Intraindividual time-varying dynamic network of affects: linear autoregressive mixed-effects models for ecological momentary assessment

Research output: Contribution to journalResearch articleContributedpeer-review


  • Shakoor Pooseh - , Center for Interdisciplinary Digital Sciences (CIDS), University of Freiburg (Author)
  • Raffael Kalisch - , Leibniz Institute of Resilience (LIR), University Medical Center Mainz (Author)
  • Göran Köber - , University Medical Center Freiburg (Author)
  • Harald Binder - , University Medical Center Freiburg (Author)
  • Jens Timmer - , University of Freiburg (Author)


An interesting recent development in emotion research and clinical psychology is the discovery that affective states can be modeled as a network of temporally interacting moods or emotions. Additionally, external factors like stressors or treatments can influence the mood network by amplifying or dampening the activation of specific moods. Researchers have turned to multilevel autoregressive models to fit these affective networks using intensive longitudinal data gathered through ecological momentary assessment. Nonetheless, a more comprehensive examination of the performance of such models is warranted. In our study, we focus on simple directed intraindividual networks consisting of two interconnected mood nodes that mutually enhance or dampen each other. We also introduce a node representing external factors that affect both mood nodes unidirectionally. Importantly, we disregard the potential effects of a current mood/emotion on the perception of external factors. We then formalize the mathematical representation of such networks by exogenous linear autoregressive mixed-effects models. In this representation, the autoregressive coefficients signify the interactions between moods, while external factors are incorporated as exogenous covariates. We let the autoregressive and exogenous coefficients in the model have fixed and random components. Depending on the analysis, this leads to networks with variable structures over reasonable time units, such as days or weeks, which are captured by the variability of random effects. Furthermore, the fixed-effects parameters encapsulate a subject-specific network structure. Leveraging the well-established theoretical and computational foundation of linear mixed-effects models, we transform the autoregressive formulation to a classical one and utilize the existing methods and tools. To validate our approach, we perform simulations assuming our model as the true data-generating process. By manipulating a predefined set of parameters, we investigate the reliability and feasibility of our approach across varying numbers of observations, levels of noise intensity, compliance rates, and scalability to higher dimensions. Our findings underscore the challenges associated with estimating individualized parameters in the context of common longitudinal designs, where the required number of observations may often be unattainable. Moreover, our study highlights the sensitivity of autoregressive mixed-effect models to noise levels and the difficulty of scaling due to the substantial number of parameters.


Original languageEnglish
Article number1213863
Pages (from-to)01-12
Number of pages12
JournalFrontiers in psychiatry
Issue number(2024)
Publication statusPublished - 20 Mar 2024

External IDs

PubMed 38585485
PubMedCentral PMC10997345


Sustainable Development Goals

ASJC Scopus subject areas


  • affect dynamics, autoregressive models, ecological momentary assessment, mixed-effects models, mood networks

Library keywords