Continous Time Modeling - What, Why and How?
Myself, Rebecca Kuiper and Ellen Hamaker have recently completed work on a book chapter, providing a broad didactical treatment of the continuous-time (CT) first-order vector autoregressive (VAR(1)) model in the context of psychological research using intensive longitudinal (ESM) data. The pre-print of this book chapter is avaiable for download here.
In this chapter we describe the conceptual and practical differences between discrete-time and continous-time approaches, as well as discussing tools like impulse response functions, vector fields and lagged-parameter plots which can be used to interpret CT-VAR(1) models.
To illustrate CT models we re-analyse a single-subject experience sampling dataset, published by Kossakowski et al. (2017) in the Journal of Open Psychology Data, available here. The analysis was conducted with the ctsem package; R code for the analysis is included in the appendix, and can also be found on my github page, along with R-code for generating all of the figures in the chapter.
This chapter is schedule to appear in print in 2018, in the book Continuous time modeling in the behavioral and related sciences edited by K. v. Montfort, J. H. L. Oud, & M. C. Voelkle.