- 61 Downloads
KeywordsShort Path Network Analysis Cluster Coefficient Edge Weight Closeness Central
A network is an abstract model, in its simplest form including only a set of nodes, that represent the elements of a phenomenon (e.g., individuals, websites, genes), and a set of edges that connect pairs of nodes. Edges can represent any kind of relationship among nodes (e.g., social connections, web links, co-expression of genes). Therefore, a phenomenon can be analyzed as a network if it can be broken down to a set of elements and as a set of pairwise interactions among them. Network analysis refers to a wide array of techniques for analyzing networks. These techniques can answer questions regarding the global structure of a network (e.g., is the network a small-world?) and the importance of specific nodes and edges (e.g., which is the most central node?). In psychology, networks have been used recently to model psychological phenomena that had been traditionally modeled almost exclusively as latent variables, including psychopathology, attitudes, and personality psychology.
Edges represent pairwise relationships among variables. There are several kinds of networks according to the type of relationships that their edges encode. In the simplest case, an edge between two nodes can be either absent or present, indicating only the presence or the absence of a relationship. These networks are said to be unweighted. Conversely, weighted networks include weights that give information about the intensity of the relationships. In Fig. 1, edge weights indicate that the strongest relationship is the one between nodes C and D. Weights are very important in psychology. For instance, in a network representing the attitudes towards presidential candidates, judging a candidate as intelligent was connected both to judging him knowledgeable and moral; however, the connection between intelligent and knowledgeable was much stronger than the connection between intelligent and moral (Dalege et al. 2015, Fig. 2). This piece of information would be lost if weights were disregarded. If edge weights can have both positive and negative signs, the network is said to be also signed. The network in Fig. 1 is signed, because it includes a negative connection between nodes A and D. Taking signs into account is also very important. For instance, in a network representing conscientiousness facets and related constructs, the node need for closure was positively connected with orderliness and negatively with industriousness (Costantini and Perugini 2016). Considering edge signs is the only way to understand these kinds of differential relationships. Directed networks additionally encode information about the direction of relationships, whereas undirected networks (such that in Fig. 1) do not encode this kind of information. In psychology, edge directions are typically used for representing processes that take place over time (Borsboom and Cramer 2013).
Psychological networks can be computed in several ways. Since nodes represent variables, a simple way to estimate their interaction is to use the Pearson’s correlation coefficient. An edge is drawn between two variables if they correlate, the weight and sign of the edge corresponding to the correlation coefficient (Cramer et al. 2012). However, to avoid spurious relationships (i.e., those due to the confounding effect of other variables in the network), partial correlations are often preferred. In this case, an edge is drawn between two nodes if they correlate after controlling for all other variables in the network. The absence of an edge in a partial correlation network is particularly informative because it indicates that two nodes are conditionally independent given the others. Regularized estimates of partial correlations can be obtained with methods such as the adaptive lasso or the graphical lasso. These methods result in sparse networks (with relatively few edges), prevent overfitting, and provide a parsimonious model of the data (Costantini et al. 2015; Epskamp et al. 2012). Time series data can be used for computing directed networks, which encode also the temporal dependencies among nodes (Borsboom and Cramer 2013).
Networks Analysis in Psychology
Once a network is computed, network analysis provides a wide array of techniques and allows extracting relevant information from the network (for a practical introduction of network analysis in personality psychology, see Costantini et al. 2015; for a general introduction of networks across disciplines, see Newman 2010). A first class of techniques investigates topology, the large-scale organization of a network. For instance, networks with a small-world topology are characterized by a clustered structure (nodes tend to coalesce into distinguishable subgroups) with bridges that connect the clusters. The small-world topology plays a crucial role in psychopathology, in which it has been advocated as an explanation of comorbidity (Borsboom and Cramer 2013).
