26 Feb 2016

  • Hamaker, E. L., & Grasman, R. P. P. P. (2014). To center or not to center? Investigating inertia with a multilevel autoregressive model. Frontiers in Psychology, 5, 1492. http://doi.org/10.3389/fpsyg.2014.01492

Experience Sampling Method (ESM)

The Dynamics of Psychology

  • 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


  • Introduction Vector Auto-regression
  • Problem 1: \(n=1\) and limited observations
    • Graphical VAR
  • Problem 2: \(n>1\)
    • Multi-level VAR
  • Problem 3: Measurement error
    • State-space models
  • Even more problems

Vector Auto-regression

Vector Auto-Regression (VAR)

  • Regress a vector of variables from a single subject on the previous time point
  • Assume multivariate normality
  • Assume errors are correlated
  • This leads to three things to estimate:
    • A vector of intercepts
    • A matrix encoding a temporal network
    • A matrix encoding a contemporaneous network
  • Can be estimated using lm() or any least squares regression method

For a single subject: \[ \begin{aligned} \pmb{y}_t &= \pmb{\tau} + \pmb{B} \pmb{y}_{t-1} + \pmb{\varepsilon}_t \\ \pmb{\varepsilon}_t &\sim N\left( \pmb{0}, \pmb{\Theta} \right). \end{aligned} \] \(\pmb{B}\) encodes a directed temporal network and \(\pmb{\Theta}\) and undirected contemporaneous network

Vector Auto-Regression (VAR)

Vector Auto-Regression (VAR)

With \(\pmb{K} = \pmb{\Sigma}^{-1}\) encoding partial correlations coefficients

Problem 1: \(n=1\) and limited observations

Networks in Clinical Practice

  • Measure a patient over a short time, estimate network structures and use these in clinical practice
  • Naturally \(n=1\) problem
    • Different estimation periods
    • Different nodes
  • Naturally a limited data problem
    • You can't measure a patient 10 times per day
    • You can't measure a patient for months

  • Only model temporal effects between consecutive measurements
    • Lag-1
  • Assume both the temporal and contemporaneous effects are sparse
    • Only a relatively little number of edges in both networks
  • To do this, we use the graphical VAR model (Wild et al. 2010)
    • Estimation via LASSO regularization, using extended 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)

Empirical Example

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