Mediation, Moderation, and Conditional Process Models (Part 1)

Week 9: March 3, 2025

Reading

Introduction to the Topic

This week, we explore mediation analysis, a statistical approach used to understand the mechanisms through which an independent variable influences a dependent variable via a third variable, known as the mediator. Mediation analysis is essential for uncovering causal pathways in research.

Key Concepts:

  • Direct Effects: The relationship between the independent variable and the dependent variable, excluding the mediator.
  • Indirect Effects: The portion of the relationship explained through the mediator.
  • Total Effects: The combined impact of direct and indirect effects.
  • Bootstrapping: A resampling method for testing the significance of indirect effects.

Relevance:

  • Students will learn how to identify and test mediating variables in a causal framework. Make sure you review our discussion of confounding
  • Students will explore how to decompose total effects into direct and indirect components to better understand relationships among variables.

Why This Is Important:

  • Mediation analysis allows researchers to move beyond simple relationships to uncover how and why effects occur.
  • Understanding mediation is critical for testing theoretical models in fields like psychology, sociology, and public health.

How This Ties Into the Overall Course:

  • Builds upon previous topics, such as regression and effect sizes, by extending these tools to explore causal pathways.
  • Prepares students for advanced concepts like moderated mediation and structural equation modeling (SEM), where mediation analysis is a core component.

By the end of this week, students will be able to conduct mediation analyses, interpret direct and indirect effects, and evaluate the significance of mediators using bootstrapping methods.

An example of logistic regression from last week

We ran out of time last week but I put together an example and write up of logistic regression. This uses the PRAMS dataset to inquire about whether stress during pregnancy predicts IPV exposure during pregnancy. Recall the variable measurements which we noted here. The JASP file is here and it is fully annotated.

In-Class Files and Data Sets

A Note on Linear Transformations

Linear Transformations: We start class today with a quick example of how to transform variables when the model assumptions are violated. As I mentioned in class, this trick has almost never worked with the datasets I use. However, I was successful in transforming the dependent variable once, using a cultivated dataset on area deprivation, housing, and “child maltreatment” substantiations which can be accessed here. I have used these data often see Elise Barboza-Salerno (2024) for an example.

The cultivated dataset comes from many sources. The H+T index comes from this website. The ADI comes from the sociome package in R, and we saw an example when we learned how to quantify effect sizes with Cohen’s D. I calculated the distances to SNAP retail locations from home addresses based on information from the SNAP retail locator, which can be accessed here.

Test yourself on partial mediation, full mediation, and supression: I created sample output for each effect, can you select the correct model that illustrates each mechanism?

Mediation: We will use a subset of the NSCAW I to examine whether symptoms of post-traumatic stress mediate the association between exposure to violence at Wave I and child externalizing behaviors at Wave III. Now DON’T LOOK at the model write-up until AFTER you have the analysis done. Then, and only then, can you take a gander at my write-up here

Lab Files

After we do the above example together, we have an in-class assessment to get a sense of how well you are comprehending the analyses. This includes some multiple choice questions along with an analysis of the Adolescent Health Survey Data which is a longitudinal dataset that has been collected since about 1995 when youth were 15 years of age. Please download the assessment here. See Elise Barboza & Siller (2021) for a similar analysis published in the Journal of Interpersonal Violence, or this paper Barboza (2020) that also used these data.

Lecture Notes

  • Download today’s slides here

R Code

I wrote the code to show you how to use PROCESS in R. Yes, R has a package that runs the same macro that SPSS can run. The example is based on the NSCAW dataset as well. Check it out here

Resources

This is an amazing resources from UCLA on introduction to mediation, moderation and conditional process models. The website has a tutorial that I am strongly suggesting you do, and also additional powerpoint slides for Andrew Hayes’ book.

Additional Notes

Stay calm and do everything in moderation.

