Variable importance based interaction modelling with an application on initial spread of COVID-19 in China.

The article focuses on the development and application of a variable importance based interaction modelling (VIBIM) procedure for selecting interaction terms in linear regression models with both continuous and categorical predictors. VIBIM addresses key limitations of existing methods—instability in high-dimensional data, inability to handle categorical predictors, and reliance on a single selected model—by leveraging model averaging and the sparsity oriented importance learning (SOIL) method to produce multiple stable and interpretable candidate models. Theoretical results establish the consistency of VIBIM in identifying true main effects and interactions under certain conditions. Applied to a COVID-19 dataset from China, VIBIM improves model interpretability, stability, reliability, and prediction accuracy compared to traditional penalized regression methods, while also resolving issues related to variable definitions and causal interpretations in prior analyses. The study highlights the importance of including certain collinear variables supported by evidence and cautions against interpreting regression coefficients as causal effects due to the observational nature of the data.