Intensive Longitudinal Data

This paper presents a hybrid sampler – alternating between one step of the No-U-Turn Sampler (NUTS) and one Gibbs step – for estimating dynamic structural equation models with binomial outcomes. The Gibbs step handles Pólya-Gamma distributed latent variables arising from a logit link, and the NUTS step uses a Kalman filter to marginalize over latent states. We demonstrate that the proposed sampler makes DSEM estimation with binomial data feasible for larger data and models than previously possible. arXiv preprint.

This paper shows that the within-level part of any dynamic structural equation model can be reformulated as a linear Gaussian state space model. Consequently, the latent states can be analytically marginalized using a Kalman filter, allowing for highly efficient estimation via Hamiltonian Monte Carlo. This makes DSEM estimation computationally tractable for much larger datasets than what has been previously possible. arXiv preprint.

Dynamic structural equation models have become extremely popular for analysis of intensive longitudinal data in the social sciences. One outstanding problem is how to handle nonlinear trends and cycles, and in this paper we propose to do this in a very flexible manner using regression splines. We test the methods in simulation studies, and then illustrate them by analyzing a diary data set on alcohol consumption and stress. Open-source Stan code is available from our OSF repository. Published in Multivariate Behavioral Research.