Investigating and Extending Bayesian Methods for Small Area Estimation

描述(由申请人提供)：研究人员通常希望根据当地人口样本的数据来描述小区域的特征，但尽管已知基于随机样本的平均值可以提供无偏估计，但当样本较小时，估计的方差可能相当大。这一问题出现在使用已公布的人口普查数据(如人口普查区域)以及许多与健康有关的大规模调查时。该项目评估了小区域估计的贝叶斯模型的性能，特别侧重于其使用人口普查提供的这类人口数据的性能。该项目利用了一种新的来源：来自1880年和1940年人口普查的100%人口数据，在这两次人口普查中，人们在城市中的位置可以进行地理编码。这使得可以随意从人口中抽取多个样本，并将这些样本的小区域估计值与实际人口值进行比较。同样的方法可以应用于低密度郊区和非中心城市县的EDS的非地理编码数据。这一方法在其他三个主要方面是创新的。首先，大多数对SAE模型性能的评估集中在面积平均值和比例估计的偏差和方差上。该项目涉及对空间人口学家至关重要的另一个问题：各地区之间的差异(用于评估空间不平等和居住隔离)。第二，认识到包括人口普查在内的大多数当代大规模调查使用样本权重来表示复杂的调查设计，并纠正单位无回答的模式，我们具体评估了将样本权重纳入分层贝叶斯框架的方法。关于在单元级空间贝叶斯模型中样本权重的使用，人们知之甚少。该项目将研究并进一步开发一种新的空间模型扩展，以处理样本权重。第三，1940年对芝加哥的估计将利用1930年枚举区层面的数据，在时间和空间上都有相关性。在比较不同模型的结果时，我们将检查一系列情景、不同的样本比例以及小地区的人口规模和地理规模，估计平均值和比例，比较不同样本设计的效果，并评估利用多个指标的贡献。这项工作的结果将包括对大多数调查人员的指导方针 适合不同设计场景下使用的统计方法。

DESCRIPTION (provided by applicant): Researchers often wish to characterize small areas based on data from a sample of the local population, but while average values based on random samples are known to provide unbiased estimates, the variance of estimates can be quite large when samples are small. This problem arises in the use of published census data (such as for census tracts) as well as for many large-scale health-related surveys. This project evaluates the performance of Bayesian models for small area estimation with a particular focus on their performance with population data of the type provided by the census. The project exploits the availability of a new source: 100% population data from the Censuses of 1880 and 1940 where people's locations within cities can be geocoded. This allows multiple samples to be drawn at will from the population, and for small area estimates from these samples to be compared with the actual population values. The same methods can be applied with non-geocoded data for EDs in low density suburbs and for non-central city counties. The approach is innovative in three other major ways. First, most assessments of SAE model performance focus on the bias and variance in estimates of area means and proportions. The project deals with another concern that is substantively important to spatial demographers: the variance across areas (which is used to assess spatial inequality and residential segregation). Second, recognizing that most contemporary large scale surveys including the census use sample weights to represent complex survey designs and correct for patterns of unit non-response, we specifically assess methods to incorporate sample weights in the hierarchical Bayesian framework. Little is known about use of sample weights in unit-level spatial Bayesian models. This project will examine and further develop a new extension of spatial models to deal with sample weights. Third, the 1940 estimates for Chicago will draw on both dependence in both time and space, using data at the Enumeration District level in 1930. In comparing results from different models we will examine a range of scenarios, varying sample proportions and the population size and geographic scale of small areas, estimating both means and proportions, comparing the effects of different sample designs, and assessing the contribution of drawing on multiple indicators. The result of this work will include guidelines for investigators for the most appropriate statistical method to use under the different design scenarios.