Advancing complex models in small area estimation and spatial statistics

推进小区域估计和空间统计中的复杂模型

• 批准号: RGPIN-2016-06046
• 负责人: Torabi, Mahmoud
• 金额: $ 1.97万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=666964
• 关键词: Advancing; complex; models; small; area

In survey sampling, policy decisions regarding allocation of resources to subgroups in a population, called small areas, are based on reliable predictors of their underlying parameters that describe resource use. However, the information is collected at a different scale than these subgroups. Hence we need to predict characteristics of the subgroups based on the coarser scale data. I plan to develop a frequentist approach for small area estimation of quantiles of Normal and non--Normal responses (e.g., median family income of small areas as Normal response). I am also interested in developing/extending my previous work in the linear mixed model (LMM) with the covariates subject to structural and functional measurement errors to non-Normal responses (e.g., binary or count response) using both frequentist and Bayesian approaches (will led by my first PhD student). My other project is to relax the linear regression assumption for the covariates of the LMM and replace them by a weaker assumption of a spline regression for the covariates subject to measurement errors (will led by my first MSc student). My plan is also to study non-ignorable missing responses and measurement errors in covariates for Normal and non-Normal responses (will led by my second PhD student).***In spatial statistics, I am pursuing research on the analysis of disease outcomes over space and time which falls under the umbrella of generalized additive mixed models. Spatio-temporal models are mainly used in disease mapping to provide a reliable estimate of the underlying disease risk by borrowing strength from neighbouring geographic sub-regions. One of my interests is to offer a frequentist approach based on maximum likelihood estimation (MLE) for complex spatio-temporal models of point-referenced datasets (also called geostatistics). In my previous work to account for seasonal effects in spatio--temporal models, I used generalized estimating equation (GEE) as an estimation approach assuming the independence structure for variance--covariance of outcome among regions which may lead to misspecification in some settings. My plan is to offer an alternative frequentist approach based on MLE to overcome this issue. My interest is also to develop mixtures of two (or more) spatial or spatio-temporal models, e.g. healthy and non-healthy populations, for disease mapping. Another project is to develop spatio-temporal for count data which may contain excess zeros because of immunity or other protective factors (will led by my second MSc student). I am also interested in working with spatial and spatio--temporal models with measurement errors (structural and functional) in covariates (will led by my third MSc student).***Ignoring proper modelling (based on the methods/models proposed above) may lead to wrong conclusions which can have clear policy implications in survey sampling and public health. *** *** *** **

在调查抽样中，有关向人口中的子群体（称为小区域）分配资源的政策决策是基于描述资源使用的基本参数的可靠预测因素。然而，信息收集的规模与这些亚组不同。因此，我们需要根据较粗尺度的数据来预测子组的特征。我计划开发一种频率论方法，用于对正常和非正常响应的分位数进行小区域估计（例如，将小区域的家庭收入中位数作为正常响应）。我也有兴趣使用频率论和贝叶斯方法（将由我的第一个博士生领导）开发/扩展我之前在线性混合模型（LMM）中的工作，其中协变量受到结构和功能测量误差的影响，对非正态响应（例如二元或计数响应）进行处理。我的另一个项目是放宽 LMM 协变量的线性回归假设，并将其替换为受测量误差影响的协变量样条回归的较弱假设（将由我的第一个理学硕士学生领导）。我的计划还包括研究正常和非正常反应的协变量中不可忽略的缺失反应和测量误差（将由我的第二个博士生领导）。***在空间统计学中，我正在研究空间和时间上疾病结果的分析，这属于广义加性混合模型的范畴。时空模型主要用于疾病绘图，通过借鉴邻近地理分区的力量，提供对潜在疾病风险的可靠估计。我的兴趣之一是为点引用数据集（也称为地质统计学）的复杂时空模型提供一种基于最大似然估计 (MLE) 的频率论方法。在我之前的工作中，为了解释时空模型中的季节性影响，我使用广义估计方程（GEE）作为估计方法，假设方差（区域之间结果的协方差）的独立结构，这可能会导致在某些情况下出现错误指定。我的计划是提供一种基于 MLE 的替代频率论方法来克服这个问题。我的兴趣还在于开发两个（或多个）空间或时空模型的混合，例如健康和非健康人群，用于疾病绘图。另一个项目是开发计数数据的时空，由于免疫或其他保护因素，这些数据可能包含多余的零（将由我的第二个理学硕士学生领导）。我还对协变量中具有测量误差（结构和功能）的空间和时空模型感兴趣（将由我的第三位理学硕士学生领导）。***忽略正确的建模（基于上面提出的方法/模型）可能会导致错误的结论，这可能对调查抽样和公共卫生产生明确的政策影响。 *** *** *** **