Statistical analysis of interactions and errors in variables

变量交互作用和误差的统计分析

• 批准号: 371504-2010
• 负责人: Liu, Juxin
• 金额: $ 1.24万
• 依托单位: University of Saskatchewan
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=550055
• 关键词: Statistical; analysis; interactions; errors; variables

This proposal addresses some emerging issues in two different research topics: interactions and errors in variables. Interaction is one of the fundamental concepts of statistical analysis and has various challenges in regression models. In particular, with many input variables, the number of possible pairwise interactions can be substantial without even considering the possibility of three-way or higher-order interactions. Conventional schemes to find the important variables and interaction terms are known to have limitations. Thus, there is a need to better interpret and detect interactions. The long-term objective with respect to interactions is twofold: (a) to develop a useful summary tool with robust or nearly robust behavior even if interactions are wrongly omitted, and (b) to construct interaction models that balance model fit with model complexity. Errors-in-variables (EIV) refers to the imprecise measurement of variables. EIV has received extensive attention in many research areas because it is commonly encountered in practice. It has long been recognized that the estimated association between a response variable and a mismeasured covariate tends to be biased when simply ignoring EIV problems. For complex data structures, the analysis of EIV problems is confronted with various difficulties. The long-term objective of the research with respect to EIV is also twofold: (a) to develop computationally efficient methods to address EIV problems for complex data structures, and (b) to develop methodology for integrating the analysis strategies of EIV problems with other statistical methods, such as variable selection. Both research topics are motivated by real-life application problems, and the results will lead to developments in theory and methodology. This research will enrich the current methodology and provide new statistical tools for solving practical problems in various disciplines such as epidemiology, environmental science, sociology, biology and genetics. The proposed program also provides a great opportunity for training highly qualified personnel.

本提案针对两个不同研究主题的一些新问题：相互作用和变量误差。交互作用是统计分析的基本概念之一，在回归模型中面临着各种挑战。特别是，对于许多输入变量，即使不考虑三种或更高阶相互作用的可能性，可能的成对相互作用的数量也会很大。众所周知，寻找重要变量和相互作用项的传统方案具有局限性。因此，有必要更好地解释和检测相互作用。关于交互的长期目标是双重的：(a)即使错误地忽略了交互，也要开发具有鲁棒性或接近鲁棒性行为的有用汇总工具，以及(b)构建平衡模型拟合和模型复杂性的交互模型。变量误差（EIV）是指对变量的不精确测量。EIV由于在实践中经常遇到，在许多研究领域受到了广泛的关注。人们早就认识到，当简单地忽略EIV问题时，响应变量和误测协变量之间的估计关联往往是有偏差的。对于复杂的数据结构，EIV问题的分析面临着各种困难。关于EIV研究的长期目标也有两个方面：(a)发展计算效率高的方法来处理复杂数据结构的EIV问题；(b)发展将EIV问题的分析策略与其他统计方法（如变量选择）相结合的方法。这两个研究课题都是由现实生活中的应用问题驱动的，其结果将导致理论和方法的发展。本研究将丰富现有的统计方法，为解决流行病学、环境科学、社会学、生物学和遗传学等各学科的实际问题提供新的统计工具。该计划还为培养高素质人才提供了很好的机会。