Randomized opinion dynamics over networks: influence estimation from partial observations

In this paper, we propose a technique for the estimation of the influence matrix in a sparse social network, in which $n$ individual communicate in a gossip way. At each step, a random subset of the social actors is active and interacts with randomly chosen neighbors. The opinions evolve according to a Friedkin and Johnsen mechanism, in which the individuals updates their belief to a convex combination of their current belief, the belief of the agents they interact with, and their initial belief, or prejudice. Leveraging recent results of estimation of vector autoregressive processes, we reconstruct the social network topology and the strength of the interconnections starting from \textit{partial observations} of the interactions, thus removing one of the main drawbacks of finite horizon techniques. The effectiveness of the proposed method is shown on randomly generation networks

Motivational Message Framing Effects on Physical Activity Dynamics in a Digital Messaging Intervention: Secondary Analysis

BackgroundDigital smartphone messaging can be used to promote physical activity to large populations with limited cost. It is not clear which psychological constructs should be targeted by digital messages to promote physical activity. This gap presents a challenge for developing optimal content for digital messaging interventions. ObjectiveThe aim of this study is to compare affectively framed and social cognitively framed messages on subsequent changes in physical activity using dynamical modeling techniques. MethodsWe conducted a secondary analysis of data collected from a digital messaging intervention in insufficiently active young adults (18-29 years) recruited between April 2019 and July 2020 who wore a Fitbit smartwatch for 6 months. Participants received 0 to 6 messages at random per day across the intervention period. Messages were drawn from 3 content libraries: affectively framed, social cognitively framed, or inspirational quotes. Person-specific dynamical models were identified, and model features of impulse response and cumulative step response were extracted for comparison. Two-way repeated-measures ANOVAs evaluated the main effects and interaction of message type and day type on model features. This early-phase work with novel dynamic features may have been underpowered to detect differences between message types so results were interpreted descriptively. ResultsMessages (n=20,689) were paired with valid physical activity monitoring data from 45 participants for analysis. Received messages were distributed as 40% affective (8299/20,689 messages), 39% social-cognitive (8187/20,689 messages), and 20% inspirational quotes (4219/20,689 messages). There were no statistically significant main effects for message type when evaluating the steady state of step responses. Participants demonstrated heterogeneity in intervention response: some had their strongest responses to affectively framed messages, some had their strongest responses to social cognitively framed messages, and some had their strongest responses to the inspirational quote messages. ConclusionsNo single type of digital message content universally promotes physical activity. Future work should evaluate the effects of multiple message types so that content can be continuously tuned based on person-specific responses to each message type