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Interaction selection for linear regression models with both continuous andcategorical predictors is useful in many fields of modern science, yet verychallenging when the number of predictors is relatively large. Existinginteraction selection methods focus on finding one optimal model. Whileattractive properties such as consistency and oracle property have been wellestablished for such methods, they actually may perform poorly in terms ofstability for high-dimensional data, and they do not typically deal withcategorical predictors. In this paper, we introduce a variable importance basedinteraction modeling (VIBIM) procedure for learning interactions in a linearregression model with both continuous and categorical predictors. It deliversmultiple strong candidate models with high stability and interpretability.Simulation studies demonstrate its good finite sample performance. We apply theVIBIM procedure to a Corona Virus Disease 2019 (COVID-19) data used in Tian etal. (2020) and measure the effects of relevant factors, including transmissioncontrol measures on the spread of COVID-19. We show that the VIBIM approachleads to better models in terms of interpretability, stability, reliability andprediction.

Variable Importance Based Interaction Modeling with an Application on Initial Spread of COVID-19 in China