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层小面积估计模型。将这些方法与现有的一些方法如伪极大似然、惩罚似然等进行比较和对比。本研究的一些新特征将是使用地层变化的回归系数，方差-协方差矩阵的新先验而不是标准的Wishart先验，允许协变量测量误差的小面积估计模型的开发，在小面积估计的背景下使用分层似然，以及在小面积估计中使用调查权重。该项目的主要应用之一将是估计各州和县的收入和贫困情况，甚至可能是每十年一次人口普查之间的较低地理水平，如人口普查区和学区（当有数据可用时）。然而，这些方法是相当普遍的，也可以应用于其他研究。其中，这些方法将应用于研究青年失业的小地区基于苏格兰学校休假调查，学校的有效性和学生性格的教育调查进行了内伦敦教育局和英国社会态度调查。术语“小区域”或“局部区域”通常用于表示小的地理区域，如县，直辖市或人口普查部门。它们也可以描述一个“小域”，也就是说，一个小的亚种群，比如一个大地理区域内的特定年龄、性别、种族群体。如今，全球都需要来自私营和公共部门的可靠的小地区统计数据。政府越来越关注分配、公平和差距问题。例如，在某一人口中可能存在着在许多方面有缺陷的地理分组，需要明确的改进。在采取补救行动之前，需要确定这些区域，因此，必须有有关地理级别的统计数据。在分配政府资金以及区域和城市规划中也需要小地区统计。此外，私营部门也有需求，因为许多企业和工业的决策取决于当地的社会经济条件。因此，小面积估计技术具有全局适用性，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.