A tutorial on group effective connectivity analysis, part 2: second level analysis with PEB

TL;DR

This paper explains how to use hierarchical Bayesian models combining DCM and PEB to analyze inter-subject variability in neural effective connectivity, with practical guidance and example data.

Contribution

It provides a detailed tutorial on applying second-level PEB analysis for group effective connectivity, integrating hierarchical modeling with DCM and GLM.

Findings

Demonstrates how to model inter-subject variability in effective connectivity

Shows how group-level priors improve subject-level parameter estimation

Provides step-by-step instructions with example data for reproducibility

Abstract

This tutorial provides a worked example of using Dynamic Causal Modelling (DCM) and Parametric Empirical Bayes (PEB) to characterise inter-subject variability in neural circuitry (effective connectivity). This involves specifying a hierarchical model with two or more levels. At the first level, state space models (DCMs) are used to infer the effective connectivity that best explains a subject's neuroimaging timeseries (e.g. fMRI, MEG, EEG). Subject-specific connectivity parameters are then taken to the group level, where they are modelled using a General Linear Model (GLM) that partitions between-subject variability into designed effects and additive random effects. The ensuing (Bayesian) hierarchical model conveys both the estimated connection strengths and their uncertainty (i.e., posterior covariance) from the subject to the group level; enabling hypotheses to be tested about the commonalities and differences across subjects. This approach can also finesse parameter estimation at the subject level, by using the group-level parameters as empirical priors. We walk through this approach in detail, using data from a published fMRI experiment that characterised individual differences in hemispheric lateralization in a semantic processing task. The preliminary subject specific DCM analysis is covered in detail in a companion paper. This tutorial is accompanied by the example dataset and step-by-step instructions to reproduce the analyses.