For the Interdisciplinary Centre of Psychopathology and Emotion Regulation at Groningen University, I performed multiple simulation studies to investigate the model selection and parameter recovery performance of the automated (n=1) VAR modeling procedure (AutovarCore) under ideal circumstances (no violated assumptions), and under the circumstance where the residuals of the VAR model are either skewnormally or truncated normally distributed.
My (recently finished) PhD project focused on further studying/developing/extending multilevel vector autoregressive models (multilevel VAR models), and was supervised by Ellen Hamaker, with Herbert Hoijtink as my promotor. I have worked on the optimal way to standardize the multilevel VAR models, and the optimal way to specify prior(s) for the covariance matrix of the random parameters for the Bayesian estimation of these models. Further, I worked on the incorporation of measurement error in n=1 and multilevel VAR modeling. For more info, see below, or download a copy of my dissertation.
Both n=1 and multilevel VAR models disregard that there may be measurement error, or other occasion-specific fluctuations in the observed scores. Disregarding such fluctuations results in (potentially severe) bias in the autoregressive and cross-lagged effects. In work together with Jan Houtveen and Ellen Hamaker I present two n=1 autoregressive models that account for such fluctuations (the ARMA model and the AR+White Noise or AR+WN model), and compare their performance in a simulation study, for both a Bayesian and a frequentist estimation procedure. In other work together with Ellen Hamaker, I present a Bayesian multilevel VAR model that accounts for measurement error. We also show how this model can be used to obtain reliability estimates for the scores of each participant separately.
Research together with Emilio Ferrer, Mieke de Boer-Sonnenschein, and Ellen Hamaker. We argue the importance of looking beyond just the fixed effects in a multilevel model, and that in order to directly compare cross-lagged coefficients in a multilevel model, these coefficients should be within-person standardized. Supplementary Materials
Research together with Ellen Hamaker and Raoul Grasman. The conjugate prior distribution for the covariance matrix of random parameters in a multilevel (hierarchical) Bayesian model is the Inverse-Wishart matrix. However, for small variances the IW-distribution is very informative (much like its univariate little brother, the Inverse-Gamma distribution, see this paper by Andrew Gelman). For stationary multilevel AR models, the variance of the autoregressive parameters will always be small. We perform a simulation study to compare various IW prior specifications suggested in the literature. Supplementary Materials
For my master thesis in 2011, under supervision of Conor Dolan at the University of Amsterdam (in 2011), I implemented a bivariate multilevel dynamic factor model in winBUGS. The model allows for random means, factor loadings, and autoregressive and cross-lagged coefficients.
During my internship for Denny Borsboom at the University of Amsterdam (in 2010), I used n=1 vector autoregressive models to create person-specific granger-causal networks (using Qgraph). VAR-based person-specific networks are currently still used for the Psychosystems project.