Ian Hunt's Contribution to the Discussion of ‘Assumption-Lean Inference for Generalised Linear Model Parameters’ by Vansteelandt and Dukes

原文摘要

This paper offers a generic and principled addition to conventional statistical modelling. It is a real advance in applicable methodology. But there is no need in the paper for the following claims: that statisticians routinely use ‘dishonest’ modelling assumptions, that statisticians should aim for ‘purely evidence-based’ inferences and that modelling assumptions are ‘almost always a pure mathematical convenience’. These sorts of claims are redundant or misleading for three reasons. First, text-book statistical inferences look like deductions. But nearly everyone wants to make inductive inferences. Statisticians assist in the leap from deduction to induction via iterations of a two-step process: step one, specify different models and estimate their parameters (adding and dropping interaction terms, using different error assumptions and so on); step two, assess and compare the models (including assumption checking). This inductive process is necessarily vague, but it embodies the key statistical tasks defined by Fisher (1959, pp. 6–8). Properly disclosed assumptions that cannot be proved, or are openly false, play an honest and essential role in inductive processes—we have to take risks to go beyond the data and what we already know. Adding assumption-lean or ‘less risky’ methods to inductive processes may prove useful but this would not be ‘more honest’. Second, if by ‘evidence’ the authors really mean data then I would argue that aiming for ‘purely evidence-based’ inferences is not ambitious enough. Seeking inductive or causal inferences is to aim higher, but ‘no causes in, no causes out’ (Cartwright, 1994) and, I argue, ‘no assumptions in, no inductions out’. In other words, substantive and risky modelling assumptions help turn data into the sort of evidence that supports causal and inductive claims. Third, I acknowledge the convenience-factor of conventional modelling assumptions; proverbial examples include simplistic error structures and the absence of model mis-specification. But with finite samples, the methodology promoted in this paper has its own hazards tucked away. For example, estimators may depend on the particular machine learning method used (kitchen-sink approaches, like SuperLearner, are no panacea); and sample-splitting or cross-fitting can cause biases (such as a tendency to over-penalize more complex models that require larger samples for adequate parameter estimation) as well as noise. Assumption-lean methods are not necessarily superior to assumption-rich methods, but they are surely complimentary. In future applied work, I look forward to adding some of these generic estimand-centric methods to my usual, honestly-reported, model comparisons and tentative inductive leaps.

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