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Testing for mediating and moderating effects with SAS

Testing for mediating and moderating effects with SAS. Contingency / elaboration / 3rd variable models. One best management practice vs. contingency perspective Failure to find main effects -> use of moderators

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Testing for mediating and moderating effects with SAS

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  1. Testing for mediating and moderatingeffectswith SAS

  2. Contingency / elaboration / 3rd variablemodels One best management practice vs. contingencyperspective Failure to find main effects -> use of moderators Morethan 50% of empiricalstrategyresearchhave a contingencyelementnowadays • Venkatraman 1989 main types: • Interactionmoderation • Subgroupmoderation • Mediation • Configurations, gestalt (clusteranalysis) Footer

  3. Contingency / elaboration / 3rd variablemodels Fairchild et al 2007, AnnualReview of Psychology 58: 593-614 Thirdvariablecouldbe • Mediator x-> z -> y • Confoundingvariable x <- z -> y (lead to spuriousx-yrelationship) • Covariate x -> y <- z or z -> x -> y • Moderator / interaction Footer

  4. Mediation

  5. MediationMathieu et al 2008, Org. Res. Meth.http://davidakenny.net/cm/mediate.htm • X -> M -> Y • Underlyingmechanismthroughwhich X predicts Y • Baron & Kenny (1986) Journal Of Personality and Social Psych., 51, 1173-1182

  6. Mediation, examplesMathieu et al 2008, Org. Res. Meth. • Structure – strategy – performance (IO paradigm) • Strategy – structure – performance (Chandler) • Theory of reasoned action (Ajzen) • Technology adoption model (Davis) • RBV

  7. Mediation e3 Mediatingvariable M a b e2 Independentvariable X Dependentvariable Y c’ Y = i1 + cX + e1 Y = i2 + c’X + bM + e2 M = i3 + aX + e3

  8. Mediation Causalsteps (Baron & Kenny 1986): • Y = i1 + cX + e1 • Y = i2 + c’X + bM + e2 • M = i3 + aX + e3 Full of partialmediationexistswhen… • cis significant • ais significant • bis significant • c’is smallerthan c

  9. Mediation, assumptions • Residuals in eq 2 and 3 areindependent • M and residual in eq 2 areindependent • No XM interaction in eq 2 • No misspecification • Causalorderx->m->ynoty->m->x • Causaldirectionm<->y • Unmeasuredvariables • Measurementerror

  10. Size of Mediation, indirect effect total effect = direct effect + indirect effect c = c’ + ab You can calculate either c – c’ from equations 1 and 2 or ab from equations 2 and 3 and test for significance using z-distribution Standard error for the indirect effect by Sobel 1982, works ok with samples n>100, but is very conservative (low power) Sobel test tool in web http://quantpsy.org/sobel/sobel.htm

  11. Pierceet al. (2004) Workenvironmentstructure and psychologicalownership: the mediatingeffects of control. The journal of social psychology, 144(5):507-534 Linear regression Gassenheimer & Manolis (2001) The influence of productcustomization and supplierselection on futureintentions: the mediatingeffects of salesperson and organizationaltrust. Journal of managerialissues, 13(4):418-435 LISREL Mediation examples

  12. Mediation, examplePierce et al 2004 Hypothesis A: controlmediates the relationshipbetween WES and ownership Hypothesis B: controlmediates the relationshipbetweentech and ownership

  13. Mediation, example with SAS Assign the library TILTU12 Open the datasetData_med_mod Test a model, whereknowledgesharing is expected to mediate the effect of collaboration on innovativeperformance • Use the Baron & Kennycausalsteps to estimate the model • Use the Sobeltestcalculator to test the significance of the indirecteffect

  14. Step 1 Footer

  15. Step 1 Footer

  16. Step 2 Footer

  17. Step 2 Footer

  18. Step 3 Footer

  19. Step 3 Footer

  20. Indirecteffect & Sobeltest • http://quantpsy.org/sobel/sobel.htm • From the SAS output youget a= .596, b=.05, c=.066 and c’=.043 • Input the a valuefromstep 3 and itsstderror • Input the b valuefromstep 2 and itsstderror • The calculatorshows • the teststatistic z = ab / stderror of ab • stderror of ab • Significancetestthat ab differsfromzero • Note: the calculatordoesnot show the value of ab (.596 * .05 in this case) Footer

  21. Indirecteffect & Sobeltest http://quantpsy.org/sobel/sobel.htm Footer

  22. Moderation

  23. Moderationhttp://davidakenny.net/cm/moderation.htm A predictorhas a differentialeffect on the outcomevariabledepending on the level of the moderatorvariable Guidelines for testing in Sharma et al (1981) JMR 18(3):291-300 Venkatraman 1989, AMR 14:423-444 Footer

