Actor-Partner Mediation: Indirect Effects

Introduction

In our last lesson, we established the conceptual and practical groundwork for specifying mediation models where a causal pathway extends across multiple individuals in the triad. Using Structural Equation Modeling (SEM) as our guiding framework, we saw how a chain of events—like a wife-bull activity influencing the wife's guilt, which in turn affects the husband's jealousy—can be represented as a formal, testable model.

Today, we transition from specifying these pathways to rigorously testing them. Our objective is to test indirect effects in actor-partner mediation models, focusing on scenarios where a mediator for one participant influences an outcome for another. You will learn how to decompose the total indirect effect into specific, meaningful pathways, how these pathways are calculated, and how their statistical significance is formally tested. We will draw heavily on published research and practical software examples to ground these methods in the applied context that is central to your work.

The Actor-Partner Interdependence Mediation Model (APIMeM)

To analyze mediation within a dyadic system, we use a specialized framework called the Actor-Partner Interdependence Mediation Model (APIMeM). As the name suggests, it integrates the principles of the Actor-Partner Interdependence Model (APIM), which accounts for non-independence in dyads, with the causal logic of mediation analysis.

This model allows us to parse out complex interpersonal dynamics. For example, in the husband-wife dyad, we can test four distinct types of indirect effects concerning a variable X's influence on an outcome Y through a mediator M:

Actor-Actor Mediation: My X → My M → My Y.
Actor-Partner Mediation: My X → My M → My Partner's Y.
Partner-Actor Mediation: My Partner's X → My M → My Y.
Partner-Partner Mediation: My Partner's X → My M → My Partner's Y.

Our focus today is on pathways like 2 and 3, where the causal chain crosses from one person to another. A superb example of this model in practice is a recent study on stress spillover in couples.

The prospective impact of extradyadic stress on depressive ...

This paper by Böhlmann et al. (2024) provides a clear, real-world application of the APIMeM to investigate how stress outside a relationship (extradyadic) affects depressive symptoms through the mediator of stress inside the relationship (intradyadic).

Please read the following sections: First, review the "Current study" section. Pay close attention to the description of the APIMeM model and the accompanying Figure 1. This diagram is a blueprint for the types of pathways we can test, clearly distinguishing between actor (A) and partner (P) effects for both the a path (X→M) and b path (M→Y). Next, read the "Data analyses" section. Focus on the description of how the authors used Mplus to evaluate the APIMeM. Note the process of calculating all four mediation pathways and the explicit reliance on the indirect effect (and its confidence interval) for interpretation, which is current best practice.

The approach outlined in this paper is directly translatable to your research. For instance, you could model how a bull's characteristic (e.g., his communication style, X_bull) influences the husband's jealousy (Y_husband) indirectly through the wife's emotional state (e.g., her guilt, M_wife). This would be a partner-partner mediation from the husband's perspective (X_partner → M_partner → Y_actor).

Testing Specific Indirect Effects

In a complex mediation model with multiple mediators, the total indirect effect is the sum of all the specific indirect pathways. SEM software often provides the total indirect effect by default, but to test specific causal theories, we need to isolate and test each pathway individually.

This involves instructing the software to calculate the product of the coefficients for a specific path. For instance, in the pathway X → M1 → Y, the specific indirect effect is the product of the path coefficients $a_{1}$ (for $X \to M_{1}$ ) and $b_{1}$ (for $M_{1} \to Y$ ).

The following image and video demonstrate precisely how this is done in the AMOS software package, but the underlying principle applies to any SEM program, including Mplus.

This image shows a path model in AMOS. The overlaid 'User-defined estimands' window contains syntax used to calculate specific indirect effects. For example, `Ind5=PartA*PartB` instructs the software to compute the product of the path coefficients labeled 'PartA' and 'PartB'.

The video below provides a step-by-step walkthrough of this process.

Testing specific indirect effects in AMOS via User defined Estimands

This tutorial from Mike Crowson's channel details the practical procedure for defining and testing specific indirect effects.

Please watch the following segments: Labeling Paths: First, see how individual paths in the model are given unique labels (e.g., p1, p2). This is a necessary first step. The Logic of Products: The presenter then explains how different specific indirect effects are simply products of different path coefficients. This section clarifies the concept of serial mediation (X → M1 → M2 → Y) as well. Syntax for Estimands: The core of the process is shown in the segment on entering syntax for "user-defined estimands". Observe how named indirect effects (e.g., sie1) are defined as the product of the path labels (e.g., p1 * p2). This is the universal logic for testing any specific indirect effect. Interpreting the Output: Finally, watch how to find and interpret the results. The key is to examine the bootstrapped confidence interval for your user-defined estimand. If the interval does not contain zero, the specific indirect effect is statistically significant.

