.
Solutions to the Limited Data Problem
- 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)
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
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
Simulation Study
Simulation Study
Recommendations
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
Thank you for your attention!
References
Abegaz, Fentaw, and Ernst Wit. 2013. “Sparse Time Series Chain Graphical Models for Reconstructing Genetic Networks.” Biostatistics. Biometrika Trust, kxt005.
Rothman, Adam J, Elizaveta Levina, and Ji Zhu. 2010. “Sparse Multivariate Regression with Covariance Estimation.” Journal of Computational and Graphical Statistics 19 (4). Taylor & Francis: 947–62.
Wild, Beate, Michael Eichler, Hans-Christoph Friederich, Mechthild Hartmann, Stephan Zipfel, and Wolfgang Herzog. 2010. “A Graphical Vector Autoregressive Modelling Approach to the Analysis of Electronic Diary Data.” BMC Medical Research Methodology 10 (1). BioMed Central Ltd: 28.