Effect of Centering and Standardization in Moderation Analysis

Transcription

1 Effect of Centering and Standardization in Moderation Analysis Raw Data The CORR Procedure 3 Variables: govact negemot Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum Label govact GOVACT: Support for government action negemot NEGEMOT: Negative emotions about climate change AGE: Respondent at last birthday Pearson Correlation Coefficients, N = Prob > r under H0: Rho=0 govact GOVACT: Support for government action govact negemot < negemot NEGEMOT: Negative emotions about climate change < AGE: Respondent at last birthday The REG Procedure Model: MODEL1 Dependent Variable: govact GOVACT: Support for government action Number of Observations Read Number of Observations Used Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq

2 Variable Label Parameter Estimates DF Parameter Estimate Standard Error t Value Pr > t Variance Inflation Intercept Intercept < negemot NEGEMOT: Negative emotions about climate change AGE: Respondent at last birthday < Interact < The effect of NegEmot here tells us how many points GovAct increases when NegEmot increases by one point and Age = 0. Since Age = 0, this test is meaningless. Likewise, the effect of Age tells us now many points GovAct increases when Age increases by one year and NegEmot = 0. Since NegEmot ranges from 1 to 6, this is also meaningless. Raw Data ******************************** PROCESS v3.1 for SAS ******************************** Written by Andrew F. Hayes, Ph.D. Model and Variables Model: 1 Y: GOVACT X: NEGEMOT W: AGE Sample size: Model Summary R R-sq MSE F df1 df2 p Model coeff se t p LLCI ULCI constant NEGEMOT AGE Int_ The tests of main effects here are identical to those from Proc Reg and also meaningless.

3 Product terms key: Int_1 : NEGEMOT x AGE Test(s) of highest order unconditional interactions: R2-chng F df1 df2 p X*W Conditional effects of the focal predictor at values of the moderator(s): AGE Effect se t p LLCI ULCI W values in conditional tables are the 16th, 50th, and 84th percentiles The conditional tests here are identical to all those below. All Variables Mean Centered Variable N Mean Std Dev Minimum Maximum GovActC E NegEmotC E AgeC E On each variable each score has the variable s mean subtracted from it. Accordingly, all of the means are 0. All Variables Mean Centered Analysis of Variance Source DF Sum of Squares Mean Square F Value Pr > F Model <.0001 Error Corrected Total Root MSE R-Square Dependent Mean Adj R-Sq Coeff Var

4 Variable DF Parameter Estimate Standard Error t Value Pr > t Variance Inflation Intercept < negemot < InteractC < Centering has greatly reduced the Variance Inflation Factors The effect of NegEmot here tells us how many points GovAct increases when NegEmot increases by one point and Age = 0. Since Age was mean-centered, the effect is evaluated at the mean level of Age. This is meaningful. Likewise, the effect of Age tells us now many points GovAct increases when Age increases by one year and NegEmot = 0. Since NegEmot was mean-centered, the effect is evaluated at the mean level of NegEmot. This is meaningful. PROCESS v3.1 for SAS Model and Variables Model: 1 Y: GOVACTC X: NEGEMOTC W: AGEC Sample size: ****************************************************************************************** OUTCOME VARIABLE: GOVACTC Model Summary R R-sq MSE F df1 df2 p Model coeff se t p LLCI ULCI constant NEGEMOTC AGEC Int_

5 Product terms key: Int_1 : NEGEMOTC x AGEC Test(s) of highest order unconditional interactions: R2-chng F df1 df2 p X*W AGEC Effect se t p LLCI ULCI W values in conditional tables are the 16th, 50th, and 84th percentiles Standardized to Mean 0, Standard Deviation 1 Variable N Mean Std Dev Minimum Maximum govact E negemot E E Standardized ******************************** PROCESS v3.1 for SAS ******************************** Model and Variables Model: 1 Y: GOVACT X: NEGEMOT W: AGE OUTCOME VARIABLE: GOVACT

6 Model Summary R R-sq MSE F df1 df2 p Model coeff se t p LLCI ULCI constant NEGEMOT AGE Int_ Test(s) of highest order unconditional interactions: R2-chng F df1 df2 p X*W Conditional effects of the focal predictor at values of the moderator(s): AGE Effect se t p LLCI ULCI These conditional effects are evaluated at z = 0 for NegEmot, which is the mean for NegEmot, so these effects are meaningful. The values of t and p are identical to those obtained with the mean-centered scores, but the effect estimates are now in standard deviation units (beta weights) Predictors only centered R R-sq MSE F df1 df2 p Model coeff se t p LLCI ULCI constant NEGEMOTC AGEC Int_ Results identical to those with all variables centered, except for the intercept.

7 Product terms key: Int_1 : NEGEMOTC x AGEC Test(s) of highest order unconditional interactions: R2-chng F df1 df2 p X*W Focal predict: NEGEMOTC (X) Mod var: AGEC (W) Conditional effects of the focal predictor at values of the moderator(s): AGEC Effect se t p LLCI ULCI W values in conditional tables are the 16th, 50th, and 84th percentiles The data used here are those from the second edition of Hayes Introduction to Mediation, Moderation, and Conditional Process Analysis, available here. Here is the SAS code: *MODERATE-GLBWARM.SAS; options pno=min nodate formdlim='-'; title 'Moderation, glbwarm Data'; proc means data=glbwarm; mean stddev min max nmiss; var GovAct NegEmot Age; run; Data Raw; set glbwarm; Interact = NegEmot * Age; Data centered; set glbwarm; GovActC=GovAct ; NegEmotC=NegEmot ; AgeC=Age ; InteractC=NegEmotC*AgeC; proc standard data=glbwarm mean=0 std=1 out=zs; data InteractionZ; set Zs; InteractZ = NegEmot*Age; title 'Raw Data'; run; proc corr data=glbwarm; var GovAct NegEmot Age; run; proc reg data=raw; model GovAct = NegEmot Age Interact / VIF; run; QUIT; %process (data=glbwarm,y=govact,x=negemot,w=age,model=1); run; title 'All Variables Mean Centered'; run; proc means data=centered; Var GovActC NegEmotC AgeC; run; proc reg data=centered; model GovAct = NegEmot Age InteractC / VIF; run; QUIT; %process (data=centered,y=govactc,x=negemotc,w=agec,model=1); title 'Standardized'; run; proc means data=zs;var GovAct NegEmot Age; run; proc reg data=zs; model GovAct = NegEmot Age InteractZ / VIF; run; QUIT; %process (data=zs,y=govact,x=negemot,w=age,model=1); title 'Predictors only centered'; run;

8 %process (data=centered,y=govact,x=negemotc,w=agec,model=1); Karl Wuensch's Statistics Lessons P Karl L. Wuensch, February, 2019