Conceptual, Methodological, and Sta3s3cal Dis3nc3ons between Modera3on and Media3on

Transcription

1 CYFS Research Methodology Series Conceptual, Methodological, and Sta3s3cal Dis3nc3ons between Modera3on and Media3on Kyongboon Kwon, Ph.D. Postdoctoral Fellow Center for Research on Children, Youth, Families, and Schools April 23, 2010

2 Overview of the Presenta3on DefiniGons/disGncGons ModeraGon IllustraGon of simple moderagon Beyond graphing Test of simple slopes MediaGon Regions of significance IllustraGon of simple and mulgple mediagon Advances in tesgng mediagon Bootstrap approach Causal inference

3 Defini3on/Dis3nc3on ModeraGon The relagon between X and Y changes as a funcgon of a moderator direcgon Strength ProtecGve factors, Buffering effects Moderator Independent variable (IV) Dependent variable (DV)

4 Defini3on/Dis3nc3on MediaGon A mediator accounts for the relagon between X and Y A mechanism of acgon or process Intervening effect Indirect effect Mediator Independent variable (IV) Dependent variable (DV)

5 General Issues Study design Experimental studies Non- experimental studies Variable types Categorical variables ConGnuous variables Can a variable be both moderator and mediator? Theory, previous research A priori

6 Why Moderators and Mediators Theory building IntervenGon/prevenGon (Kraemer et al., 2008) Moderator For whom, under what condigons? Mediator How does an intervengon work?

7 ModeraGon

8 Test of Modera3on: Example Example of simple moderagon Do parent- teacher relagonships moderate the relagon between parents perceived responsibility and school involvement? P- T relagonships Responsibility School involvement Outcome: School involvement (M = 46.86, SD = 8.25) Predictor: Responsibility (M = 5.21, SD =.48) Moderator: Parent- teacher relagonships (M = 4.08, SD =.71) ModeraGon = InteracGon

9 Test of Modera3on Step 1: Transform predictor and moderator variables Categorical variables Dummy coding, effect coding, contrast coding ConGnuous variables Centering Variable score mean Responsibility_C (M = 0, SD =.48) RelaGonships_C (M = 0, SD =.71) Standardizing M = 0, SD = 1 Reduces mulgcolliniarity problems Makes interpretagon meaningful

10 Test of Modera3on Step 2: Create product terms MulGply predictor and moderator Step 3: Analyze Hierarchical mulgple regression Include all variables included in the product term Step 1: predictor, moderator Step 2: interacgon term

11 Test of Modera3on Step 4: InterpretaGon Interpret the unstandardized coefficients (B) rather than standardized coefficients (β) Zx*Zz (product of standardized variables) Zxz (standardizing product variables)

12 Test of Modera3on Step 5: Plot Low relagonship (relagonship = - 1) Average relagonship (relagonship = 0) High relagonship (relagonship = 1)

13 Test of Modera3on Follow- up analysis Test simple slopes (Aiken & West, 1991) Y = b0 + b1x + b2z + b3xz Y = (b1 + b3z)x + (b2z + b0) Simple slope: (b1 + b3z) Standard errors: sb = s11: Variance of b1 s33: Variance of b3 s13: Covariance of b1 and b3 T- test: Simple slope / SE of slope Degrees of freedom: n k - 1

14 Test of Modera3on Test simple slopes Y = X +.71Z XZ Y = ( Z)X Z Z L = - 1 Y = 2.16X Z M = 0 Y = 6.24X Z H = 1 Y = 10.32X

15 Test of Modera3on Test simple slopes Variance/covariance of coefficients

16 Test of Modera3on Follow- up test: Regions of Significance The Johnson- Neyman Technique (Johnson & Neyman, 1936) IdenGfy values of a predictor/moderator that yields a significant t- stagsgcs (Dearing & Hamilton, 2006) Programs to plot and test simple slopes and regions of significance: www. quantpsy.org (Preacher et al., 2006)

17 Test of Modera3on Design issues Effect size to determine sample size R² change associated with the interacgon term Categorical variable Sample size across groups ConGnuous variable Reliability, range restricgon

18 MediaGon

19 Media3on Terms Predictor (X) c Outcome (Y) c: Total effect a Mediator (M) b Predictor (X) c Outcome (Y) ab: Indirect effect c : Direct effect c = c + ab

20 Test of Media3on Causal steps approach (Baron & Kenny, 1986) Significant relagon between predictor and outcome (total effect) c Predictor (X) Outcome (Y) Significant relagon between predictor and mediator a Mediator (M) Predictor (X) Significant relagon between mediator and outcome auer controlling for predictor Mediator (M) a Predictor (X) ReducGon in the relagon between predictor and outcome when mediator is included (direct effect) Mediator (M) a b Outcome (Y) b Predictor (X) c Outcome (Y)

21 Test of Media3on Test the product of paths a and b Sobel test (1982) Standard error of ab Compare ab/s ab to a crigcal value at α =.05 from the z- distribugon

