  Interaction selection for linear regression models with both continuous and
categorical predictors is useful in many fields of modern science, yet very
challenging when the number of predictors is relatively large. Existing
interaction selection methods focus on finding one optimal model. While
attractive properties such as consistency and oracle property have been well
established for such methods, they actually may perform poorly in terms of
stability for high-dimensional data, and they do not typically deal with
categorical predictors. In this paper, we introduce a variable importance based
interaction modeling (VIBIM) procedure for learning interactions in a linear
regression model with both continuous and categorical predictors. It delivers
multiple strong candidate models with high stability and interpretability.
Simulation studies demonstrate its good finite sample performance. We apply the
VIBIM procedure to a Corona Virus Disease 2019 (COVID-19) data used in Tian et
al. (2020) and measure the effects of relevant factors, including transmission
control measures on the spread of COVID-19. We show that the VIBIM approach
leads to better models in terms of interpretability, stability, reliability and
prediction.
