# Assumption-lean inference for generalised linear model parameters

arXiv: https://arxiv.org/abs/2006.08402 · HTML: https://mlsanity.com/paper/2006.08402/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 9 of 9)

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- [BELIEF in Dependence: Leveraging Atomic Linearity in Data Bits for Rethinking Generalized Linear Models](https://mlsanity.com/paper/2210.10852/) (2022)
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- [Non-parametric efficient estimation of marginal structural models with multi-valued time-varying treatments](https://mlsanity.com/paper/2409.18782/) (2024)
- [Assumption-Lean Post-Integrated Inference with Surrogate Control Outcomes](https://mlsanity.com/paper/2410.04996/) (2024)

## Abstract (arXiv)

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.