Hi! I am trying to analyze a moderated mediation using mplus. I first started with a simple mediation, so X -> M -> Y. Path a (X -> M) is not significant, while Path b (M -> Y) is significant in the simple mediation (p=0.004).
However, when I introduced the moderator, it was found that Path a becomes significant (p=0.011), but Path b becomes only marginally significant (p=0.066), and the moderating effect is also significant (p=0.048). While of course it is good to see that the moderating effect is significant, I wonder why path b would become insignificant in my moderated mediation model? It is quite a big jump from p=0.004 to p=0.066, so it is really weird to me. Is it because Mplus allows the paths a and b to covariate? If so, are there any ways I could relax such default constraint and see the effect?
Any suggestions or recommended readings on this are highly appreciated!
Many thanks!
It is impossible to give you a useful answer without seeing the details of your analysis. For example, which path was moderated by what type of moderator (continuous or categorical?)? Did you center any variables prior to introducing the moderator (interaction term)? When moderation is introduced, the interpretation of some of the path coefficients becomes more complex (as it does in moderated regression). More details are needed to understand what exactly it is that you specified. Perhaps you could post the relevant sections of your Mplus syntax and output.
Hi @Christian Geiser,
Sure! Please find below the input in Mplus (for both moderated mediation and simple mediation) for your reference. I have attached the photos for the outputs too. Thank you for your great help!
I have done experiment, so the X1, X2, and Mo are all categorical variable, with only 0 and 1. Me1, Me2, and y1 are continuous. Me1 and Me2 are two parallel mediators, and I moderate the first paths from X1 to Me1 and X2 to Me2. The other moderated mediations are just to control their effects.
Input for MODERATED MEDIATION.
Define:
! Predictor variable - X1, X2
! Mediator variable(s) - Me1, Me2
! Moderator variable(s) - Mo
! Outcome variables - y1
X1=INSupp;
X2=EMSupp;
Mo=Climate;
Me1=Threat;
Me2=Justice;
y1=AcceptH;
CENTER X1 X2 Mo (GRANDMEAN);
Inter1 = X1*Mo;
Inter2 = X2*Mo;
VARIABLE:
names = Climate Support INSupp EMSupp Warmth Sincere Threat
Shame Justice AcceptH WHelp Leave Involve Realism;
missing = all(99.99);
usevariable = X1 X2 Mo Me1 Me2 y1 Inter1 Inter2;
! Standard deviation of W = 0.497
ANALYSIS: TYPE = GENERAL;
Estimator = ML;
Bootstrap = 5000;
! In model statement name each path and intercept using parentheses
MODEL:
y1 on Me1 (b11)
Me2 (b21)
X1
X2
Mo
Inter1
Inter2;
[Me1] (a0);
Me1 on X1 (a11)
X2 (a21)
Mo
Inter1 (m11)
Inter2 (m21);
Me2 on X1 (a12)
X2 (a22)
Mo
Inter1 (m12)
Inter2 (m22);
MODEL CONSTRAINTS:
! X1*W on M1
NEW(modh1 modl1 modd1);
modh1=a11+m11*0.497;
modl1=a11-m11*0.497;
modd1=modh1 - modl1;
! X1*W on M2
NEW(modh2 modl2 modd2);
modh2=a12+m12*0.497;
modl2=a12-m12*0.497;
modd2=modh2 - modl2;
! X2*W on M1
NEW(modh3 modl3 modd3);
modh3=a21+m21*0.497;
modl3=a21-m21*0.497;
modd3=modh3 - modl3;
! X2*W on M2
NEW(modh4 modl4 modd4);
modh4=a22+m22*0.497;
modl4=a22-m22*0.497;
modd4=modh4 - modl4;
! Moderated mediation
! X1*W on M1 on Y
NEW(momeh1 momel1 momed1);
momeh1=a11*b11 + m11*b11*0.497;
momel1=a11*b11 - m11*b11*0.497;
momed1=momeh1 - momel1;
! X1*W on M2 on Y
NEW(momeh2 momel2 momed2);
momeh2=a12*b21 + m12*b21*0.497;
momel2=a12*b21 - m12*b21*0.497;
momed2=momeh2 - momel2;
! X2*W on M1 on Y
New(momeh3 momel3 momed3);
momeh3=a21*b11 + m21*b11*0.497;
momel3=a21*b11 - m21*b11*0.497;
momed3=momeh3 - momel3;
! X2*W on M2 on Y
New(momeh4 momel4 momed4);
momeh4=a22*b21 + m22*b21*0.497;
momel4=a22*b21 - m22*b21*0.497;
momed4=momeh4 - momel4;
OUTPUT: Tech1 Tech3 Tech8 Cinterval(BCBOOTSTRAP);
PLOT: TYPE=PLOT2;
**************************
Input for Simple MEDIATION. They are largely the same, just that the moderating effects have been removed:
Define:
! Predictor variable - X1, X2
! Mediator variable(s) - Me1, Me2
! Outcome variables - Y
X1=INSupp;
X2=EMSupp;
Me1=Threat;
Me2=Justice;
Y=AcceptH;
VARIABLE:
names = Climate Support INSupp EMSupp Warmth Sincere Threat
Shame Justice AcceptH WHelp Leave Involve Realism;
missing = all(99.99);
usevariable = X1 X2 Me1 Me2 Y;
ANALYSIS: TYPE = GENERAL;
Estimator = ML;
Bootstrap = 5000;
! In model statement name each path and intercept using parentheses
MODEL:
Y ON Me1 (b1);
Y ON Me2 (b2);
Y ON X1 (cdash1); ! direct effect of X1 on Y
Y ON X2 (cdash2); ! direct effect of X2 on Y
Me1 ON X1 (a11);
Me2 ON X1 (a12);
Me1 ON X2 (a21);
Me2 ON X2 (a22);
MODEL CONSTRAINTS:
NEW(a11b1 a12b2 TOTALIND1 TOTAL1);
a11b1 = a11*b1;
! Specific indirect effect of X1 on Y via M1
a12b2 = a12*b2;
! Specific indirect effect of X1 on Y via M2
TOTALIND1 = a11*b1 + a12*b2;
! Total indirect effect of X1 on Y via M1, M2
TOTAL1 = a11*b1 + a12*b2 + cdash1; ! Total effect of X1 on Y
NEW(a21b1 a22b2 TOTALIND2 TOTAL2);
a21b1 = a21*b1;
! Specific indirect effect of X2 on Y via M1
a22b2 = a22*b2;
! Specific indirect effect of X2 on Y via M2
TOTALIND2 = a21*b1 + a22*b2;
! Total indirect effect of X2 on Y via M1, M2
TOTAL2 = a21*b1 + a22*b2 + cdash2; ! Total effect of X2 on Y
OUTPUT: STAND Cinterval(BCBOOTSTRAP);
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