Testing Moderation and Mediation in Subjective Wellbeing

A comprehensive guide using stress and social support in Stata

social support, stress, well being statistical analysis

Highlights

Conceptual Clarity: Understand the distinctions between mediators and moderators and their roles in influencing subjective wellbeing.
Stata Implementation: Detailed Stata commands are provided to analyze both moderation and mediation using stress as either moderator or mediator.
Comparative Testing: Guidance for comparing models to determine whether stress better explains the causal pathway (mediation) or alters the strength/direction (moderation) between social support and SWB.

Introduction

In research on subjective wellbeing (SWB), it is crucial to determine not only the relationship between independent variables and outcomes but also to understand the mechanisms underlying these relations. In this context, we often evaluate whether a variable such as stress plays a role as a mediator, explaining the process through which an independent variable affects SWB, or as a moderator, altering the strength or direction of this relationship.

For the purpose of this guide, the independent variable (IV) chosen is social support. Social support has been widely recognized to positively influence subjective wellbeing. We will use stress as a potential mediator and moderator in order to address two questions:

Does stress explain how social support impacts SWB (mediation)?
Does stress change the strength or direction of the relationship between social support and SWB (moderation)?

We will illustrate how each analysis can be conducted using Stata, followed by a comparative assessment to determine whether stress acts more strongly as a mediator or a moderator.

Conceptual Foundations

Mediator vs. Moderator

Mediator: A mediator is a variable that explains the mechanism or process through which an independent variable influences a dependent variable. In the mediation model, the independent variable (social support) affects the mediator (stress), which in turn influences the dependent variable (subjective wellbeing). Mediation implies a causal sequence:

Social Support → Stress → Subjective Wellbeing

If incorporating stress into the regression model reduces or nullifies the effect of social support on SWB, it suggests that stress mediates the relationship. Statistical significance of the indirect effect is commonly tested using methods such as the Sobel test or bootstrapping.

Moderator:

Moderator: A moderator is a variable that affects the strength or direction of the relationship between an independent and a dependent variable. In other words, the relationship between social support and SWB might differ in intensity depending on the level of stress. This implies that stress interacts with social support in predicting SWB:

Social Support × Stress → Subjective Wellbeing

A significant interaction term in the regression indicates moderation; the effect of social support on SWB changes at different levels of stress.

Stata Analyses

We now provide a detailed step-by-step guide to run both moderation and mediation analyses in Stata using stress as the focal variable.

Data Preparation and Preliminary Steps

Cleaning and Organizing Data

Before running any analyses, ensure that the data is properly prepared. Check for missing values, outliers, and normality in the variables 'social_support', 'stress', and 'swb' (subjective wellbeing). Appropriate data cleaning steps should include:

Descriptive statistics and visualization of key variables.
Correlation analyses to observe preliminary relationships.
Assessment of measurement integrity.

Once data quality is assured, you can proceed to test the hypothesized relationships in Stata.

Moderation Analysis Using Stata

Step 1: Creating the Interaction Term

In moderation analysis, an interaction term is created by multiplying the independent variable (social support) with the moderator (stress). This new term helps determine if the effect of social support on SWB varies depending on stress levels.


  // Generate the interaction term
  gen interaction_term = social_support * stress

Step 2: Running the Moderation Regression

The regression model will include social support, stress, and the interaction term as predictors of subjective wellbeing:


  // Moderation regression: Testing if stress moderates the effect of social support on subjective wellbeing
  regress swb social_support stress interaction_term

Analyze the output by focusing on the coefficient of the interaction term. A statistically significant coefficient (p-value < 0.05) on the interaction term indicates that stress significantly moderates the relationship between social support and subjective wellbeing.

Mediation Analysis Using Stata

Step 1: Testing the Path from IV to Mediator

The first step is to examine whether social support (IV) is significantly related to stress (mediator). This is done using a simple regression:


  // Testing effect of social support on stress (path a)
  regress stress social_support

A significant result supports the first requirement for mediation.

Step 2: Testing the Mediator’s Effect on the Dependent Variable

Next, test whether stress affects subjective wellbeing after controlling for social support:


  // Testing the effect of stress on swb, while controlling for social support (path b)
  regress swb stress social_support

The significance of the coefficient for stress here suggests that stress is a meaningful predictor of SWB.

Step 3: Testing the Total Effect of Social Support on SWB

It is important to confirm that social support has a direct effect on subjective wellbeing:


  // Testing the total effect of social support on swb (path c)
  regress swb social_support

Step 4: Calculating the Indirect Effect

Compute the indirect effect of social support on subjective wellbeing via stress. This can be calculated using the product of the coefficients obtained from path a (social support → stress) and path b (stress → swb). The nlcom command in Stata is useful for this:


  // Calculation of the indirect effect: a*b
  nlcom (indirect_effect: _b[stress]*_b[social_support])

A significant indirect effect indicates mediation. For more robust results, bootstrapping can be performed to obtain confidence intervals for the indirect effect.