Network analysis provides also a wide array of centrality metrics, which quantify the relative importance of specific nodes. Each index reflects a different way in which a node can be important. First, a node can be central simply because it has many neighbors, nodes that are directly connected to it (degree centrality). In weighted networks, this property can be generalized to take into account edge weights (strength centrality). In Fig. 1, node A is the most degree-central and node C is the most strength-central: Even if node A has four neighbors and node C has only two, the sum of the absolute weights connecting C with its neighbors is larger than for A. Degree and strength indicate how much a node can influence other nodes directly, without intermediaries. However, indirect connections can play a role too: In network analysis, there are algorithms that allow identifying efficiently the shortest paths connecting any two nodes (Newman 2010). Closeness centrality is a measure of how much a node is connected to all other nodes by short paths. In Fig. 1, node B is the most closeness central, because all other nodes can be reached relatively quickly from its position. Yet another way in which a node can be central is because that node is particularly important for the other nodes to interact with each other. A node that often lies on the shortest paths connecting other nodes is said to be betweenness-central. In Fig. 1, node A is the most betweenness-central, since it provides the only connections between node E and all other nodes. The clustering coefficient is the tendency of a node’s neighbors to be connected to each other. The more the neighbors of a node are also connected, the less that node is fundamental for its neighbors to reach each other. In Fig. 1, node F has the highest clustering coefficient, since its only two neighbors (A and B) are also connected to each other. Therefore, F does not appear to play a crucial role in the network.
Network analysis allows investigating mechanisms that could be easily missed if one simply assumed, by default, that psychological phenomena are manifestations of unobservable latent variables. For instance, in the case of personality, it has been typically assumed that the pattern of covariation among specific behaviors (e.g., doing homework), emotions (e.g., experiencing pride), cognitions (e.g., focusing on future), and motivations (e.g., being sensitive to positive outcomes) indicates the presence of a latent variable (e.g., conscientiousness). Whereas latent variables constitute useful and succinct summaries of individual differences, they do not have, by themselves, explanatory power (Mõttus 2016). From the network perspective, the coalescence of individual differences into broad personality traits is not an explanation but a phenomenon to explain. In this view, personality dimensions are considered emergent phenomena that arise from a network of more basic individual differences. For instance, a student that focuses on the future and is motivated by positive results is likely to spend more effort in school activities, such as doing homework, and will eventually obtain better grades, of which she would be proud (Costantini and Perugini 2016; Cramer et al. 2012). Not only networks provide an explanation of why broad personality factors emerge but also of why more specific clusters, such as personality facets, emerge as well. In the case of conscientiousness, all facets have been shown to share common features (i.e., common neighbors in the network), which make them clump together into a single dimension, and unique features, that make them different from each other (Costantini and Perugini 2016). Similar arguments can be made also for attitude research, in which the coalescence of evaluative reactions into an overall attitude is explained in terms of network processes (Dalege et al. 2015), and in psychopathology, in which the emergence of a disorder as a unique entity and the onset and the termination of a psychopathology are explained in terms of interactions among problems within a network (Borsboom and Cramer 2013; van de Leemput et al. 2014).
Network analysis includes a vast array of models and methods that are established in several scientific fields (e.g., physics, biology, computer science, sociology) and have recently found many applications in several branches of psychology. These techniques are implemented in software packages that make them relatively easy to apply (e.g., Costantini et al. 2015; Epskamp et al. 2012). Network analysis offers a new perspective to phenomena such as personality, attitudes, and psychopathology. However, it should not be considered in contrast to latent variable modeling: Some of the most interesting developments are likely to come from the combination of these traditions into more general models (Epskamp et al. in press).
- Costantini, G., & Perugini, M. (2016). The network of conscientiousness. Journal of Research in Personality, 65(1), 68–88. doi:10.1016/j.jrp.2016.10.003.Google Scholar
- Costantini, G., Epskamp, S., Borsboom, D., Perugini, M., Mõttus, R., Waldorp, L. J., & Cramer, A. O. J. (2015). State of the aRt personality research: A tutorial on network analysis of personality data in R. Journal of Research in Personality, 54, 13–29. doi:10.1016/j.jrp.2014.07.003.CrossRefGoogle Scholar
- Cramer, A. O. J., van der Sluis, S., Noordhof, A., Wichers, M., Geschwind, N., Aggen, S. H., …, & Borsboom, D. (2012). Dimensions of normal personality as networks in search of equilibrium: You can’t like parties if you don’t like people. European Journal of Personality, 26(4), 414–431. doi:10.1002/per.1866.Google Scholar
- Epskamp, S., Rhemtulla, M., & Borsboom, D. (in press). Generalized network psychometrics: Combining network and latent variable models. Psychometrika.Google Scholar
- van de Leemput, I. A., Wichers, M., Cramer, A. O. J., Borsboom, D., Tuerlinckx, F., Kuppens, P., …, & Scheffer, M. (2014). Critical slowing down as early warning for the onset and termination of depression. PNAS, 111(1), 87–92. doi:10.1073/pnas.1312114110.Google Scholar