Compositional vs. Relational Effects

From Individual Traits to Relational Dynamics

Let's begin by formally defining these two categories, which build directly on the sources we identified previously.

• Compositional Effects are sources of non-independence that arise from the stable characteristics of the individuals who form the group. These are the traits, tendencies, and dispositions that each person brings into the relationship. This category directly includes the "compositional effects" (like non-random sorting) we discussed last time, and it is also the home of what the Social Relations Model (SRM) calls perceiver effects (a person's tendency to see others in a certain way) and target effects (a person's tendency to be seen by others in a certain way). In short, compositional effects are about the properties of the people themselves.

• Relational Effects are sources of non-independence that emerge from the unique interactions and shared history between specific members of the group. These effects are not reducible to the individual participants' traits; they are properties of the dyad or triad itself. This category encompasses the "partner effects," "mutual influence," and dyad-specific "common fate" events from our last lesson. In SRM terminology, this is the relationship effect—the unique feeling or perception that exists between two people, above and beyond their individual tendencies.

To deepen this conceptual distinction, we can turn to a framework from relationship science called Mate Evaluation Theory. While its focus is on mate selection, its concepts for partitioning sources of attraction are perfectly analogous to partitioning sources of emotion in an established triad.

Let's translate this framework to your research context:

• Perceiver Lens (Compositional): The husband has a generally anxious attachment style. This "lens" causes him to interpret many of his wife's actions—whether with the bull or with others—through a filter of potential abandonment. This is a perceiver effect. It is a property of the husband.
• Common Lens / Target Effect (Compositional): The bull is exceptionally handsome and charming by conventional standards. Most people, including the wife and other potential partners, would agree on his high "mate value." The general reaction he elicits from his partners' husbands is a target effect. It is a property of the bull.
• Target-Specific Lens (Relational): The husband and wife have a 20-year history that includes overcoming a specific past infidelity. An action by the wife (e.g., staying out late with the bull) might trigger a jealousy response that is entirely shaped by that unique, path-dependent history. This feeling is not substitutable; it would not be the same with a different wife or a different bull because it is born from their shared narrative. This is a purely relational effect.

Deconstructing Relational Effects: Is It the Type or the Person?

The "Mate Evaluation Theory" paper offers an even finer distinction within the relationship effect itself. It suggests that what we call "compatibility" or "chemistry" isn't a single phenomenon. It can arise from two distinct sources, which is a critical insight for your work.

This distinction is subtle but powerful. Let's apply it to the wife's feelings of guilt.

1. Feature Lens (Attribute Matching): The wife feels less guilt when interacting with bulls who are highly emotionally intelligent and good communicators. Her feeling of reduced guilt is a reaction to a feature. If the current bull were replaced by another man who was equally emotionally intelligent, she would likely feel a similarly low level of guilt. This is an effect of Perceiver (wife) x Target Feature (bull's emotional intelligence). It feels relational, but it's based on a generalizable preference for a certain type of partner.

2. Target-Specific Lens (Emergent & Idiosyncratic): The wife feels less guilt with the current bull because he was the one who helped her navigate a difficult conversation with her husband two years ago. Her sense of safety and reduced guilt is tied to him and their shared history. It is non-substitutable and path-dependent. This is a "pure" relational effect, an emergent property of that specific wife-bull dyad.

Understanding this difference is vital. An intervention aimed at reducing the wife's guilt would be very different depending on the source. If it's feature-based, the intervention might be to select partners with specific traits. If it's target-specific, the intervention would focus on building shared history and trust within the specific dyad.

Statistical Partitioning with the Social Relations Model

These conceptual distinctions are not merely philosophical. They map directly onto the parameters of statistical models designed to handle non-independent data. The Social Relations Model (SRM) is the classic formulation for this.

A paper by Loeys et al. on using SRM with missing data provides a clear statistical definition and a compelling empirical example of partitioning these effects.

The study you just read about is a perfect illustration of distinguishing compositional from relational effects. The researchers wanted to know if a woman's perception of her friends' "body talk" was more about her friends' actual behavior (a relational or target effect) or her own preoccupation with the topic (a compositional/perceiver effect).

Here’s what they found and how it applies to your work:

• They found a large ego effect (which they call projection or assimilation). A woman's perception of how much her friends talked about bodies was strongly correlated with her own tendency to make body comparisons. This is a classic compositional effect. The perception was more a reflection of the perceiver than the person being perceived.
• They found a small alter effect (which they call consensus). There was very little agreement among peers about who talked about bodies the most. This suggests the relational/target component was weak.
• The conclusion was that these perceptions were driven primarily by compositional variance (the perceiver's own tendencies) rather than relational variance (what the targets were actually doing).

In your study, you could use SRM to ask: Is a husband's jealousy score primarily explained by his own disposition (a large ego/perceiver effect), or is there a consensus among the wife and bull that his jealousy is a reaction to specific, observable behaviors (a large alter/target effect for the wife/bull dyad)? The model would allow you to partition the variance and quantify the contribution of each source.

The Multilevel Modeling Perspective

This partitioning of variance between individuals and the groups they belong to is the central idea behind multilevel models (MLM), a topic we will explore in great depth later. For now, a brief preview will help solidify the concepts of compositional and relational effects.

As the video explains, MLM is a framework to handle nested data (e.g., individuals nested within triads). It explicitly models variance at different levels.

• Level 1 (The Individual Level): Variation among observations for the same person over time, or variation among individuals within a triad. This level helps us understand individual tendencies, akin to compositional effects.
• Level 2 (The Triad Level): Variation between triads. Why is Triad A, on average, less jealous than Triad B? This variance is attributable to the group, capturing the relational effects that make each triad a unique system.

In fact, advanced forms of MLM can even distinguish between different factor structures at the individual and group levels.

The key idea here is that the structure of emotional dynamics could be different at the compositional versus the relational level. For instance, at the individual level (within-person), a person's emotions might be organized into two factors: "positive affect" and "negative affect" (a compositional structure). However, at the triad level (between-triad), the variance might be explained by just one factor: "overall dyadic trust" (a relational structure). Good-functioning triads have high trust and positive emotions, while poor-functioning triads have low trust and negative emotions. The factors are different at each level of analysis.

Conclusion

In this lesson, we moved beyond simply listing the sources of non-independence to organizing them into a theoretically and statistically meaningful framework.

Key Takeaways:

• Non-independence can be broadly categorized into compositional effects (arising from individual traits) and relational effects (arising from emergent dyadic/triadic dynamics).
• In the language of SRM, compositional effects are captured by perceiver (ego) and target (alter) effects, while relational effects are captured by the relationship effect.
• The relationship effect itself can be decomposed into feature-based (substitutable attribute-matching) and target-specific (idiosyncratic, path-dependent) components.
• Statistical methods like SRM and MLM are designed to partition the total variance in an outcome (like jealousy) into these different sources, allowing you to quantify whether emotion is driven more by the individuals or the relationships between them.

You now possess a much sharper lens for viewing the causal processes in your triadic system. You can distinguish between what individuals bring to the relationship and what emerges from it.

In our next lesson, we will address a critical question: what are the statistical consequences of getting this wrong? We will explore precisely what happens when you apply standard regression models that assume independence to relational data that are inherently non-independent. This will underscore why the specialized models we've begun to discuss are not just optional, but absolutely necessary.