A Person- and Time-Varying Vector Autoregressive Model to Capture Interactive Infant-Mother Head Movement Dynamics

Abstract

Head movement is an important but often overlooked component of emotion and social interaction. Examination of regularity and differences in head movements of infant-mother dyads over time and across dyads can shed light on whether and how mothers and infants alter their dynamics over the course of an interaction to adapt to each others. One way to study these emergent differences in dynamics is to allow parameters that govern the patterns of interactions to change over time, and according to person- and dyad-specific characteristics. Using two estimation approaches to implement variations of a vector-autoregressive model with time-varying coefficients, we investigated the dynamics of automatically-tracked head movements in mothers and infants during the Face-Face/Still-Face Procedure (SFP) with 24 infant-mother dyads. The first approach requires specification of a confirmatory model for the time-varying parameters as part of a state-space model, whereas the second approach handles the time-varying parameters in a semi-parametric (“mostly” model-free) fashion within a generalized additive modeling framework. Results suggested that infant-mother head movement dynamics varied in time both within and across episodes of the SFP, and varied based on infants’ subsequently-assessed attachment security. Code for implementing the time-varying vector-autoregressive model using two R packages, dynr and mgcv, is provided.

Keywords:

• Time-varying parameters
• vector autoregressive models
• state-space models
• generalized additive models
• parent-infant interactions
• head movements
• still-face paradigm

Article information

Conflict of interest disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was supported by National Institutes of Health (NIH) grant R01GM105004, the NIH Intensive Longitudinal Health Behavior Cooperative Agreement Program U24AA027684, National Institute of Mental Health grant MH096951, National Institute of General Medical Sciences grant 1R01GM105004, National Science Foundation grants BCS-1052736, IGE-1806874, IIS-1418026, SES-1357666, IBSS-L 1620294, and the Pennsylvania State University Quantitative Social Sciences Initiative and UL TR000127 from the National Center for Advancing Translational Sciences.

Role of the funders/sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments

The authors would like to thank the associate editor Dr. Zhiyong Zhang, the anonymous reviewers, Dr. László A. Jeni, Dr. Nilam Ram, and various colleagues and students in the QuantDev group of the Pennsylvania State University for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions or funding agencies is not intended and should not be inferred.

Notes

1 The current version of the software is now publicly available at https://github.com/department-of-psychology/AFARtoolbox.

2 R code for simulating data and reproducing Figure 3 is included in the Supplementary Material.

3 In thin plate regression splines, the basis is obtained through eigen-decomposition of a data-determined matrix. Please refer to Wood (2003) for details.

4 Due to the observability constraint (elaborated in the Discussion) of the original VAR model, we can only fit up to two TVPs at a time.