Mplus code for mediation, moderation, and moderated mediation modelsModel 5 (latent variable version): 1 or more mediators, in parallel if multiple, 1 moderator of direct IVDV path only Example Variables: 1 latent predictor X measured by 4 observed variables X1X4; 1 latent mediator M measured by 4 observed variables M1M4, 1 latent moderator W measured by 4 observed variables W1W4, 1 latent outcome Y measured by 4 observed variables Y1Y4 Preliminary notes: The code below assumes that
Model Diagram (factor indicator variables omitted for space/clarity reasons):
Statistical Diagram (factor indicator variables omitted for space/clarity reasons):
Model Equation(s): Y = b0 + b1M + c1'X + c2'W + c3'XW
Algebra to calculate indirect and/or conditional effects by writing model as Y = a + bX: Y = b0 + b1M + c1'X + c2'W + c3'XW
Y = b0 + b1(a0 + a1X) + c1'X + c2'W + c3'XW
Y = b0 + a0b1 + a1b1X + c1'X + c2'W + c3'XW
Y = (b0 + a0b1 + c2'W) + (a1b1 + c1' + c3'W)X
One indirect effect of X on Y: a1b1 One direct effect of X on Y, conditional on W: c1' + c3'W
Mplus code for the model:
! Latent predictor variable X measured by X1X4
USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
ANALYSIS:
! In model statement first state measurement model
MODEL: ! Measurement model
W@1; ! Create latent interactions
! Fit structural model and name parameters
Y ON X (cdash1);
! Use model constraint subcommand to test simple slopes
! Since we have standardised factors, this is simple  use moderator values of 1, 0, 1 ! ! Also calculate total effects at lo, med, hi values of moderator MODEL CONSTRAINT:
LOW_W = 1; ! 1 SD below mean of W
! Now calc indirect effect  and conditional direct effects for each value of W a1b1 = a1*b1; DIR_LO = cdash1 + cdash3*LOW_W;
TOT_LO = DIR_LO + a1b1;
! Use loop plot to plot total effects of X on Y for low, med, high values of W
PLOT(LOMOD MEDMOD HIMOD); LOOP(XVAL,3,3,0.1); LOMOD = TOT_LO*XVAL;
PLOT:
OUTPUT:
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