Dyadic Effects on Jealousy and Guilt in Marital Relationships

Estimating the Saturated Model

In our previous lesson, we defined the equations for the husband's and wife's emotional outcomes. Let's use a specific example grounded in your research interests. Suppose you want to test how a husband's Attachment Anxiety and a wife's Communication Openness (regarding her lifestyle activities) predict the husband's Jealousy and the wife's Guilt.

The model equations would be:

Here's what each path represents:

• ${\beta }_{aH}$ (Husband's Actor Effect): The effect of his own anxiety on his jealousy.
• ${\beta }_{pH}$ (Wife's Partner Effect on Husband): The effect of her communication openness on his jealousy.
• ${\beta }_{aW}$ (Wife's Actor Effect): The effect of her own communication openness on her guilt.
• ${\beta }_{pW}$ (Husband's Partner Effect on Wife): The effect of his anxiety on her guilt.

When you "estimate" this model using SEM software, the program uses a method like maximum likelihood to find the values for these $\beta$ coefficients (and all other model parameters like variances and covariances) that make the model-implied covariance matrix most closely match the observed covariance matrix from your data.

The first step in analysis is always to estimate the saturated model. This is the model where all theoretically plausible paths are included and freely estimated, just as we specified. The output you receive will provide, at a minimum:

1. An unstandardized regression coefficient ($b$) for each path. This is your effect size.
2. A standard error (SE) for each coefficient, indicating its precision.
3. A p-value, indicating the statistical significance of the effect.

For a practical guide on this initial step, let's turn to a helpful tutorial.

Interpreting the Effects: Uncovering Dyadic Patterns

Simply determining whether an actor or partner effect is statistically significant is only the first layer of interpretation. The true richness of APIM comes from examining the relationship between the actor and partner effects for a given outcome. These relationships form distinct "dyadic patterns" that tell a story about the nature of interdependence.

Four prototypical patterns are particularly useful:

• Actor-Only Pattern ($p\approx 0$): The predictor variable influences only the person who possesses it. For instance, if a husband's anxiety significantly predicts his own jealousy, but the wife's openness has no effect on his jealousy, you have an actor-only pattern for the husband's outcome. The dynamic is primarily intrapersonal.
• Partner-Only Pattern ($a\approx 0$): The predictor variable influences only the partner. For example, if a wife's openness has no effect on her own guilt, but a husband's anxiety significantly increases her guilt, you have a partner-only pattern for the wife's outcome. The dynamic is purely interpersonal.
• Couple Pattern ($a\approx p$): The actor and partner effects are approximately equal and in the same direction. For instance, if a husband's high self-esteem increases his relationship satisfaction, and his wife's high self-esteem also increases his satisfaction by a similar amount, it suggests that both personal and partner characteristics contribute equally and positively to his well-being.
• Contrast Pattern ($a\approx -p$): The actor and partner effects are equal in magnitude but opposite in direction. Imagine a wife's openness decreases her guilt (actor effect), but her husband's anxiety increases her guilt (partner effect) by a similar magnitude. This suggests a push-and-pull dynamic where a positive personal factor is counteracted by a negative partner factor.

To formally test for these patterns, researchers compute a parameter, $k$, defined as the ratio of the partner effect to the actor effect ($k=p/a$). The value of $k$ provides a direct index of the underlying pattern:

• A $k$ value not significantly different from 0 suggests an actor-only pattern.
• A $k$ value not significantly different from 1 suggests a couple pattern.
• A $k$ value not significantly different from -1 suggests a contrast pattern.

The following reading will walk you through the logic of these patterns and the use of the $k$ parameter.

An Applied Example: Playfulness and Jealousy

To see these concepts in action, let's examine a published study that uses APIM to investigate a topic related to your interests: romantic jealousy. The study by Brauer et al. (2024) explores how different facets of a personality trait called "playfulness" predict jealousy in couples. This provides an excellent template for how you might report and interpret your own findings.

Let's dissect one of their findings to illustrate the interpretation process:

• Finding: "Lighthearted playfulness related to greater cognitive jealousy in their partners, b = 0.06, p = 0.017."
• Interpretation: This is a statistically significant partner effect. It means that the more lighthearted and spontaneous a person is, the more their partner tends to worry and ruminate about the relationship's stability (cognitive jealousy).
• Application to your research: You might find an analogous result. For example, the more Social Events the wife attends with the bull (a predictor), the greater the husband's Cognitive Jealousy (an outcome), demonstrating a clear partner effect.

The authors also found that "Whimsical playfulness related to the partners reporting less emotional jealousy." This is a partner effect in the opposite direction, showing that a different aspect of a person's personality can be soothing to their partner. In your work, you might find that the wife's Communication Openness (predictor) is associated with less Emotional Jealousy in the husband (outcome), demonstrating a buffering partner effect.

By analyzing the full pattern of actor and partner effects, you can build a nuanced causal story about how the husband and wife influence each other's emotional worlds.

Conclusion

In this lesson, you have learned how to take the APIM from a theoretical specification to an interpretable set of results. We covered the initial step of estimating the saturated model and then moved to the more nuanced task of interpreting the resulting actor and partner effects, both individually and as part of broader dyadic patterns.

Key Takeaways:

• The first analytical step is to estimate a saturated APIM, which provides regression coefficients ($b$) for all actor and partner paths.
• The interpretation of these effects hinges on their magnitude, sign (positive or negative), and statistical significance.
• A deeper interpretation involves identifying dyadic patterns (actor-only, partner-only, couple, contrast) by examining the relationship between actor and partner effects.
• The k parameter ($k=p/a$) is a formal metric used to test which dyadic pattern best describes the data for a given outcome.
• Applying these interpretations allows you to construct a detailed account of interpersonal influence, such as identifying if a wife's behavior buffers or exacerbates her husband's jealousy.

You now have the complete toolkit for analyzing the husband-wife dyad. In our next lesson, we will extend this powerful framework to a different, yet equally critical, dyad in your research: the wife-bull dyad. We will explore how to specify and interpret an APIM in a context defined by specific activities rather than a marital partnership.