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

本研究计画主要针对小面积估测之贝氏与似然多阶模式。 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。本研究的一些新特征将是使用层变回归系数，方差-协方差矩阵的新先验而不是标准Wishart先验，允许协变量测量误差的小区域估计模型的发展，在小区域估计中使用分层似然法，以及在小区域估计中使用调查权重。 该项目的主要应用之一将是估计州和县的收入和贫困，甚至可能是较低水平的地理，如人口普查区和学区（当数据可用时）。 然而，这些方法是相当普遍的，也可以应用于其他研究。 其中，这些方法将用于研究基于苏格兰学校毕业生调查、内伦敦教育局进行的教育调查中的学校和学生性格的有效性以及英国社会态度调查的小区域的青年失业情况。“小区域”或“局部区域”通常用于表示小的地理区域，例如县、市、或人口普查部门。 他们也可以描述一个“小领域”，即一个小的亚人口，如一个大的地理区域内的特定年龄-性别-种族群体。 目前，全球都需要私营和公共部门的可靠的小区域统计数据。 政府越来越关注分配、公平和差距问题。 例如，在某一特定人口中，可能存在在许多方面有残疾的地理分组，需要明确的改善。 在采取补救行动之前，需要确定这些区域，因此，必须有相关地理层面的统计数据。 在政府资金分配、区域和城市规划中也需要小面积统计。 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，小区域估计技术具有全球适用性，并且对于不同的应用是有用的。

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.