Dynamic Network Analysis

An Introduction

Björn Siepe

bjoern.siepe@uni-marburg.de

Psychological Methods Lab, University of Marburg

October 23, 2024

Materials and Goals

Slides at bsiepe.github.io/workshops

Understand advantages and structure of time series data and dynamic networks
Interpret dynamic networks
Get to know core assumptions, evidence, and limitations
Learn about new developments and future research topics

What we don’t cover (in detail)

Planning of longitudinal studies
Panel Data
Data and preprocessing (very important)
Clinical theory

Hype Cycle

Dynamic Networks

General principles

Dynamic associations within individuals
Across time points and at the same time frames
\(n = 1\) (idiographic) and \(n > 1\)
Commonly some form of vector autoregressive (VAR) model
Often some sparsity

Time Series Data

Experience Sampling

Autoregressive

Cross-Lagged

Estimation of idiographic networks

Model Equations

For our example:

\[\begin{aligned} \color{darkred}{Sad_{t}} = \color{blue}{\beta_{11}}*\color{darkred}{Sad_{t-1}} + \color{blue}{\beta_{12}}*\color{darkred}{Rumination_{t-1}} + \color{orange}{\epsilon_{t,1}} \\ \color{darkred}{Rumination_{t}} = \color{blue}{\beta_{21}}*\color{darkred}{Rumination_{t-1}} + \color{blue}{\beta_{22}}*\color{darkred}{Sad_{t-1}} + \color{orange}{\epsilon_{t,2}} \end{aligned}\]

More generally: \[ \color{darkred}{Y_{t}} = \color{blue}{\boldsymbol{B}} \color{darkred}{Y_{t-1}} + \color{orange}{\Sigma} \]

Red: Data at current (\(t\)) and previous (\(t-1\)) time point
Blue: Coefficients for autoregressive and cross-lagged effects
- used for temporal effects
Orange: Residuals/Innovations (in \(\Sigma\) )
- used for contemporaneous effects

Maths Break

Intermediate Summary

Networks are everywhere
Almost any multivariate model can be a network
A lot of cross-sectional studies with limited informativeness
Longitudinal data allows for new insights
Effects across time points and variables

Interpreting dynamic networks

Temporal Network

Effect of variables on themselves and on others over time
Directed effects
Mostly: lag 1
“Granger causality”

“Contemporaneous” Network

Partial correlation of residuals (innovations)
undirected effects not captured by temporal network
For example: effects faster than sampling frequency
Example: \[ Stress \rightarrow Expect\ Panic \rightarrow Fear \]

Putting Things Together

Estimation

large variety of estimation approaches:
- Maximum Likelihood (psychonetrics)
- State-Space Frameworks (dynr)
- Continuous Time Models (ctsem)
- Bayesian Estimation (tsnet)
often induce sparsity via regularization or heuristics

Example: Epskamp et al. (2018)

\(n >1\) Networks

Often used: multilevel modeling
Popular alternative: GIMME
Advantages:
- pool information from individuals
- more power
- Consideration of heterogeneity
- fewer time points necessary
mlVAR (Epskamp et al. 2018)
GIMME (Beltz et al. 2016)
DSEM (Hamaker et al. 2018)

mlVAR and GIMME

mlVAR

Borrow quantitative information
Individual network parameters come from a shared probability distribution
Parameters are “pulled together”
“Between-person” network

GIMME

Borrow qualitative information
Individual networks, but partially common structure
Group, subgroup, individual networks
Heuristic algorithm

Multilevel Example

GIMME Example

Interpretation: Time Intervals

Equal time intervals between measurements. Problem?
- Night effect (Berkhout, Schuurman, and Hamaker 2024)

Interpretation: Time Intervals

Alternative: Continuous time (Ryan and Hamaker 2022)
Correct time intervals for constructs to be measured
- Stress vs. depression

Interpretation: Change over Time

Stationarity assumption: Means, variances, covariances are constant over time
Realistic?

Interpretation: Change over Time

Common solution: Some form of detrending, or modeling change over time (see later slides)
Detrending: Remove change over time

Interpretation: Other Stuff

Causality
Measurement (Bringmann et al. 2022)
Variable selection
Sparsity
Missing data
Distributional assumptions

Optional: Practical Exercise

If time permits:

Open file dynamic_network_exercise.R
Work alone or in groups of 2-3

Google colab link (.ipynb)

Optional: Practical Exercise Discussion

Evidence and Pitfalls

Topics to be covered

Estimation Requirements
Clinical Practice
Density/Centrality
Prediction

Understanding Heterogeneity

Problem: Estimation Instability

# Simulate 20 identical twins
for(i in 1:20){
  l_data[[i]] <- 
    graphicalVAR::graphicalVARsim(
      nTime = 70,
      beta = person_1$beta,
      kappa = person_1$kappa
      )
# Fit network models
  l_fits[[i]] <- graphicalVAR(l_data[[i]])
}

