Statistical inference in zero-inflated random effects models with missing data

相关数据在生物、生态、健康和医学研究等各种学科中很常见。例如，由于重复测量、或巢设计、或单位的自然层次结构，数据是相关的。随机效应模型(或混合模型或分层模型)被广泛用于分析这些数据，其中引入随机效应来考虑层次内的相关性。例如，在医学纵向研究中，随机效应经常被用来模拟受试者之间的异质性。这些随机效应表现了受试者对某些疾病的不同易感性。 在对相关数据进行建模时，经常会遇到大量的零。例如，在对保险索赔的研究中，大量的人在某一段时间内将没有索赔。此外，由于某些原因，一些数据可能会丢失。数据的存在和零通胀以及缺失数据给数据分析带来了挑战。在拟议的研究中，我将为存在零通货膨胀和缺失数据的随机效应模型开发有效的数据分析方法。我还将在这方面进行变量选择和模型评估。由于这些数据的复杂性在许多学科中都很常见，有待开发的方法将得到广泛应用。这些方法将很容易被应用研究人员通过工作示例和用户友好的程序包使用。

Correlated data are common in a variety of disciplines such as biological, ecological, health and medical studies. Data are correlated due to, for example, repeated-measures, or a nest design, or a natural hierarchy of units. Random effects models (or mixed models or hierarchical models) are widely used to analyse these data, in which random effects are introduced to account for correlation within a hierarchy. For example, in medical longitudinal studies, random effects are often used to model the heterogeneity between subjects. These random effects characterize the varying susceptibilities of subjects to certain diseases. In modelling correlated data, it is common to encounter a large number of zeros. For example, in studies of insurance claims, a large number of people will have zero claims during a certain period of time. In addition, some data may be missing for certain reasons. The presence and zero-inflation and missing data poses challenges to data analysis. In the proposed research I will develop efficient data analysis methods for random effects models with the presence of zero-inflation and missing data. I will also pursue variable selection and model assessment in this context. As these data complexities are common in many disciplines, the methods to be developed will be widely applicable. The methods will be easily accessible to applied researchers through worked examples and user-friendly packages.