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A Continuous-Time Dynamic Factor Model for Intensive Longitudinal Data Arising from Mobile Health Studies.

Madeline R Abbott1, Walter H Dempsey1, Inbal Nahum-Shani2

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Summary

This study introduces a dynamic factor model to analyze intensive longitudinal data (ILD) from mobile health (mHealth) studies. The model simplifies complex emotion dynamics into interpretable latent processes for better behavioral science insights.

Keywords:
Ornstein-Uhlenbeck stochastic processdynamic factor modelintensive longitudinal datamobile health

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Area of Science:

  • Psychology
  • Statistics
  • Mobile Health

Background:

  • Intensive longitudinal data (ILD) from mobile health (mHealth) studies offer rich insights into dynamic outcomes.
  • Analyzing multivariate longitudinal outcomes requires sophisticated statistical models.

Purpose of the Study:

  • To develop a dynamic factor model for summarizing ILD into low-dimensional, interpretable latent processes.
  • To capture the continuous-time dynamics of multivariate latent processes using an Ornstein-Uhlenbeck (OU) stochastic process.

Main Methods:

  • A dynamic factor model combining a factor analysis measurement submodel and an OU stochastic process structural submodel.
  • Derivation of a closed-form likelihood and a sparse precision matrix for computational efficiency.
  • A block coordinate descent algorithm for model estimation, validated through simulation studies.

Main Results:

  • The proposed dynamic factor model effectively summarizes complex ILD.
  • Simulation studies demonstrate good statistical properties for the estimation algorithm with ILD.
  • Application to mHealth data reveals interpretable latent factors summarizing the dynamics of 18 emotions.

Conclusions:

  • The dynamic factor model provides a powerful tool for analyzing emotion dynamics in mHealth data.
  • The model facilitates the interpretation of momentary emotions and latent psychological states.
  • Findings can advance behavioral science theories on emotion dynamics and psychological states.