Advocating a New Default for Time Series Modeling: Asymmetric Temporal Dynamics using Threshold Dynamics Parameters

Abstract

The availability of intensive longitudinal data has rapidly increased, and with it our ability to understand how behavior evolves. Statistical models to analyze such data often include dynamics parameters that capture dependencies within or between variables over time. However, these dynamics parameters are typically thought to operate independently of the current value of the time series. Here, we argue that by doing so important information on psychological processes is overlooked. We therefore propose the DYNamics of ASymmetric TIme series (or DYNASTI) approach in which dynamics parameters are allowed to differ, depending on whether they operate above, or below, the time series mean of a given person or unit of analysis. For instance, the effect of exercise on health outcomes may vary depending on whether a person exercises more, or less, than average. Or, the inertia of sleep may vary depending on whether a person sleeps more, or less, than their average. Through extensive simulations, we show that DYNASTI implementations of two commonly used time series models (DSEM and RI-CLPM) are able to adequately recover both symmetric and asymmetric temporal dynamics above and below the time series mean. Importantly, we also show that assuming symmetric dynamics (as in the vast majority of the literature) when processes are in fact asymmetric leads to incorrect conclusions about these dynamics. We further illustrate the workings of DYNASTI implementations and how they can lead to new insights in empirical examples regarding negative affect, smoking urges, and anxiety. To implement, and extend, DYNASTI models we provide an annotated, open source code base built in RStan. Together, these results advocate DYNASTI implementations as a new default for time series modeling.

Authors 5

1. Jessica Vera Schaaf corresponding

   Radboud University Medical Center · Donders Institute for Brain, Cognition and Behaviour

   Affiliation as printed

   Cognitive Neuroscience Department, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, Netherlands

2. Øystein Sørensen

   University of Oslo

   Affiliation as printed

   Department of Psychology, University of Oslo, Oslo, Norway

3. Ethan Michael McCormick Aachen Methodology and Statistics Department Institute of Psychology, Leiden University

   Leiden University · University of North Carolina at Chapel Hill

   Affiliation as printed

   University of North Carolina at Chapel Hill

   Methodology & Statistics Department, Institute of Psychology, Leiden University, Leiden, Netherlands

4. Michael Aristodemou

   Radboud University Medical Center · Donders Institute for Brain, Cognition and Behaviour

   Affiliation as printed

   Cognitive Neuroscience Department, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, Netherlands

5. Rogier Kievit

   University of Cambridge · Radboud University Medical Center · Donders Institute for Brain, Cognition and Behaviour · MRC Cognition and Brain Sciences Unit

   Affiliation as printed

   Cognitive Neuroscience Department, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, Netherlands

   MRC Cognition and Brain Sciences Unit, University of Cambridge, Cambridge, United Kingdom