Mediation and Moderation Analysis Guide: Complete Report

Analysis Type Determination

Model Type: Moderated Mediation (PROCESS Model 14)

Rationale:

• Mediator (M): Coping Strategies (explains HOW stress affects burnout)
• Independent Variable (X): Job Stress
• Dependent Variable (Y): Burnout
• Moderator (W): Emotional Stability (affects WHEN/FOR WHOM the mediation occurs)

Recommended Model: Model 14 (W moderates both a and b paths)

• Use Model 7 if you only expect W to moderate the M→Y path
• Use Model 8 if you only expect W to moderate the X→M path

Conceptual Path Diagram

                    Coping Strategies (M)
                    ↗                   ↘
                  a(W)                 b(W)  ← Both moderated by Emotional Stability
                 ↗                       ↘
    Job Stress (X) ─────── c'(W) ────────→ Burnout (Y)
                               ↑
                   Emotional Stability (W)
                   (moderates all paths)

Conditional indirect effect = a(W) × b(W)
Index of moderated mediation tests if indirect effects differ across W levels

Runnable Code

SPSS PROCESS (Model 14)

PROCESS y=Burnout /x=JobStress /m=CopingStrategies /w=EmotionalStability 
        /model=14 /boot=5000 /conf=95 /plot=1.

R (lavaan for moderated mediation)

library(lavaan)

# Mean-center moderator
df$ES_c <- scale(df$EmotionalStability, center = TRUE, scale = FALSE)

# Define moderated mediation model (Model 14)
model <- '
  # Regressions
  CopingStrategies ~ a1*JobStress + a2*EmotionalStability + a3*JobStress:ES_c
  Burnout ~ b1*CopingStrategies + b2*EmotionalStability + b3*CopingStrategies:ES_c + 
            c1*JobStress + c2*JobStress:ES_c
'

# Fit model with bootstrap
fit <- sem(model, data = df, se = "bootstrap", bootstrap = 5000)
summary(fit, ci = TRUE)

Python (statsmodels with bootstrap)

import pandas as pd
import numpy as np
import statsmodels.api as sm

# Mean-center all variables
df['Stress_c'] = df['JobStress'] - df['JobStress'].mean()
df['ES_c'] = df['EmotionalStability'] - df['EmotionalStability'].mean()

# Create interaction terms
df['Stress_ES'] = df['Stress_c'] * df['ES_c']
df['Coping_ES'] = df['Coping_c'] * df['ES_c']

# Model 1: X → M (a path moderation)
X_a = sm.add_constant(df[['Stress_c', 'ES_c', 'Stress_ES']])
model_a = sm.OLS(df['CopingStrategies'], X_a).fit()
print(model_a.summary())

# Model 2: M → Y (b path moderation)
X_b = sm.add_constant(df[['Stress_c', 'Coping_c', 'ES_c', 'Coping_ES']])
model_b = sm.OLS(df['Burnout'], X_b).fit()
print(model_b.summary())

Interpretation Guide

Key Tests

APA-Formatted Results Section

To test whether Emotional Stability moderated the indirect effect of Job Stress 
on Burnout through Coping Strategies, we conducted a moderated mediation analysis 
using PROCESS Model 14 (Hayes, 2022) with 5,000 bootstrap samples.

Results indicated that Emotional Stability significantly moderated the relationship 
between Job Stress and Coping Strategies (b = [coef], SE = [se], t = [t], p = [p]). 
Emotional Stability also significantly moderated the relationship between Coping 
Strategies and Burnout (b = [coef], SE = [se], t = [t], p = [p]).

Conditional indirect effects were examined at low (-1 SD), mean, and high (+1 SD) 
levels of Emotional Stability. At low Emotional Stability, the indirect effect 
was significant (effect = [coef], 95% CI [[LL], [UL]]). At mean Emotional 
Stability, the indirect effect was [significant/non-significant] (effect = [coef], 
95% CI [[LL], [UL]]). At high Emotional Stability, the indirect effect was 
[significant/non-significant] (effect = [coef], 95% CI [[LL], [UL]]).

Critically, the index of moderated mediation was significant (index = [coef], 
95% CI [[LL], [UL]]), indicating that the strength of the indirect effect 
significantly differed across levels of Emotional Stability.

Sample Size Considerations

N = 250: Adequate for Model 14 with moderate effect sizes.

• Model 14 requires detecting 2 interactions + conditional indirect effects
• With N=250, you have ~80% power to detect R² change of ~.03-.04 per interaction
• Bootstrap CI with 5,000 samples is robust at this N

Cross-Sectional Data Limitations

Critical caveat: You CANNOT establish causality with cross-sectional data.

What you CAN say:

• “Consistent with the hypothesis that…”
• “The pattern of associations suggests…”

What you CANNOT say:

• “Job stress causes burnout through coping strategies”

Reference

Hayes, A. F. (2022). Introduction to mediation, moderation, and conditional process analysis (3rd ed.). Guilford Press.