22 Test of Media3on Problem of Sobel test DeviaGon from a normal distribugon (ab) Biased test- stagsgcs Lacks stagsgcal power StaGsGc St. Error stagsgc/st. Error Skewness Kurtosis

23 Test of Media3on Problem of Sobel test DeviaGon from a normal distribugon (ab) StaGsGc St. Error StaGsGc/St. Error Skewness Kurtosis

24 Test of Media3on Problem of Sobel test DeviaGon from a normal distribugon (ab) StaGsGc St. Error StaGsGc/St. Error Skewness Kurtosis OK when N 400 (MacKinnon et al., 2002)

25 Test of Media3on Bootstrap Approach What is bootstrap? The populagon is to the sample as the sample is to the bootstrap samples (Fox, 2002) Random resampling procedure with replacement Original Sample 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 N = 10 M = 15.5 Sample 1 Sample 2 Sample n 11, 12, 13, 13, 14, 15, 20, 19, 16, 16 N = 10 M = , 14, 14, 17, 18, 12, 16, 20, 19, 18 N = 10 M = , 11, 12, 13, 15, 14, 15, 13, 13, 11 N = 10 M = 12.8

26 Test of Media3on Bootstrap approach of tesgng indirect effects (Shrout and Bolger, 2002) Step 1: From original data set of N cases create a bootstrap sample of N cases by random sampling with replacement Step 2: Calculate a, b, and indirect effects (a x b) based on the bootstrap sample, and save the results to a file Step 3: Repeat steps 1 and 2 mulgple Gmes ( ) Step 4: From the distribugon of esgmates from step 3, if α =.05, determine the 2.5%ile and 97.5%ile values of a x b PercenGle confidence interval Bias corrected Bias corrected and accelerated

27 Test of Simple Media3on: Example Does parengng efficacy mediate the relagon between parengng stress and home involvement? ParenGng efficacy ParenGng stress Home involvement

28 Test of Media3on Structural equagon modeling package SPSS, SAS Macro (Preacher & Hayes, 2008) INDIRECT Y = Involvement/ X = Stress / M = Efficacy / NORMAL = 1/ BOOT = 1000 / CONF = 95/ PERCENT = 1/ BC = 1/ BCA = 1.

29 Test of Media3on SPSS, SAS Macro (Preacher & Hayes, 2008)

30 Test of Mul3ple Media3on: Example Do parengng efficacy and perceived responsibility mediate the relagon between parengng stress and home involvement? efficacy ParenGng stress Home involvement responsibility Child age

31 Test of Media3on SPSS, SAS Macro (Preacher & Hayes, 2008) INDIRECT Y = Involvement/ X = Stress / M = Efficacy Responsibility Childage / C =1 / CONTRAST = 1/ BOOT = 1000 / CONF = 95/ PERCENT = 1/ BC = 1/ BCA = 1.

32 Test of Media3on SPSS, SAS Macro (Preacher & Hayes, 2008)

33 Media3on: Debates Is the total effect required for tesgng mediagon? YES! Conceptually.. MediaGon accounts for the associagon between X and Y No associagon to be mediated First requirement according to Baron & Kenny (1986)

34 Media3on: Debates Is the total effect required for tesgng mediagon? No! (Hayes, 2009; Shrout & Bolger, 2002) Suppression The relagon between X and Y is suppressed by M Indirect effect (ab) has the opposite sign of direct effect (c ) Example + Support seeking - Stress event Distress +

35 Media3on: Debates Is the total effect required for tesgng mediagon? No! (Hayes, 2009; Shrout & Bolger, 2002) Suppression Inconsistent mediagon: mulgple mediators Mediator Independent variable (IV) Dependent variable (DV) + - Mediator 2 Distal causal process

36 Media3on: Debates Inconsistent terminology Is mediagon = indirect effect? Discipline specific (MacKinnon et al., 2002) MediaGon is a special case of indirect effects (Holmbeck, 1997; Preacher & Hayes, 2004) Intervening effects (Mathieu & Taylor, 2006) MediaGon Indirect effects

37 Causal Inference No stagsgcal analysis can test causagon Problems with cross- secgonal design M X X Y M Y M Y X InterpretaGon: The finding is consistent with the assumed causal model (Stone- Romero & Rosopa, 2008).

38 Causal Inference No stagsgcal analysis can test causagon Instead.. Experimental design Theory Establishing causagon (Shadish et al., 2002) AssociaGon between two variables Non- spurious associagon: the associagon b/w X and Y are not due to another variable DirecGonal relagon from cause to effect (not necessarily the Gming of measurement)

39 Summary ModeraGon Change relagon between X and Y Follow- up tests auer plo{ng interacgons MediaGon Accounts for the relagon between X and Y Bootstrap approach Extensions Moderated mediagon Mediated moderagon Longitudinal mediagon models MulGlevel moderagon and mediagon

40 References

41 References

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