• Psychological constructs can be conceptualized as dynamical systems, featuring complex emergent behavior:
  • Correlated responses
  • Stable "traits"
  • Phase transitions
  • Individual Differences
• These systems can be portrayed as networks

Van der Maas et al. (2006)

Video

• What is the structure of psychology?

• Cross-sectional analysis
  • Portrays pairwise effects and conditional independences in a dataset between persons
  • Undirected networks or directed acyclic networks
• \(N=1\) longitudinal analysis
  • Shows the intra-individual dynamics of a single person
  • Temporal (directed) and contemporaneous (undirected) networks
• \(N>1\) longitudinal analysis (multi-level)
  • Shows general intraindividual dynamics as well as size of inter-individual differences
  • Temporal (directed) networks

• \(B\) separates \(A\) and \(C\)
• \(A \!\perp\!\!\!\perp C \mid B\)

• A well accepted approach for jointly model selection and parameter estimation is the least absolute shrinkage and selection operator (LASSO)
  • Penalized maximum likelihood estimation
• LASSO utilizes a penalty parameter, which can be chosen to optimize some information criterion
  • Extended Bayesian information criterion (EBIC)

• Binary data:
  • LASSO: IsingFit (cran.r-project.org/package=IsingFit)
  • No LASSO: IsingSampler (cran.r-project.org/package=IsingSampler)
• Multivariate normal data:
  • LASSO: qgraph with option graph = "glasso"
  • No LASSO: qgraph with option graph = "pcor"
  • cran.r-project.org/package=qgraph

I will analyze the BFI dataset from the pych package:

• 25 items
• 2800 subjects
• Five items for each of the five central personality traits

library("psych")
?bfi

Am indifferent to the feelings of others.

Inquire about others' well-being.

Know how to comfort others.

Love children.

Make people feel at ease.

Am exacting in my work.

Continue until everything is perfect.

Do things according to a plan.

Do things in a half-way manner.

Waste my time.

Don't talk a lot.

Find it difficult to approach others.

Know how to captivate people.

Make friends easily.

Take charge.

Get angry easily.

Get irritated easily.

Have frequent mood swings.

Often feel blue.

Panic easily.

Am full of ideas.

Avoid difficult reading material.

Carry the conversation to a higher level.

Spend time reflecting on things.

Will not probe deeply into a subject.

• Only model temporal effects between consecutive measurements
  • Lag-1
• Assume both the temporal and contemporaneous effects are sparse
  • Only a relatively little amount of edges in both networks
• To do this, we use the graphical VAR model (Wild et al. 2010)
  • Estimation via LASSO regularization, using BIC to select optimal tuning parameter (Rothman, Levina, and Zhu 2010; Abegaz and Wit 2013).
• We implemented these methods in the R package graphicalVAR (cran.r-project.org/package=graphicalVAR)

Data collected by Date C. Van der Veen, in collaboration with Harriette Riese en Renske Kroeze.

• Patient suffering from panic disorder and depressive symptoms
  • Perfectionist
• Measured over a period of two weeks
• Five times per day
• Items were chosen after intake together with therapist

Feeling worthless interacts with feeling helpless

Feeling stressed interacts with feeling the need to do things

Central node: Feeling sad

Cycle of enjoyment, feeling sad, feeling worthless and being active

Having to had to do things leads to letting important things pass

Fear of panic attack is not connected

Graphical VAR can be used in a clinical setting with:

• At least 30 measurements
  • More than two measurements per day for a two-week period
• At most 10 nodes
  • Unless the amount of measurements is high

• When multiple persons are measured over a period of time, multi-level VAR can be used
• Estimates fixed effects temporal networks as well as variation due to individual differences
• Explained by Bringmann et al. (2013)
• Implemented in mlVAR (https://github.com/SachaEpskamp/mlVAR)

Lag-1 model

Level 1: \[ \pmb{y}_t^{(p)} = \pmb{B}^{(p)} \pmb{y}_ {t-1}^{(p)} + \pmb{\varepsilon}_t^{(p)} \]

Level 2: \[ \begin{aligned} \pmb{\beta}_ {ij}^{(p)} &= b_{ij} + u^{(p)}_{ij} \\ u^{(p)}_{ij} &\sim N(0, \sigma_{ij}) \end{aligned} \]

Lag-2 model

Level 1: \[ \pmb{y}_t^{(p)} = \pmb{B}_1^{(p)} \pmb{y}_ {t-1}^{(p)} + \pmb{B}_2^{(p)} \pmb{y}_ {t-2}^{(p)} + \pmb{\varepsilon}_t^{(p)} \]

Level 2: \[ \begin{aligned} \pmb{\beta}_ {lij}^{(p)} &= b_{lij} + u^{(p)}_{lij} \\ u^{(p)}_{lij} &\sim N(0, \sigma_{lij}) \end{aligned} \]

• For each node:
• Start with model containing only auto-regression (fixed + random)
• Remove or re-add edges (fixed + random) as long as it improves AIC/BIC