MoST: model specification test by variable selection stability

Abstract

One of the major challenges in empirical studies is to construct an appropriate statistical model that accounts for the uncertainty of statistical methods and model specifications. An improperly specified model may bring the potential risk for the interpretation of conclusions and subsequent decision-making. In this paper, we introduce a Model Specification Test (MoST) inspired by the concept of model confidence bounds and variable selection deviation. To obtain the p-value of our proposed test, we develop an efficient single-layer bootstrap procedure. Our method can be readily applied to existing variable selection strategies without additional assumptions. Extensive numerical experiments demonstrate the feasibility and interpretability of our approach in various scenarios.