Statistical analysis of interactions and errors in variables

这一建议解决了两个不同的研究主题中出现的一些问题：变量的相互作用和误差。交互作用是统计分析的基本概念之一，在回归模型中存在各种挑战。特别是，在许多输入变量的情况下，可能的成对相互作用的数量可能是相当大的，甚至不考虑三向或更高阶相互作用的可能性。传统的计划，以找到重要的变量和相互作用项是已知的有局限性。因此，需要更好地解释和检测相互作用。关于相互作用的长期目标是双重的：（a）开发一个有用的摘要工具，即使相互作用被错误地忽略，也具有稳健或接近稳健的行为，以及（B）构建平衡模型拟合与模型复杂性的相互作用模型。变量误差（EIV）是指变量的不精确测量。由于EIV在实践中的普遍性，它在许多研究领域受到了广泛的关注。长期以来，人们已经认识到，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的研究的长期目标也是双重的：（a）开发计算效率高的方法来解决复杂数据结构的EIV问题，以及（B）开发将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。这两个研究主题都是由现实生活中的应用问题，其结果将导致理论和方法的发展。这项研究将丰富目前的方法，并为解决流行病学、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。拟议的方案还提供了一个很好的机会，培养高素质的人才。

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.