Comparative Analysis: Moderator vs. Mediator

To determine whether stress is more appropriately modeled as a moderator or a mediator in the relationship between social support and subjective wellbeing, several analytical steps and comparisons can be undertaken:

Comparing Model Fit and Variance Explained

Qualitatively evaluate both models by considering:

Significance of Key Coefficients: In the moderation model, focus on whether the interaction term is statistically significant. In the mediation analysis, check if the indirect effect is statistically significant.
Variance Explained (R-squared): Compare the R-squared values from both regression models. An increase in explained variance when including the interaction term may support a moderation effect, while a significant decrease in the direct effect of social support on subjective wellbeing when including stress (as mediator) can indicate mediation.
Model Fit Indices: If using structural equation modeling (SEM), compare fit indices such as the Akaike Information Criterion (AIC), the Bayesian Information Criterion (BIC), and other goodness-of-fit statistics across models.

Table: Comparative Overview

Aspect	Moderation	Mediation
Theoretical Perspective	The effect of social support on SWB varies by levels of stress.	Stress explains how social support influences SWB.
Stata Implementation	Create and include an interaction term in regression: `gen interaction_term = social_support * stress`	Perform sequential regressions and calculate the indirect effect using `nlcom` or `sem`.
Key Result	Significance of the interaction term.	Significance of the indirect effect (product of paths a and b).
Research Implication	Indicates that the impact of social support changes at different stress levels.	Reveals that the relationship between social support and SWB is mediated by stress.

Testing for Moderated Mediation

In some cases, the role of stress might not be strictly one or the other. Testing for moderated mediation can help assess if stress plays both roles simultaneously. Tools such as the PROCESS macro in SPSS or advanced SEM approaches in Stata can help model these complex relationships.

A basic SEM model capturing both effects in Stata might be structured as:


  // Example code for a combined SEM model
  sem (stress <- social_support)
      (swb <- social_support stress)
  // Optionally, include an interaction term if required by model complexity.

Then compare model fit indices for the pure mediation, pure moderation, and moderated mediation models to identify which model offers a better explanation of the relationship between social support and subjective wellbeing.

Interpretation and Reporting

Interpreting Moderation Output

In the moderation analysis, if the coefficient for the interaction term is statistically significant (typically p < 0.05), the interpretation is as follows:

“The relationship between social support and subjective wellbeing is moderated by stress. That is, the influence of social support on SWB varies depending on an individual’s stress level.”

Interpreting Mediation Output

For mediation, the key is to examine the indirect effect along with the direct effect:

If the indirect effect (social_support → stress → swb) is statistically significant and the direct effect of social support on SWB reduces when accounting for stress, this indicates mediation.
For full mediation, the direct effect becomes non-significant when the mediator is included; for partial mediation, the direct effect remains significant but is reduced in magnitude.

Determining Whether Stress Acts More as a Moderator or Mediator

After running both analyses, compare which model explains more variance in SWB and which set of coefficients are more robust:

Stronger Interaction Term: A significant and large interaction effect supports the moderation hypothesis.
Robust Indirect Effect: A significant indirect effect along with a reduction in the direct effect of social support on SWB lends support to the mediation model.
Model Fit: Compare overall model fit indices (e.g., AIC, BIC in SEM) to determine the model that best represents the data.

Based on the results, you might conclude that stress functions solely as a moderator if only the interaction term is significant, solely as a mediator if only the indirect effect is significant, or as both if both sets of analyses show significant effects.

Conclusion

This guide has provided a systematic framework for testing the dual role of an independent variable (social support) in predicting subjective wellbeing with stress as a potential mediator or moderator. We began by outlining the theoretical differences between mediators and moderators, followed by detailed Stata commands and step-by-step procedures for assessing each role.

By generating an interaction term, you can examine if the effect of social support on SWB is conditional upon levels of stress, thereby revealing moderation. Conversely, structured regression analyses allow you to test the mediation pathway, confirming whether stress explains the mechanism behind the effect of social support on subjective wellbeing. Finally, comparing the significance and model fit of both approaches provides a comprehensive understanding of whether stress acts primarily as a moderator, mediator, or perhaps even both via moderated mediation.

This holistic approach not only ensures robust statistical analysis but also brings clarity to theoretical underpinnings in psychological research, ultimately guiding researchers in framing their hypotheses, selecting suitable statistical methods, and interpreting their empirical findings accurately.

References

Mediator vs. Moderator Variables - Scribbr
Mediator vs Moderators in Research - Dovetail
Mediation and Moderation Analyses - Statistics Solutions
Chapter 14: Mediation and Moderation - UIC