Flexible Marginal Models for Dependent Data

TL;DR

This paper introduces a flexible marginal additive model (MAM) for analyzing dependent data with non-linear associations, providing a unified framework for estimation, inference, and prediction in clustered data.

Contribution

The paper presents a novel MAM framework that handles non-linear population-averaged associations in dependent data, with an efficient fitting algorithm and comprehensive inference tools.

Findings

Demonstrated effectiveness through simulations

Applied to beaver foraging behavior study

Analyzed Loaloa infection spatially in West Africa

Abstract

Models for dependent data are distinguished by their targets of inference. Marginal models are useful when interest lies in quantifying associations averaged across a population of clusters. When the functional form of a covariate-outcome association is unknown, flexible regression methods are needed to allow for potentially non-linear relationships. 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. R code for implementing the proposed methodology is available at https://github.com/awstringer1/mam.