Collaborative Research: Bayesian and Likelihood Based Multilevel Models for Small Area Estimation

本课题主要研究基于贝叶斯和似然的多水平小区域估计方法。这些方法将与现有的一些方法进行比较和对比，如伪最大似然法、惩罚准似然法等。这项研究的一些新特点将是使用分层变化的回归系数，方差-协方差矩阵的新先验而不是标准的Wishart先验，开发允许协变量测量误差的小区域估计模型，在小区域估计的背景下使用分层似然，以及使用调查权重进行小区域估计。该项目的主要应用之一将是估计各州和县的收入和贫困，甚至可能在十年一次的人口普查之间估计较低的地理水平，如人口普查地区和学区(如果有数据可用)。但这些方法具有一定的通用性，也可应用于其他研究。其中，这些方法将被应用于研究小地区的青年失业问题，这些方法基于苏格兰学校树叶调查，内伦敦教育局进行的一项教育调查中的学校有效性和学生特征，以及英国社会态度调查。“小地区”或“当地”一词通常用于表示小地理区域，如郡、市或人口普查部门。他们也可以描述一个“小领域”，即在一个大的地理区域内的一个小的亚群，比如特定的年龄、性别和种族群体。如今，全球都需要来自私营部门和公共部门的可靠的小区域统计数据。政府对分配、公平和不平等问题的担忧日益加剧。例如，在给定的人口中，可能存在在许多方面有残疾的地理亚群，需要进行明确的升级。在采取补救行动之前，有必要确定这些区域，因此，必须有相关地理区域的统计数据。在政府资金的分配以及区域和城市规划中也需要小范围的统计数据。此外，还有私营部门的需求，因为许多企业和行业的决策取决于当地的社会经济条件。因此，小区域估计技术具有全球适用性，并适用于各种应用。

This research project focuses on Bayesian and likelihood based multilevel models for small area estimation. These methods will be compared and contrasted against some of the existing methods, such as the pseudo maximum likelihood, penalized quasilikelihood, etc. Some of the novel features of this research will be the use of stratum varying regression coefficients, new priors for the variance-covariance matrix rather than the standard Wishart prior, development of small area estimation models allowing measurement errors for covariates, use of hierarchical likelihood in the context of small area estimation, and the use of survey weights for small area estimation. One of the major applications of this project will be the estimation of income and poverty for states and counties, and possibly even for lower levels of geography such as census tracts and school districts (when data become available) between decennnial censuses. However, the methods are fairly general, and can be applied to other studies as well. Among others, these methods will be applied to study youth unemployment for small areas based on the Scottish School Leavears Survey, effectiveness of schools and student character in an education survey conducted by the Inner London Education Authority, and a British Social Attitudes Survey.The terms "small area'' or "local area" are commonly used to denote a small geographical area, such as a county, a municipality, or a census division. They may also describe a "small domain;" that is, a small subpopulation such as a specific age-sex-race group of people within a large geographical area. In these days, there is a global need for reliable small area statistics both from the private and public sectors. There are increasing government concerns with issues of distribution, equity, and disparity. For example, there may exist geographical subgroups within a given population that are handicapped in many respects, and need definite upgrading. Before taking remedial action, there is a need to identify such regions, and accordingly, one must have statistical data at the relevant geographical levels. Small area statistics also are needed in the apportionment of government funds, and in regional and city planning. In addition, there are demands from the private sector since the policy-making of many businesses and industries relies on local socio-economic conditions. Thus, small area estimation techniques have global applicability, and are useful for diverse applications.