Introduction to mediation analysis Changiz Mohiyeddini

1. Introduction to mediation analysis Changiz Mohiyeddini Professor of Personality Psychology and Research Methods

2. Content • 1. Lecture rationale • Expected learning outcomes • Introduction • Rationale of variance explanation • 5. Mediation Analysis: How/why can X predict Y? • 6. Main conditions of mediation analysis • Conducting a mediation analysis • Calculating power • 9. Interpreting the results • 10. Choosing a mediator variable • Summary of the lecture • Main key words • Learning check • Reading list

3. 1 Lecture rationale • The prediction of human behavior and experience is a major focus of theory, research, and practice in psychology. • This lecture will give an introduction into mediation analysis.

4. 1 Lecture rationale • The prediction of human behavior and experience is a major focus of theory, research, and practice in psychology. • This lecture will give an introduction into mediation analysis. • Mediation analysis is a tool to explain why one variable can predict another one. • The lecture will explain the rationale of variance explanation, variance prediction and the most crucial conditions of mediation analysis.

5. 2 Expected learning outcomes • Students who successfully complete this lecture will be able to demonstrate an understanding of • variance, variance explanation and variance prediction • the purpose of mediation analysis; • the main conditions of mediation analysis; • the process of mediation analysis; • the difference between partial and total mediation

6. 3 Introduction • The purpose of scientific psychology: • to describe, explain and predict human experiences and behavior.

7. 3 Introduction • The purpose of scientific psychology: • to describe, explain and predict human experiences and behavior. • more precisely: to describe, explain and predict the variancein human experiences and behavior

8. 3 Introduction • The purpose of scientific psychology: • to describe, explain and predict human experiences and behavior. • more precisely: to describe, explain and predict the variancein human experiences and behavior • Variance: What dose it mean?

9. 3 Introduction • The purpose of scientific psychology: • to describe, explain and predict human experiences and behavior. • more precisely: to describe, explain and predict the variancein human experiences and behavior • Variance: What dose it mean? • Variance means differences

10. 4 Rationale of variance explanation • In general: Explaining a phenomenon means to find the reason why this phenomenon is how it is

11. 4 Rationale of variance explanation • In general: Explaining a phenomenon means to find the reason why this phenomenon is how it is • How do we perform variance explanation in psychology?

12. 4 Rationale of variance explanation • In general: Explaining a phenomenon means to find the reason why this phenomenon is how it is • How do we perform variance explanation in psychology? • We use the variance of one variable to explain the variance of another variable.

13. 4 Rationale of variance explanation Variable y

14. 4 Rationale of variance explanation Population Variable y

15. 4 Rationale of variance explanation Population Sample Variable y

16. 4 Rationale of variance explanation Population Sample Variable x Variable y

17. 4 Rationale of variance explanation Population Sample Intention x Behavior y

18. 4 Rationale of variance explanation Intention x Behavior y

19. 4 Rationale of variance explanation Intention x Behavior y • Are X and Y associated?

20. 4 Rationale of variance explanation Intention x Behavior y • Are X and Y associated? Intention x Behavior y

21. 4 Rationale of variance explanation Intention x Behavior y

22. 4 Rationale of variance explanation

23. 4 Rationale of variance explanation Co-Variance

24. 4 Rationale of variance explanation Co-Variance Correlation

25. 4 Rationale of variance explanation Co-Variance Correlation Positive correlation

26. 4 Rationale of variance explanation Sample Co-Variance Intention Behavior Correlation Positive correlation

27. 4 Rationale of variance explanation Co-Variance Correlation Negative correlation

28. 4 Rationale of variance explanation Sample Co-Variance Intention Behavior Correlation Negative correlation

29. 4 Rationale of variance explanation Co-Variance Correlation

30. 4 Rationale of variance explanation Co-Variance Correlation helps us to understand the variance of a variable

31. 4 Rationale of variance explanation Co-Variance Correlation helps us to understand the variance of a variable Theory helps us to predict the variance of a variable Regression

32. 4 Rationale of variance explanation Co-Variance Correlation helps us to understand the variance of a variable Theory helps us to predict the variance of a variable Regression How? Why?

