合建模时空数据的方法，包括计数数据、连续数据和半连续数据。我建议开发一种基于Twedie混合模型的计算更简单的方法，以整体的方式联合模型计数、连续和半连续数据。

My proposed research is mainly focusing on random effect modeling of longitudinally, spatially and spatiotemporally correlated skewed data occurring in medical, health, ecological, environmental and biological studies. To be specific, we model data that are observed over time (time series), on many individuals over time (longitudinal), over space/location (e.g. spatial), over space and time (e.g. spatiotemporal). My research interest lies in the following three areas.First, I would continue working on random effect modeling of the longitudinal skewed data with particular interest in zero-inflated data. In longitudinal count data, responses collected over time frequently suffer the presence of excessive zero. In the literature, two-part model (also known as delta-gamma approach) is commonly used to model longitudinal skewed data, where the presence-absence and the positive responses are modeled separately. As this type of separate modeling of breaking between zero and non-zero values presents unnatural discontinuity in density function, it destroys the serial correlation structures commonly present in the longitudinal data. To overcome this problem, I propose to incorporate distribution-free random effects into the flexible class of Tweedie generalized linear models to model various types of zero-inflated longitudinal skewed responses. Second, I will extend methodologies proposed in the previous research area to spatial and spatiotemporal skewed datadata. My focus will be to develop the methodology to handle the data where response observed overtime at different spatial locations which are nested within other spatial locations for skewed continuous, semi-continuous and count data. I propose to develop Tweedie mixed models considering two levels of spatial random effects, which can also accommodate various flexible spatiotemporal correlation structures. Third, I will focus on joint modeling of mixed types of spatiotemporal data including count, continuous and semi-continuous data where responses are jointly collected along with various covariates for number of years from ecological districts which are nested within ecological regions. Failure to take appropriate account of this joint modeling phenomenon of the data set can lead to biased estimation of the regression parameters. Joint modeling has received increasing attention in the recent years due to the fact that it may increase statistical efficiency by using all of the data simultaneously in a single model. In the literature there are few approaches available to model longitudinal and survival data jointly. To the best of our knowledge there is nothing available to model spatiotemporal data jointly including count, continuous and semi-continuous data. I propose to develop a Tweedie mixed model based computationally simpler approach to jointly model count, continuous and semi-continuous data in an integral way.