Exploratory Continuous-Time Modeling (Expct): Extracting Dynamic Features from Irregularly Spaced Time Series

When collecting intensive longitudinal data in the social, behavioral and biomedical sciences irregularly spaced data (i.e., data that are not collected at equal intervals) are the norm rather than the exception. However, most of the techniques and models that are used to analyze these data in practice were designed for equally spaced data. Although continuous time vector autoregressive models (CT-VAR) have been recently used to examine the relationship between variables across time differences, the current implementation of these models makes strong assumptions about the functional relationships between variables within the system. The current paper introduces the novel exploratory continuous-time models (expct), which allow for the continuous estimation of multivariate (or univariate) predictors with multivariate outcomes with regularly or irregularly-spaced data. As demonstrated in the Monte-Carlo simulation study, the expct models are able to efficiently model complex auto- and cross-regressive system dynamics without bias. The expct model: (1) addresses intensive data across virtually any time scheme, (2) allows for data collected at different time scales to predict themselves and one another, and (3) makes fewer assumptions about the functional forms of the longitudinal system dynamics between variables.