# Jointly estimating individual and group networks from fMRI data

## TL;DR

This paper introduces a multilevel method to estimate brain networks from fMRI data, capturing both individual and group-level connectivity patterns.

## Contribution

A novel multilevel approach combining Gaussian and Curie-Weiss graphical models for fMRI network estimation.

## Key findings

- The proposed method outperforms individual or aggregate analysis in recovering network edges.
- The method recovers seven known resting-state networks at the group level while revealing individual variability.
- Multilevel modeling is shown to be necessary to avoid paradoxical results from ignoring nested data structures.

## Abstract

In fMRI research, graphical models are used to uncover complex patterns of relationships between brain regions. Connectivity-based fMRI studies typically analyze nested data; raw observations, for example, BOLD responses, are nested within participants, which are nested within populations, for example, healthy controls. Often, studies ignore the nested structure and analyze participants either individually or in aggregate. This overlooks the distinction between within-participant and between-participant variance, which can lead to poor generalizability of results because group-level effects do not necessarily reflect effects for each member of the group and, at worst, risk paradoxical results where group-level effects are opposite to individual-level effects (e.g., Kievit, Frankenhuis, Waldorp, & Borsboom, 2013; Robinson, 2009; Simpson, 1951). To address these concerns, we propose a multilevel approach to model the fMRI networks, using a Gaussian graphical model at the individual level and a Curie-Weiss graphical model at the group level. Simulations show that our method outperforms individual or aggregate analysis in edge retrieval. We apply the proposed multilevel approach to resting-state fMRI data of 724 healthy participants, examining both their commonalities and individual differences. We not only recover the seven previously found resting-state networks at the group level but also observe considerable heterogeneity in the individual-level networks. Finally, we discuss the necessity of a multilevel approach, additional challenges, and possible future extensions.