Mediation: Background, Motivation, and Methodology

Transcription

1 Mediation: Background, Motivation, and Methodology Israel Christie, Ph.D. Presentation to Statistical Modeling Workshop for Genetics of Addiction 2014/10/31

2 Outline & Goals Points for this talk: What is mediation? Why are people (researchers) interested? How is (simple) mediation assessed? Extension to more complex models. Example from a project at MDA. Available software.

3 But first... How many of you have experience with mediation? Requests from PI or collaborators? Speak up!

4 What is mediation?...represents the generative mechanism through which the focal independent variable is able to influence the dependent variable of interest. 1 X? Y Warning: There be sloppy language... 1 Baron & Kenny (1986)

5 Why are people interested? Psychologists love mechanisms! Theory building & Intervention design For example: Stress & heart disease Functional brain imaging & neural networks Intervention for sun protection 1986 publication 1 generally regarded as kicking off modern thinking on mediation 1 Baron & Kenny (1986)

6 How is mediation assessed? Historically, three(ish) major approaches The magic triangle c X Y Y = cx M a b M = ax X c' Y Y = bm + c'x c = c + ab OR c c = ab

7 How is mediation assessed? The Causal steps method 1 1. X predicts Y (c is sig.) 2. X predicts M (a is sig.) c 3. M predicts Y, controlling for X (b is sig.) 4. When M is in model, X no longer predicts Y (c is zero) X X a M c' b Y Y It s just bad... 1 Baron & Kenny (1986)

8 How is mediation assessed? The Sobel Test method 1 Sometimes called the delta method Simple formula that approximates the standard error of ab Very low power 2 (due to mismatch between assumed a & actual distribution of ab) X M c' b Y 1 Sobel (1982) 2 MacKinnon, Warsi, & Dwyer (1995)

9 How is mediation assessed? The Bootstrap method 1 Non parametric method involving sampling with replacement Confidence intervals derived from bootstrap sample (e.g., bias corrected, percentile) X a M c' b Y 1 Shrout & Bolger (2002)

10 How is mediation assessed? The Monte Carlo method 1 Generate random normal deviates representing a and b (m a and s a ; m b and s b ) CI derived as quantiles of ab X a M c' b Y 1 Preacher & Selig (2012)

11 How is mediation assessed? What are the relative merits? 1 Power: BC bootstrap but can be too liberal 2 Type I: Monte Carlo Best balance: Percentile CI 1 Hayes & Sharkow (2013) 2 Fritz, Taylor, and MacKinnon (2012)

12 Multiple Mediators Seldom interested in a single variable More likely multiple candidate variables mediating relationship between variables of interest In reality, these multiple mediators likely don t operate independently of one another Natural extension to multiple mediators Parallel & Serial paths

13 Parallel mediators Recall the single mediator Only one additional formula required for each parallel mediator M a b M = ax X c' Y Y = bm + c'x

14 Parallel mediators Recall the single mediator Only one additional formula required for each parallel mediator M 1 a 1 b 1 X c' Y M 1 = a 1 X M 2 = a 2 X Y = b 1 M 1 + b 2 M 2 + c'x a 2 b M 2 2

15 Serial mediators Mediators are placed in series M 1 a 3 M 2 b 2 a 1 b 1 X a 2 c' Y M 1 = a 1 X M 2 = a 2 X + a 3 M 1 Y = b 1 M 1 + b 2 M 2 + c'x

16 Serial mediators Creates an additional path M 1 a 3 M 2 b 2 a 1 b 1 X a 2 c' Y

17 Serial mediators Creates an additional path M 1 a 3 M 2 b 2 a 1 b 1 X a 2 c' Y 1) a 1 b 1

18 Serial mediators Creates an additional path M 1 a 3 M 2 b 2 a 1 b 1 X a 2 c' Y 1) a 1 b 1 2) a 2 b 2

19 Serial mediators Creates an additional path M 1 a 3 M 2 b 2 a 1 b 1 X a 2 c' Y 1) a 1 b 1 2) a 2 b 2 3) a 1 a 3 b 2

20 An example Sun protection intervention Target population: Melanoma survivors with a child 12 years old N = 281 Primary outcome: Children s wide brimmed hat use

21 Variables X: Treatment (vs. Control) Mediators: Self Efficacy Expectancy Intention Knowledge Y: Hat use

22 Single Mediators Treatment B = 0.069; Pm = Self Efficacy Hat B = 0.138; Pm = Treatment Expectancy Hat Treatment B = 0.089; Pm = Intention Hat Treatment B = 0.033; Pm = Knowledge Hat

23 Parallel Mediators Treatment B = 0.016; Pm = Self Efficacy B = 0.116; Pm = Expectancy B = 0.062; Pm = Intention Hat B = 0.031; Pm = Knowledge

24 Serial Mediators B = 0.084; Pm = Expectancy Treatment Self Efficacy B = 0.040; Pm = Hat Intention B = 0.025; Pm = Knowledge B = 0.031; Pm = 0.126

25 Serial Mediators B = 0.084; Pm = Expectancy Treatment Self Efficacy B = 0.040; Pm = Hat Intention B = 0.025; Pm = Knowledge B = 0.031; Pm = 0.126

26 Serial Mediators B = 0.084; Pm = Expectancy Treatment Self Efficacy B = 0.040; Pm = Hat Intention B = 0.025; Pm = Knowledge B = 0.031; Pm = 0.126

27 Serial Mediators B = 0.084; Pm = Expectancy Treatment Self Efficacy B = 0.040; Pm = Hat Intention B = 0.025; Pm = Knowledge B = 0.031; Pm = 0.126

28 Serial Mediators B = 0.084; Pm = Expectancy Treatment Self Efficacy B = 0.040; Pm = Hat Intention B = 0.025; Pm = Knowledge B = 0.031; Pm = 0.126

29 Available Software PROCESS for SPSS and SAS 1 mediation package in R 2 (potential outcomes framework) Online resources 3 Any number of packages for SEM Of course, not that hard to code... 1 Hayes (2013) 2 Imai (2014) 3 Selig & Preacher (2008)

30 Thanks!