To apply this to your scenario Wife-Bull Activity (X) → Wife's Guilt (M) → Husband's Jealousy (Y), you would:

Label the path from Activity to Guilt as, say, a_path.
Label the path from Guilt to Jealousy as b_path.
Define a new estimand: indirect_effect := a_path * b_path.
Run the analysis with bootstrapping and check the confidence interval for indirect_effect.

Interpreting an Actor-Partner Indirect Effect

Now, let's return to the Böhlmann et al. (2024) paper to see a real-world interpretation of a cross-person indirect effect.

The prospective impact of extradyadic stress on depressive ...

This portion of the paper presents and discusses the results of the APIMeM, including the crucial test of the cross-person indirect effect.

Please read the following sections from the results and discussion: First, carefully read the "Partner effects" subsection of the results. The key finding is here: the authors test several partner pathways and find a significant indirect effect. Note how they state that while there was no direct effect, an indirect pathway was significant. This is a classic mediation finding. Next, read the "Results when controlling for autoregression" subsection. This is a sensitivity analysis. For your level of statistical expertise, this is important. Notice how the previously significant partner indirect effect becomes non-significant when controlling for prior levels of the mediator and outcome. This demonstrates how to test the robustness of your findings. Finally, read the discussion of the "between-partner effects". This section provides the conceptual interpretation. The authors explain the mechanism: a partner's stress doesn't directly cause depression, but it increases conflict within the relationship, and it is this increased conflict that leads to depressive symptoms. This is the causal story supported by their APIMeM results.

This paper provides a complete template: you specify the model, test the specific indirect effects using bootstrapping, interpret the significance of the product term, check for robustness with sensitivity analyses, and then construct a causal narrative that explains the mechanism you've uncovered.

Advanced Application: Mediation with Longitudinal Dyadic Data

The principles we've discussed can be extended to more complex longitudinal designs. A powerful method for this is the Dyadic Latent Growth Curve Mediation Model (DLGCMM), which models change over time for both members of a dyad. While we will cover longitudinal models in detail in Module 6, examining how mediation is tested in this context will solidify your understanding of the core logic.

A Tutorial on Dyadic Growth Curve Mediation Modeling - PMC - NIH

This tutorial by Hoegler Dennis et al. provides a technical guide to testing mediation in a longitudinal dyadic context, complete with model equations and code.

Focus on the logic of testing the indirect effects: First, read the section on "Latent Growth Curve Mediation Modeling (LGCMM)" to understand the general procedure for testing mediation within this framework. The logic is identical: estimate the a and b paths and then compute the indirect effect as their product. Next, jump to the section "Addressing Research Questions Four, Five, and Six: Dyadic Linear Growth Curve Mediation Modeling". Skim the equations and focus on the R code blocks. You will see the exact implementation of what we've been discussing. For example, the code defines the indirect effect with the line ind_f_1_1 := a1f*b1f. This demonstrates how path labels (a1f, b1f) from the model are used to explicitly define the product term for testing. Look at Figure 4 in this paper for an excellent visualization of these paths. Finally, review the "Results of DLGCMM" section. Here, the authors interpret the findings. They find a significant indirect effect for fathers but not for mothers, highlighting how these models can reveal person-specific pathways. Notice again the reliance on the bootstrapped confidence interval: the key finding is identified because its 95% CI [0.007, 0.086] does not include zero.

This tutorial reinforces that regardless of the complexity of the model—whether it's a simple cross-sectional path model or a dyadic growth curve model—the fundamental procedure for testing a specific indirect effect remains the same: define the pathway, multiply the coefficients, and test the significance of the product using bootstrapped confidence intervals.

Conclusion

In this lesson, we have moved from the specification to the formal testing of indirect effects in actor-partner models. You now have a comprehensive toolkit for investigating the mechanisms of influence that cross from one person to another within a dyadic or triadic system.

Key Takeaways:

The Actor-Partner Interdependence Mediation Model (APIMeM) is the formal framework for testing mediation in dyadic data, allowing for the decomposition of effects into actor and partner pathways.
A specific indirect effect is calculated as the product of the path coefficients forming the causal chain (e.g., $a \times b$ ).
Modern SEM software allows you to define these specific indirect effects as "user-defined estimands," giving you the power to test precise theoretical hypotheses.
The standard for testing the significance of an indirect effect is bootstrapping. A significant indirect effect is indicated by a confidence interval that does not contain zero.
The interpretation of a significant cross-person indirect effect allows you to build a causal narrative that explains how one person's state or behavior influences another's outcome via a specific mediating process.

In our next lesson, we will explore another critical component of causal pathways: moderation. We will specify and test models that ask not just "how" an effect occurs, but "when" or "for whom" it is stronger or weaker. This involves shifting our focus from indirect effects to interaction effects within the actor-partner framework.