Barboza, G. E. (2020). Child Maltreatment, Delinquent Behavior, and School Factors as Predictors of Depressive Symptoms from Adolescence to Adulthood: A Growth Mixture Model. Youth & Society, 52(1), 27–54. https://doi.org/10.1177/0044118X17721803
Previous methodological approaches have not been flexible enough to model the heterogeneity of depressive symptoms or to identify variations between prototypical trajectories conditional on risk and protective factors. The current study examined latent class trajectories of depressive symptoms using data from 3,819 respondents of the Adolescent Health Survey. Four trajectory profiles of depressive symptoms were identified: low-stable, high-decreasing, low-increasing, and moderate-decreasing. A broad array of risk factors were included into the modeling procedure to identify predictors of group membership. Relative to the low-stable group, membership in one of the three symptomatic groups (i.e., heightened depressive symptoms) was predicted by poverty, low self-esteem, gender, drinking frequency, poor academic outcomes, delinquency, and child maltreatment type. This study contributes to our understanding about the longitudinal manifestations of depression and identifies a broad array of factors significantly related to pathways of resilience.
Elise Barboza, G., & Siller, L. A. (2021). Child Maltreatment, School Bonds, and Adult Violence: A Serial Mediation Model. Journal of Interpersonal Violence, 36(11-12), NP5839–NP5873. https://doi.org/10.1177/0886260518805763
Physically abused youth are vulnerable to experiencing difficulties across multiple domains of school functioning. Most of the literature examining the relationship between child physical abuse (CPA) and adult violence has focused narrowly on academic outcomes rather than taking a broader view that explores the processes undergirding school engagement and connections. The present study adopted Connell?s model of school engagement, connectedness and outcomes within a social bond framework to examine (a) the link between CPA and school social bonds, (b) the link between CPA and adult violence persistence, and (c) the mediational (parallel, serial) effects of school bonds (engagement, connection, and achievement) on violence perpetration in adulthood. Consistent with previous research, results indicated that children who experience physical abuse have poorer academic performance, which, in turn, is related to future violent trajectories. We further found that the relationship between CPA and violence persistence is mediated by a process of bonding to school that begins with being actively engaged in school activities and ends with higher levels of academic achievement. In particular, some of the ?school achievement? effect found in previous research operates through behavioral and emotional manifestations and may be partly explained through physically abused children?s lessened ability to be engaged with and connected to school activities. We conclude with a discussion of the policy implications stemming from our findings.
Elise Barboza-Salerno, G. (2024). Material Hardship, Labor Market Characteristics and Substantiated Child Maltreatment: A Bayesian Spatiotemporal Analysis. Children and Youth Services Review, 157, 107371. https://doi.org/10.1016/j.childyouth.2023.107371
Child maltreatment is a critical public health problem whose structural underpinnings underscore the need to move prevention efforts from individual-level risk factors to social policy. Despite previous studies exploring the evolution of child maltreatment risk in socially vulnerable contexts, little is known about how neighborhood level material deprivation and job market characteristics, beyond the employment context, impact substantiated maltreatment risk. The present analysis integrates multiple streams of data to explore the complexity of child maltreatment in the most populous county in New Mexico as a case-study. A geospatial model was used to produce posterior risk estimates and exceedance probabilities of substantiated child maltreatment derived from administrative records controlling for financial strength, economic inequality and hardship, educational attainment, housing and food insecurity and labor market characteristics. Findings showed that over the nine-year study period, the average relative risk of child maltreatment increased substantially, however, there was substantial regional and temporal heterogeneity. More specifically, substantiated child maltreatment risk became more highly concentrated into the most deprived 20% of neighborhoods over time. The results showed a very strong area deprivation effect such that: (1) the risk of maltreatment in the most deprived 20% of neighborhoods on financial strength was 130.78% higher compared to the least deprived 20% of neighborhoods; and (2) maltreatment rates in the bottom 20% of neighborhoods on economic inequality and hardship were 40.52% higher compared to the least deprived 20% of neighborhoods. Finally, substantiated child maltreatment was significantly associated with multiple labor market characteristics including commuting times to work, origin–destination job flows, and mode of transportation to work. From a policy perspective, the results of this study support structural interventions aimed at reducing neighborhood-level material hardship and labor market disadvantage as avenues to support parents so that children and families can thrive.