  Longitudinal interaction studies with Socially Assistive Robots are crucial
to ensure that the robot is relevant for long-term use and its perceptions are
not prone to the novelty effect. In this paper, we present a dynamic Bayesian
network (DBN) to capture the longitudinal interactions participants had with a
teleoperated robot coach (RC) delivering mindfulness sessions. The DBN model is
used to study complex, temporal interactions between the participants
self-reported personality traits, weekly baseline wellbeing scores, session
ratings, and facial AUs elicited during the sessions in a 5-week longitudinal
study. DBN modelling involves learning a graphical representation that
facilitates intuitive understanding of how multiple components contribute to
the longitudinal changes in session ratings corresponding to the perceptions of
the RC, and participants relaxation and calm levels. The learnt model captures
the following within and between sessions aspects of the longitudinal
interaction study: influence of the 5 personality dimensions on the facial AU
states and the session ratings, influence of facial AU states on the session
ratings, and the influences within the items of the session ratings. The DBN
structure is learnt using first 3 time points and the obtained model is used to
predict the session ratings of the last 2 time points of the 5-week
longitudinal data. The predictions are quantified using subject-wise RMSE and
R2 scores. We also demonstrate two applications of the model, namely,
imputation of missing values in the dataset and estimation of longitudinal
session ratings of a new participant with a given personality profile. The
obtained DBN model thus facilitates learning of conditional dependency
structure between variables in the longitudinal data and offers inferences and
conceptual understanding which are not possible through other regression
methodologies.
