  Inference for the parameters indexing generalised linear models is routinely
based on the assumption that the model is correct and a priori specified. This
is unsatisfactory because the chosen model is usually the result of a
data-adaptive model selection process, which may induce excess uncertainty that
is not usually acknowledged. Moreover, the assumptions encoded in the chosen
model rarely represent some a priori known, ground truth, making standard
inferences prone to bias, but also failing to give a pure reflection of the
information that is contained in the data. Inspired by developments on
assumption-free inference for so-called projection parameters, we here propose
novel nonparametric definitions of main effect estimands and effect
modification estimands. These reduce to standard main effect and effect
modification parameters in generalised linear models when these models are
correctly specified, but have the advantage that they continue to capture
respectively the primary (conditional) association between two variables, or
the degree to which two variables interact (in a statistical sense) in their
effect on outcome, even when these models are misspecified. We achieve an
assumption-lean inference for these estimands (and thus for the underlying
regression parameters) by deriving their influence curve under the
nonparametric model and invoking flexible data-adaptive (e.g., machine
learning) procedures.
