It’s easy to think of mental states like depression or anxiety as lists of unrelated symptoms. Even though it’s helpful to think about each individual symptom, it’s also important to remember that symptoms can be related to each other in complex ways. That’s the main idea behind network psychometrics, where psychologists examine the relationships between lots of different measured variables. In a network analysis, variables are placed on a graph that shows the connections between different pairs of variables. This allows you to answer questions about the centrality (Are any symptoms highly connected to other symptoms?) and modularity (Do some symptoms tend to cluster together?) of the network.

Even though they are very useful, the usual kinds of psychometric graphs are limited because they can only tell us things about pairwise relationships among variables. What if we want to know about the relationships between 3 or more variables at a time? This is where hypergraphs come in. Despite its name, a hypergraph isn’t just a very energetic graph, it’s a kind of network where relationships between any number of variables can be highlighted and analyzed.

In their research published in Behavior Research Methods, authors Daniele Marinazzo*, Jan Van Roozendaal, Fernando E. Rosas*, Massimo Stella*, Renzo Comolatti*, Nigel Colenbier*, Sebastiano Stramaglia & Yves Rosseel* (*pictured below) provide a step-by-step guide for creating hypergraphs, and offer some examples from real research.

In a network analysis, one way the variables could be related is through synergy, where the variables together provide more information than the sum of their parts. Instead, the variables might show redundancy, wherein they share lots of overlapping information. You could think of synergy and redundancy as opposites, and researchers may be interested in which one better describes a relationship among several variables. This can be measured using a measurement called O-information, which is the difference between measures of synergy and redundancy. A positive O-information means that the variables are more redundant than synergetic, and a negative O-information means just the opposite. 

To build a hypergraph, the first thing you’ll do is calculate the O-information for lots of different groups of variables, of all sorts of sizes. Separate the groupings into negative (synergetic) and positive (redundant). Then, determine which groups are the most meaningful by comparing the amount O-information they account for. For example, does the grouping A-B-C-D account for more O-information than the grouping A-B-C? If not, then only A-B-C, not A-B-C-D, will be represented in the hypergraph. Through this process, you develop a synergetic and redundant hypergraph, giving you insights into the interdependencies among variables.

Reanalysis of an empathy dataset

To further illustrate how this methodology works in practice, the researchers analyzed several existing datasets, one of which included data related to the empathy construct from Briganti et al. (2018). This dataset included various questionnaire items related to empathy, and with this method, each questionnaire item within the study is treated as a node within the hypergraph. Traditional methods used in the past look at how pairs of these nodes relate, as shown in the figure below. Although this method is useful, the approach is limited because it cannot capture relationships that involve three or more variables (higher-order relationships), such as redundant or synergistic interdependencies among them.

Using their new approach, which allowed the researchers to identify these higher-order relationships between variables, the authors followed the following analytic pipeline. First, the researchers calculated the O-information for groups of variables (multiplets) consisting of three or more variables. Next, they sorted these groups based on the sign of the O-information, with positive values indicating redundancy and negative values indicating synergy. Then, the researchers used bootstrapping, a method where they repeatedly shuffle the data and calculate confidence intervals each time for the O-information values which helps them assess how reliable the results are. After that, they compare the confidence intervals of the larger groups of variables with those of the smaller subsets of those larger groups. If the confidence intervals overlap, it means the larger group doesn’t provide any additional meaningful information, so it is removed.

In the final step of the analytic process, the researchers built two different types of hypergraphs: one set showcasing the redundant relationships and another displaying the synergistic relationships. The figure below shows the three hypergraphs of redundant relationships, each representing groupings of 3, 4, or 5 variables (i.e., items from the questionnaire). By looking at these hypergraphs, we can see that the graphs with multiplets of a size of 3 or 4 identify the same key components that were first identified in the original paper that used pairwise analysis (traits including fantasy, perspective taking, personal distress and empathetic concern). In the network, items that were more connected, meaning that they were involved in many multiplets at once, tended to appear near the center of the hypergraph. These hypergraphs allow us to visually confirm what Briganti and colleagues already found, which is that empathic concern (light blue colored nodes on the hypergraphs below) is central to understanding empathy because it’s connected to so many other items.

However, what’s interesting is that empathic concern only shows up as the central item when looking at redundant relationships in smaller groups (3s and 4s). When they looked at larger groups that had 5 items, fantasy, a trait that involves imagining oneself in fictional situations, became the more central or important factor instead (see the red nodes below in the Order 5 hypergraph on the right). The importance of fantasy within this study would not have been detectable with the simple pairwise approach, which is what makes this new higher-order approach so valuable.  

Alternatively, the hypergraph below showcases the synergistic relationships calculated using this new method. For example, item 3 in the questionnaire is related to the ability to perspective-take and item 24 is related to emotion regulation and distress. When these two items are observed in a traditional network that only examines pairwise relationships, you can see they do not show a strong connection (shown in the pairwise network graph above). However, when those items are analyzed together with a third item, the pairing appears in several synergistic groupings. Thus, the relationship between items 3 and 24 only becomes meaningful when they are observed across these larger combinations of items and is not obvious with a simple pairwise network approach. These findings may suggest that how people perspective-take and how they emotionally respond may be interconnected in ways that only become clear when analyzed as part of a larger pattern. 

This reanalysis of the empathy dataset is an incredible demonstration of how this new analysis approach can be used to detect trends within datasets that would not have been possible without examining these higher-order relationships between variables. This approach does not replace the traditional pairwise method but rather complements and expands upon it. Its goal is to reveal the types of information shared across different behavioral variables or symptoms. It’s a valuable approach, and if you are a psychometrician, we hope you will also add it to your toolbox!

Featured Psychonomic Society article

Marinazzo, D., Van Roozendaal, J., Rosas, F. E., Stella, M., Comolatti, R., Colenbier, N., Stramaglia, S., & Rosseel, Y. (2024). An information-theoretic approach to build hypergraphs in psychometrics. Behavior Research Methods, 56(7), 8057–8079. https://doi.org/10.3758/s13428-024-02471-8