Formalizing psychological interventions through network control theory

Abstract

Despite the growing deployment of network representation to comprehend psychological phenomena, the question of whether and how networks can effectively describe the effects of psychological interventions remains elusive. Network control theory, the engineering study of networked interventions, has recently emerged as a viable methodology to characterize and guide interventions. However, there is a scarcity of empirical studies testing the extent to which it can be useful within a psychological context. In this paper, we investigate a representative psychological intervention experiment, use network control theory to model the intervention and predict its effect. Using this data, we showed that: (1) the observed psychological effect, in terms of sensitivity and specificity, relates to the regional network control theoretic metrics (average and modal controllability), (2) the size of change following intervention negatively correlates with a whole-network topology that quantifies the "ease" of change as described by control theory (control energy), and (3) responses after intervention can be predicted based on formal results from control theory. These insights assert that network control theory has significant potential as a tool for investigating psychological interventions. Drawing on this specific example and the overarching framework of network control theory, we further elaborate on the conceptualization of psychological interventions, methodological considerations, and future directions in this burgeoning field.

Figure 1

A schematic view of the data and network control theory approach to quantify and predict the effect of interventions. (A) Thirty participants answered eleven questions about their attitude towards the consumption of meat. Based on their responses, they are asked to contemplate certain scenarios that are designed to alter their opinion. After this “intervention”, the participants are once more asked the same questions and asked to draw a schematic of connections between the items. (B) The effect of interventions in the context of psychological networks can be understood in terms of network control theory. Each network structure dictates the possible transitions of network values (illustrated here in terms of the arrows). The geometry of these arrows relates to the network structure and the dynamic imposed on them and can be linear or nonlinear. Figure 1A adapted from Hoekstra et al.

Figure 2

Sensitivity and specificity of interventions across items and participants. (A, B) Sensitivity is defined by the normalized changes in the responses (Methods, Eq. 2). Positive values indicate a change in the expected direction i.e., when the intervention was meant to reduce the rating, the subsequent rating after the intervention was indeed reduced and when the intervention was meant to increase the rating, the subsequent rating was indeed increased. (C, D) Specificity is defined by the relative absolute change of the intervened item compared to the average change of all the other items (Methods, Eq. 3). All specificity values are positive and higher values (of more than 1) indicating that perturbed items change more than the average of the other 10 items.

Figure 3

Network structure determines the success of psychological interventions. (A, B) Sensitivity is negatively associated with the network control theoretic estimation of the required energy to change the items only based on the generative model. (C, D) For both models (data-driven generative model as well as self-constructed networks), specificity is negatively related to the required energy but to a lesser extent compared to sensitivity.

Figure 4

The generative model of psychological intervention accurately predicts the responses to the intervention. (A, B) Correlations between the predicted and actual responses averaged over items and participants for self-constructed networks. (C, D) Correlations between the predicted and actual responses averaged over items and participants for the generative model.