Does Preliminary Model Checking Help With Subsequent Inference? A Review And A New Result
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Statistical methods are based on model assumptions, and it is statistical folklore that a method's model assumptions should be checked before applying it. We review literature that investigated combined test procedures, in which model assumptions are checked first. Then, in case that the model assumption is passed, a test based on the model assumption is run, and otherwise a test with less strong assumptions. Much literature is surprisingly critical of this approach, owing also to the observation that conditionally on passing a model misspecification test, the model assumptions are automatically violated ("misspecification paradox"). We also review controversial views on the role of model checking in statistics, and literature investigating empirically to what extent model assumptions are checked in practice. We suspect that the benefit of preliminary model checking is currently underestimated, and we present a general setup not yet investigated in the literature, in which we can show that preliminary model checking is advantageous.
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