Using Bayesian Nonparametric Hidden Semi-Markov Models to Disentangle Affect Processes during Marital Interaction

Abstract

Sequential affect dynamics generated during the interaction of intimate dyads, such as married couples, are associated with a cascade of effects-some good and some bad-on each partner, close family members, and other social contacts. Although the effects are well documented, the probabilistic structures associated with micro-social processes connected to the varied outcomes remain enigmatic. Using extant data we developed a method of classifying and subsequently generating couple dynamics using a Hierarchical Dirichlet Process Hidden semi-Markov Model (HDP-HSMM). Our findings indicate that several key aspects of existing models of marital interaction are inadequate: affect state emissions and their durations, along with the expected variability differences between distressed and nondistressed couples are present but highly nuanced; and most surprisingly, heterogeneity among highly satisfied couples necessitate that they be divided into subgroups. We review how this unsupervised learning technique generates plausible dyadic sequences that are sensitive to relationship quality and provide a natural mechanism for computational models of behavioral and affective micro-social processes.

Fig 1. Process Flow Of Data Preparation, Modeling, and Simulation.

Fig 2. States Data Reduction Scheme.

Original categories are shown at the top; these were collapsed and summed within dyad. Profiles of possible frequencies and summed values are shown at the bottom, left and right, respectively.

Fig 3. Feature Set Correlation Matrix.

MAT refers to marital satisfaction; Mean refers to States mean; Std refers to States standard deviation.

Fig 4. Distribution of Normalized Features.

MAT refers to reported marital satisfaction; States Mean refers to joint affect expression. MAT and Mean are inversely scales.

Fig 5. Stacked bars showing PMF and CDF of Clusters 1 and 4.

States distributions indicate that unlike the couples in Cluster 4, Cluster 1 couples distribute affect across the range of States.

Fig 6. Jensen-Shannon Matrix.

Note the large divergence between Clusters 1 and 4, both high marital satisfaction clusters.

Fig 7. Estimated Hamming Distance Between Simulated and Realized Data by Cluster.

Vertical bars reflect the Standard Error.

Fig 8. Simulated Distributions Of A Single Dyad From Cluster 1.

The upper graphs show a simulated dyadic 2-d Gaussian of male and female joint affect and the simulated duration distribution. The middle graph illustrates the state sequence with durations indicated by band width. Positive affect is indicated by cooler, bluer colors. The final graphs show male-female interactions for simulated and original data, respectively.

Fig 9. Simulated Sequence Of Dyadic States From Cluster 1.

The realized States sequence derived from male-female affect scores is shown below the simulated sequence.

Fig 10. Comparison Of Simulated States Sequences By Cluster.

Simulated Clusters show clear States differences consistent with the realized data.