A hierarchical state space approach to affective dynamics

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Abstract

Linear dynamical system theory is a broad theoretical framework that has been applied in various research areas such as engineering, econometrics and recently in psychology. It quantifies the relations between observed inputs and outputs that are connected through a set of latent state variables. State space models are used to investigate the dynamical properties of these latent quantities. These models are especially of interest in the study of emotion dynamics, with the system representing the evolving emotion components of an individual. However, for simultaneous modeling of individual and population differences, a hierarchical extension of the basic state space model is necessary. Therefore, we introduce a Bayesian hierarchical model with random effects for the system parameters. Further, we apply our model to data that were collected using the Oregon adolescent interaction task: 66 normal and 67 depressed adolescents engaged in a conflict-oriented interaction with their parents and second-to-second physiological and behavioral measures were obtained. System parameters in normal and depressed adolescents were compared, which led to interesting discussions in the light of findings in recent literature on the links between cardiovascular processes, emotion dynamics and depression. We illustrate that our approach is flexible and general: The model can be applied to any time series for multiple systems (where a system can represent any entity) and moreover, one is free to focus on various components of this versatile model.

Introduction

The role affect and emotions play in our daily life can hardly be overestimated. Affect and emotions produce the highs and lows of our lives. We are happy when a paper gets accepted, we are angry if a colleague intentionally spreads gossip about us and we feel guilty when we cross a deadline for a review. For some people, their affect is a continuous source of trouble because they suffer from affective disorders, such as a specific phobia or depression.

As for any aspect of human behavior, emotions are extremely complex phenomena, for several reasons. First, they are multicomponential, consisting of experiential, physiological and behavioral components (Gross, 2002). If you are afraid when walking alone on a deserted street late at night, this may lead to bodily effects such as heart palpitations but also to misperceptions of stimuli in the environment and a tendency to walk faster. Second, an emotion fluctuates over time. Without going into the muddy waters of what the exact definition of an emotion is (see Bradley & Lang, 2007), it is clear that emotions function to signal relevant events for our goals (Oatley & Jenkins, 1992). Because of their communicative function, emotions have a clear temporal component (see e.g.,Frijda, Mesquita, Sonnemans, & Van Goozen, 1991) and therefore a genuine understanding of emotions implies an understanding of their underlying dynamics. Third, emotional reactions are subject to contextual and individual differences (see e.g., Barrett et al., 2007, Kuppens et al., 2009).

These complicating factors make the study of affective dynamics a challenging research domain, which requires an understanding of the complex interplay between the different emotion components across time, context and individual differences (Scherer, 2000, Scherer, 2009). Despite its importance and complexity, research on emotion dynamics is still in its infancy (Scherer, 2000). Aside from the lack of a definite theoretical understanding of affective phenomena, a large part of the reason for this lies in the complexity of the data involved in such an enterprise. For instance, because of the prominent physiological component of affect, biological signal processing techniques are required and these are typically not part of the psychology curriculum. On the other hand, the existing methods, traditionally developed and studied in the engineering science, are not directly applicable. As we explain below, we believe one of the major bottlenecks is the existence of individual differences. Indeed, as noted by Davidson (1998), one of the most striking features of emotions is the presence of significant individual differences in almost all aspects involved in their elicitation and control. Incorporating such differences is therefore crucial, not only to account fully for the entire range of emotion dynamics across individuals, but also for studying the differences between individuals characterized by adaptive or maladaptive emotional functioning.

As an example, let us introduce the data that will be discussed and investigated below. Two groups of adolescents (one with Major Depressive Disorder and the other without any emotional or behavioral problems) engaged in an interaction task with their parents during a few minutes in which they discussed and tried to resolve a topic of conflict. During the task, several physiological measures were recorded from the adolescent. Moreover, the behavior of the adolescent and parents was observed and micro-socially coded. All measures were obtained on a second-to-second basis. Several possible research questions are: In what way do the physiological dynamics differ between depressed adolescents and healthy controls (hereafter referred to as normals)? What is the effect of the display of angry behavior by a parent on the affective physiology observed in the adolescent, and is this effect different for depressed and normal adolescents?

A powerful modeling framework that is capable for addressing the above questions is provided by state space modeling. State space models will be explained in detail in the next section, but for now it suffices to say that they have been developed to model the dynamics of a system from measured inputs and outputs using latent states. Usually, it is a single system that is being studied. However, in the particular example in this paper there are as many systems as participants. Because a single state space is already a complex model for statistical inference, studying several of these state space models simultaneously is a daunting task. However, in the present paper we offer a solution to this problem by incorporating state space models in a hierarchical Bayesian framework, which allows one to study multiple systems (e.g., individuals) simultaneously, and thus allows one to make inferences about differences between individuals in terms of their affective dynamics. Markov chain Monte Carlo methods make the task of statistical inference for such hierarchical models more digestible and the Bayesian approach lets us summarize the most important findings in a straightforward way.

In sum, the goal of this paper is to introduce a hierarchical state space framework allowing us to study individual differences in the dynamics of the affective system. The outline of the paper is as follows. In the next section, we introduce a particular state space model, the linear Gaussian state space model, and extend it to a hierarchical model. In subsequent section, we illustrate the framework by applying it to data consisting of cardiovascular and behavioral measures that were taken during the interaction study introduced above. By focusing on various aspects of the model, we will show how our approach allows us to explore several research questions and address specific hypotheses that are discussed in the literature on the physiology and dynamics of emotions. Finally, the discussion reviews the strengths and limitations of the model, and we make some suggestions for future developments.

Section snippets

Hierarchical state space modeling

We will present a model for the affective dynamics of a single person and then extend this model hierarchically: The basic model structure for each person’s dynamics will be of the same type, and the hierarchical nature of the model allows for the key parameters of the model to differ across individuals.

The single individual’s model will be a linear dynamical systems model, cast in the state space framework. In the next paragraphs, the key concepts will be explained verbally and in the next

Application to emotional psychophysiology

We will now apply the presented hierarchical state space model to the data that reflect the affective physiological changes in depressed and non-depressed adolescents during conflictual interactions with their parents (Sheeber, Davis, Leve, Hops, & Tildesley, 2007). The study was carried out with adolescents because mood disorders often emerge for the first time during this stage of life (Allen & Sheeber, 2008). Depression, cardiovascular physiology and affective dynamics form a three-node

Discussion

In this paper, we introduced a hierarchical extension for the linear Gaussian state space model. The extended model proved to be very useful when studying individual differences in the dynamics of emotional systems. Applying it to the Oregon adolescent interaction data led to interesting discussions about hypotheses on the relations between cardiovascular processes, emotion dynamics and depression. On the whole, it was clear that applying the hierarchical state space approach to these data

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