Multiple regression model

• Model 2: X on M:
  • M = b0 + b1X + e2
  • We test if SES (X) significantly predicts access to healthcare (M).
• Model 3: M on Y (controlling for X):
  • Y = b0 + b1X + b2M + e3
  • We test if access to healthcare (M) significantly predicts health outcomes (Y) while controlling for SES (X).

3. Analyzing the Output and Interpreting Mediation:

• Significant Total Effect (Model 1):
  • If b1 in Model 1 is significant, there is a total effect of SES on health outcomes.
• Significant X on M (Model 2):
  • If b1 in Model 2 is significant, SES significantly predicts access to healthcare.
• Significant M on Y (Model 3):
  • If b2 in Model 3 is significant, access to healthcare significantly predicts health outcomes, controlling for SES.
• Reduction in X on Y Effect (Model 3):
  • If b1 in Model 3 is smaller than b1 in Model 1, there is evidence of mediation.
  • If b1 in Model 3 is no longer significant, there is evidence of complete mediation.
  • If b1 in Model 3 is still significant but smaller, there is evidence of partial mediation.
• Bootstrapping:
  • A more robust method is to use bootstrapping to estimate the indirect effect (a*b) and its confidence interval.
  • If the confidence interval does not include zero, the indirect effect is considered significant, indicating mediation.

Interpretation:

• Complete Mediation: If the effect of SES on health outcomes is no longer significant when access to healthcare is included in the model, it suggests that access to healthcare fully explains the relationship.
• Partial Mediation: If the effect of SES on health outcomes is reduced but still significant when access to healthcare is included, it suggests that access to healthcare partially explains the relationship.

4. Possible Implications of Social Change:

• Addressing Health Disparities: If mediation is significant, it highlights the importance of improving access to healthcare for individuals with lower SES to reduce health disparities.
• Policy Implications: Findings can inform policies aimed at increasing access to healthcare, such as expanding insurance coverage, increasing the availability of community health centers, and addressing transportation barriers.
• Social Justice: Mediation analysis can shed light on the mechanisms through which social inequalities translate into health disparities, supporting arguments for social justice interventions.
• Community Interventions: If access to healthcare is a mediator, community-based programs that improve access to preventative care, health education, and social support services can be developed.
• Economic Impacts: If a population has better access to healthcare, that could improve the populations ability to work, and thus improve the overall economic situation of that population.

Important Notes:

• Correlation does not equal causation. Even with significant mediation, we cannot definitively prove causality.
• This is a simplified example. Real-world mediation analyses often involve more complex models and control variables.
• Always check the assumptions of multiple regression.
• Consider using bootstrapping for more robust mediation testing.
• Use up to date statistical software, that has built in mediation analysis tools.

Hypothetical Scenario:

We'll examine the relationship between:

• Causal Variable (X): Socioeconomic Status (SES)
• Mediating Variable (M): Access to Healthcare
• Outcome Variable (Y): Overall Health Outcomes

We hypothesize that SES (X) influences access to healthcare (M), which in turn influences overall health outcomes (Y). We want to test if access to healthcare mediates the relationship between SES and health outcomes.

1. Assumptions of Multiple Regression:

Before fitting the model, we must consider the assumptions of multiple regression:

• Linearity: The relationships between variables are linear.
• Independence of Errors: The errors (residuals) are independent.
• Homoscedasticity: The variance of errors is constant across levels of the predictor variables.
• Normality of Errors: The errors are normally distributed.
• No Multicollinearity: Predictor variables are not highly correlated.

We would need to check these assumptions using diagnostic plots and statistical tests (e.g., scatterplots, residual plots, VIF) after fitting the model.

2. Fitting the Mediation Model:

We will use a series of regression models to test for mediation, typically following Baron and Kenny's (1986) approach, or a more robust approach such as bootstrapping.

• Model 1: Total Effect (X on Y):
  • Y = b0 + b1X + e1
  • We test if SES (X) significantly predicts health outcomes (Y).