  24. Moderation Homologizer: Errorterm is function of z, R square is dependent on z If the sample is split into subgroupsaccording to values of z, weobservedifferent R squares in the subgroups Pure and Quasimoderator: The regression coefficient of x is a function of z Pure y = a + b1 x + b2 xzor y = a + (b1 + b2 z)x Quasi y = a + b1 x + b3z + b2xz -> either x or z canbe the moderator A. Subgroupanalysis Split the sample into subgroupsbased on the moderator (z) and run the x-ymodelseparately in eachsubgroup Compare the R squares (and/orparameterestimates) of the subgroups, Chowtestcanbeused for testing the significance of the difference in R squares Difference in parameterestimates d= B1 – B2 Standard error of the differenceSEd= SQRT (SEB12 + SEB22) If |d| > 1.96* SEd, it is significant at p<.05 Footer

  25. Moderation B: MRA (interaction) The variablesshould (maybe, seeEchambadi & Hess 2004) bemean-centered (orresidual-centered, seeLance 1988) to avoidcollinearity • Y = a + b1 x • Y = a + b1 x + b2 z • Y = a + b1 x + b2 z + b3xz Interpretation: Z is a predictorifb3= 0 and b2≠ 0 Z is a pure moderatorifb2= 0 and b3≠ 0 Z is a quasimoderatorifb2≠ 0, ja b3≠ 0 Usegraphics to help interpretation of results

  26. Moderation

  27. Moderation Summary, firstrun MRA • Ifxz-interaction is significant • If the main effect of z is significant -> quasi • If the main effect of z is notsignificant -> pure • Ifxz-interaction is notsignificant • If the main effect of z is significant->predictor • If the main effect of z is notsignificant, and z is unrelatedwith x -> split into subgroupsbased on z and runx-y regression • If the R square is different in the subgroups -> homologizer • If the R square is notdifferent in the subgroups -> z plays no role Examples: Wiklund & Shepherd (2005) Entrepreneurialorientation and small business performance: a configurationalapproach. Journal of business venturing, 20(1):71-91 Rasheed (2005) Foreignentrymode and performance: The moderatingeffects of environment. Journal of small business management, 43(1):41-54

  28. Footer

  29. Footer

  30. Dataset TAPDATA Examine the relationshipsbetween an individual’ssex, height, and the parents’ heights Main effects Interactioneffect of parents’ heights? Is sex a moderator, and whattype of moderator? Firstassign the library and thenopen the data and create a scatterplot SAS example on moderation

  31. SAS example on moderation

  32. SAS example on moderation

  33. Data transformations Create a new file into yourlibraryselectingonlyvariablesyouwillneed (sukup, pituus, isanpit, aidipit) Add a computedcolumncalledmale, whereyouhaverecodedsukup= 2 as 0 Sort the data according to the variablemale

  34. Main effects

  35. Model diagnostics & SAS code PROC REG DATA=tiltu12.recodedsorted_tap PLOTS(ONLY)=ALL ; Linear_Regression_Model: MODEL pituus = male isanpit aidipit /SELECTION=NONE SCORR1 SCORR2 TOL SPEC ; RUN;

  36. Output Significantmodel, high R square, homoskedastic, allparameterssignificant, no collinearity

  37. Centering the data for interactionanalysis

  38. Build the interaction variable

  39. Main effects with centered data

  40. Test the significance of interaction using SAS code PROC REG DATA=TILTU12.INTER_STD_TAP PLOTS(ONLY)=ALL ; MODEL pituus = malestnd_isanpitstnd_aidipit; MODEL pituus = malestnd_isanpitstnd_aidipitmom_dad; test mom_dad=0; RUN;

  41. Output: no interaction

  42. Use the fileinteraktio_simple.xls Standard deviationsare 6.676 for dad and 5.220 for mom (bothmeansare 0) Meanvalue for Male is .346 Plot the interaction

  43. Subgroup analysis for sex

  44. Output: R square seems better for men and mom’s height more important for men

  45. Chow test proves that models for men and women are different (data must be sorted!) PROC AUTOREG DATA=TILTU12.INTER_STD_TAP PLOTS(ONLY)=ALL ; MODEL pituus = stnd_isanpitstnd_aidipit /CHOW=(83) ; RUN;

  46. d = bmen– bwomen Standard error for differenceSEd= SQRT (SE bmen2+ SE bwomen2) Testvalue z= d/SEdthencompare z to standardnormal d= .73 - .45 = .28 SEd= sqrt (.1182 + .0962)= sqrt (.023)= .152 Z= 1.84 < 1.96 notsignificant at 5% level Is the effect of mom different for men and women?

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