Inferences in generalized linear longitudinal mixed models

在社会经济和生物医学研究领域中存在许多情况，其中在小的时间段内从大量独立家庭的成员重复收集二进制和计数响应沿着合适的多维时间依赖协变量。这种类型的家庭纵向二进制和计数数据的分析可能并不容易，因为在建模其潜在的家庭纵向相关结构的困难。此外，由于相关性模型的复杂性，开发用于适当推断的所谓似然方法可能是不可能的或极其复杂的。最近，基于一类自相关结构，Sutradhar（2003年，统计科学），Sutradhar，Jowaheer和Sneddon（2008年，斯堪的纳维亚统计杂志），Sutradhar，Rao和Pandit（2008年，Sankhya B，《印度统计杂志》），除其他外，开发了一个统一的广义准似然（GQL）的方法，在纵向和/或家庭纵向模型计数和/或二进制数据的推断。然而，这些GQL推断是针对标准情况开发的，例如当数据完整时，它们既不包含任何离群值，也不包含任何测量误差。该建议的主要目标是在三种非标准和高度实用的情况下开发一致和有效的推理技术：（1）家庭纵向数据可能会随机缺失;（2）家庭纵向设置中的协变量可能会受到污染;（3）家庭纵向设置中的响应或协变量可能包含测量误差。因此，拟议的研究计划将显着推进复杂但重要的社会问题的分析方法的发展，在家庭纵向设置为二进制和计数数据。预计这项工作将对未来涉及社会经济和生物医学数据的统计研究产生重大影响，并将有利于加拿大和国外的政府统计机构，医院和/或临床研究人员以及卫生政策制定者。

There are many situations in socio-economic and biomedical research fields, among others, where binary and count responses along with suitable multi-dimensional time-dependent covariates are repeatedly collected over a small period of time, from the members of a large number of independent families. The analysis of this type of familial-longitudinal binary and count data may not be easy, because of the difficulties in modeling their underlying familial-longitudinal correlation structures. Furthermore, due to the complex nature of the correlation models, it may be either impossible or extremely complicated to develop the so-called likelihood approach for suitable inferences. Recently, based on a class of auto-correlation structures, Sutradhar (2003, Statistical Science), Sutradhar, Jowaheer and Sneddon (2008, The Scandinavian Journal of Statistics), and Sutradhar, Rao and Pandit (2008, Sankhya B, The Indian Journal of Statistics), among others, developed a unified generalized quasi-likelihood (GQL) approach for inferences in longitudinal and/or familial-longitudinal models for count and/or binary data. These GQL inferences are, however, developed for standard situations such as when the data are complete, and they neither contain any outliers, nor, any measurement errors. The main objective of this proposal is to develop consistent and efficient inference techniques under three non-standard and highly practical situations: (1) where familial-longitudinal data may be subject to missing at random; (2) where the covariates in the familial-longitudinal set up may be subject to contamination; (3) where the responses or covariates in the familial-longitudinal set up may contain measurement errors. Thus, the proposed research program will significantly advance the methodological developments for the analysis of complex but important societal problems in the familial-longitudinal set up for binary and count data. It is anticipated that the proposed work will have significant impact on future statistical research involving socio-economic and bio-medical data and will be of benefit to goverment statistical agencies, hospital and/or clinical researchers, and health ploicy makers in Canada and abroad.