Marginal additive models for population‐averaged inference in longitudinal and cluster‐correlated data

Abstract

We propose a novel marginal additive model (MAM) for modelling cluster‐correlated data with non‐linear population‐averaged associations. The proposed MAM is a unified framework for estimation and uncertainty quantification of a marginal mean model, combined with inference for between‐cluster variability and cluster‐specific prediction. We propose a fitting algorithm that enables efficient computation of standard errors and corrects for estimation of penalty terms. We demonstrate the proposed methods in simulations and in application to (i) a longitudinal study of beaver foraging behaviour, and (ii) a spatial analysis of Loaloa infection in West Africa.This article is protected by copyright. All rights reserved.

A transformation perspective on marginal and conditional models

“…Naturally, the questions arises which model is to be preferred: a marginal, a conditional, or a marginally interpretable one? In this case, the “right” model is not the model which most closely reflects the data generating process, which is usually unknown, but rather the model that allows the user to answer the research question at hand by interpreting the estimated parameters, as McGee and Stringer (2022) point out. An advantage of transformation models is that besides allowing for interpretation of the fixed-effects on a marginal level, they also yield valid models for the whole marginal distribution (2.1) of the response given the covariates.…”

“…Later, marginalized multilevel models ( Heagerty, 1999 ; Heagerty and Zeger, 2000 ) were introduced providing a likelihood-based approach to estimate marginal coefficients in the framework of a conditional model. Gory and others (2021) contribute a model definition allowing parameters estimated in a conditional model to be interpreted in a marginal fashion, and McGee and Stringer (2022) discuss marginal additive models for potentially nonlinear population-averaged associations, starting from a generalized additive mixed-model framework.…”