33. 4 Rationale of variance explanation Co-Variance Correlation helps us to understand the variance of a variable Theory helps us to predict the variance of a variable Regression How? Why? Mediation Analysis

34. 5 Mediation Analysis: How/why can X predict Y? • Mediator analysis establishes "how" or "why" one variable predicts or causes an outcome variable (Baron & Kenny, 1986).

35. 5 Mediation Analysis: How/why can X predict Y? • Mediator analysis establishes "how" or "why" one variable predicts or causes an outcome variable (Baron & Kenny, 1986). • A mediator is defined as a variable that explains the relation between a predictor and an outcome variable (Baron & Kenny, 1986; Holmbeck, 1997).

36. 5 Mediation Analysis: How/why can X predict Y? • Mediator analysis establishes "how" or "why" one variable predicts or causes an outcome variable (Baron & Kenny, 1986). • A mediator is defined as a variable that explains the relation between a predictor and an outcome variable (Baron & Kenny, 1986; Holmbeck, 1997). Mediator Predictor:Intention Outcome:Behavior

37. 5 Mediation Analysis: How/why can X predict Y? • Mediator analysis establishes "how" or "why" one variable predicts or causes an outcome variable (Baron & Kenny, 1986). • A mediator is defined as a variable that explains the relation between a predictor and an outcome variable (Baron & Kenny, 1986; Holmbeck, 1997). MediatorPos. Emotion Predictor:Intention Outcome:Behavior

38. 6 Main conditions of mediation analysis According to Baron and Kenny (1986; MacKinnon, 2008) 4 conditions must be met when a variable functions as a mediator variable: Mediator:Positive emotions Predictor:Intention Outcome:Behavior

39. 6 Main conditions of mediation analysis According to Baron and Kenny (1986; MacKinnon, 2008) 4 conditions must be met when a variable functions as a mediator variable: Condition 1: The link between the predictor and the outcome variable must be significant. Mediator:Positive emotions Predictor:Intention Outcome:Behavior c

40. 6 Main conditions of mediation analysis Condition 2: The link between the predictor and the mediator variable must be significant. Mediator:Positive emotions a Predictor:Intention Outcome:Behavior

41. 6 Main conditions of mediation analysis Condition 3: the link between the mediator variable and the outcome variable must be significant. Mediator:Positive emotions b Predictor:Intention Outcome:Behavior

42. 6 Main conditions of mediation analysis Condition 4: The mediator variable has to reduce (partial mediation) or eliminate (total mediation) the link between the predictor and the outcome variable. Mediator:Positive emotions b a Predictor:Intention Outcome:Behavior c C’

43. 7 Calculating Power Path a = Path b More powerful if Path b > Path a

44. 7 Calculating Power • Path a = Path b • More powerful if Path b > Path a • effective sample size: N (1 – rxm2) • N = sample size • and rxm is the correlation between the predictor and the mediator.

45. 7 Calculating Power • Path a = Path b • More powerful if Path b > Path a • effective sample size: N (1 – rxm2) • N = sample size • and rxm is the correlation between the predictor and the mediator. • Assuming N = 700 and rxm = .30, the effective sample size is 637.

46. 7 Calculating Power • Path a = Path b • More powerful if Path b > Path a • effective sample size: N (1 – rxm2) • N = sample size • and rxm is the correlation between the predictor and the mediator. • Assuming N = 700 and rxm = .30, the effective sample size is 637. • If rxm = .60, the effective sample size is 448 ( the sample size is effectively 448 rather than 700).

47. 7 Calculating Power The reliability of the mediator: Specifically, with lower reliability, the effect of the mediator on the outcome variable (Path b) is underestimated and the effect of the predictor variable on the outcome variable (Path c’) is overestimated

48. 7 Calculating Power The reliability of the mediator: Specifically, with lower reliability, the effect of the mediator on the outcome variable (Path b) is underestimated and the effect of the predictor variable on the outcome variable (Path c’) is overestimated Note: statistical analyses, such as multiple regression, that ignore measurement error underestimate mediation effects.

49. 8 Conducting a mediation analysis Using multiple regression: the outcome variable is regressed on the predictor to establish that there is an effect to mediate (path c)

50. 8 Conducting a mediation analysis Using multiple regression: the outcome variable is regressed on the predictor to establish that there is an effect to mediate (path c) the mediator is regressed on the predictor variable to establish (Path a)