Feasibility of Idiographic Networks

The robustness of network results now firmly ranks as one of the field’s top priorities. (Marsman and Rhemtulla 2022)

often only have vague rules of thumb
Number of time points?
Number of variables?
- always think about number of paths to estimate!
- idiographic gVAR:
  - 3 variables: \(9 + 3 = 12\) parameters
  - 5 variables: \(25 + 10 = 35\) parameters

Solutions for Estimation Instability

Tests to compare idiographic networks
- Hoekstra, Epskamp, et al. (2024): R package INIT based on SEM
- Siepe, Kloft & Heck (2024): R package tsnet based on Bayesian estimation
With \(n > 20\) (or so): Go multilevel/GIMME
- Multilevel often outperforms \(n = 1\), even if true model is idiographic (Lafit, Meers, and Ceulemans 2021)
Sample size planning for \(n = 1\) (Revol, Lafit, and Ceulemans 2024)

Solutions for Estimation Instability

Evidence in Clinical Practice

Frumkin et al. (2021)
- Few case studies
- Patients more convinced than therapists
Levinson et al. (2023)
- n = 79, eating disorders
- Module selection based on networks
Hall et al. (2022)
- Individual case study on TheraNET
- Good example of detailed, network-based feedback
- Apparently RCT planned
No clear evidence
Many different possibilities for use (Schumacher, Burger, et al. 2024)

Recent developments

Cooperation between therapist/patient and data
Changes over time
Prediction of therapy outcomes

PECAN

PREMISE

Time varying networks

Centrality/Density

When does it make sense to assume that a higher density is “bad”?

Centrality/Density: Consider Uncertainty

Prediction

Prediction

Johal and Rhemtulla (2024):
- Using network-derived metrics to predict an outcome
- Network features did not work very well
Schumacher, Klein, et al. (2024)
- Using pairwise symptom associations and centrality to predict an outcome

Tip

Start simple instead of complicated (Bringmann 2024)

It is hard to beat the mean (Dejonckheere et al. 2019)

Which analyses?

Analytic uncertainty: Go multiverse

Which analyses? Consider Theory

What is the VAR-based network representing, and what hypotheses are we testing with it? […] can be more explicit about which connections in the network are to be expected and which are contrary to previous knowledge (Bringmann 2021)

Come up with strong tests:

compare network models with simpler models
compare network feedback with placebo/simpler feedback
compare network centrality with simpler features

Summary

Outlook

Main Takeaways

Networks are conceptually attractive
Longitudinal data give us new information … but also new problems
High diversity in network approaches
Evidence of utility is still scarce
Embrace simplicity and uncertainty

Questions or Comments? 💡

Get in Touch

Feel

free

contact

bjoern.siepe@uni-marburg.de

Resources

Materials

PNAWS 2020 - freely accessible. Partly served as inspiration for this workshop, especially the slides by Julian Burger.

Psych Networks Blog - no longer active, but interesting backlog

Workshops by Noémi Schuurman - multiple materials for multilevel models in R and MPlus

Applied Workshop by Me - slides including more code examples etc.

Figures

Jeremykemp at English Wikipedia (https://commons.wikimedia.org/wiki/File:Gartner_Hype_Cycle.svg), „Gartner Hype Cycle”, https://creativecommons.org/licenses/by-sa/3.0/legalcode

Foto von Sabina auf Unsplash

Foto von Jonas Leupe auf Unsplash

Rumination icons created by Freepik - Flaticon

Shiny App Screenshot from https://gitlab.kuleuven.be/ppw-okpiv/researchers/u0148925/shinyapp-paa_var_n1

Hehe GIF from giphy

Treadmill GIF from tenor

Regression Meme created with ImgFlip

References

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Berkhout, Sophie W., Noémi Katalin Schuurman, and Ellen Hamaker. 2024. “Let Sleeping Dogs Lie? How to Deal with the Night Gap Problem in ESM Data.” May 28, 2024. https://doi.org/10.31234/osf.io/2hec8.

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———. 2024. “The Future of Dynamic Networks in Research and Clinical Practice.” World Psychiatry 23 (2): 288–89. https://doi.org/10.1002/wps.21209.

Bringmann, Laura F., Casper Albers, Claudi Bockting, Denny Borsboom, Eva Ceulemans, Angélique Cramer, Sacha Epskamp, et al. 2022. “Psychopathological Networks: Theory, Methods and Practice.” Behaviour Research and Therapy 149 (February): 104011. https://doi.org/10.1016/j.brat.2021.104011.

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