Statistical analysis of interactions and errors in variables

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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.