Mplus code for mediation, moderation, and moderated mediation models
Model 1a (latent variable version): 1 moderator [BASIC MODERATION]
Example Variables: 1 latent predictor X measured by 4 observed variables X1X4, 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
 The latent IV (factor X) is measured by continuous observed variables X1X4.
 Any latent moderator(s) (factors W, V, Q, Z) are measured by continuous observed variables W1W4, Z1Z4, V1V4, Q1Q4 respectively.
 Any latent mediator(s) (factor M, or factors M1, M2, etc.) are measured by continuous observed variables M1M4 or M1_1M14, M2_1M2_4 respectively.
 The latent outcome Y is measured by continuous observed variables Y1Y4.
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 + b1X + b2W + b3XW
Algebra to calculate indirect and/or conditional effects by writing model as Y = a + bX:
Y = b0 + b1X + b2W + b3XW
Hence... grouping terms into form Y = a + bX
Y = (b0 + b2W) + (b1 + b3W)X
Hence...
One direct effect of X on Y, conditional on W:
b1 + b3W
Mplus code for the model:
! Latent predictor variable X measured by X1X4
! Latent moderator W measured by W1W4
! Latent outcome variable Y measured by Y1Y4
USEVARIABLES = X1 X2 X3 X4
W1 W2 W3 W4
Y1 Y2 Y3 Y4;
ANALYSIS:
TYPE = GENERAL RANDOM;
ESTIMATOR = ML;
ALGORITHM = INTEGRATION;
! In model statement first state measurement model
! Then create any latent interactions required
! Then state structural model naming each path and intercept using parentheses
MODEL:
! Measurement model
! Identify moderator factor by fixing variance = 1 (instead of first loading)
! This makes this factor standardised
X BY X1 X2 X3 X4;
W BY W1* W2 W3 W4;
Y BY Y1 Y2 Y3 Y4;
W@1;
! Create latent interactions
XW  X XWITH W;
! Fit structural model and name parameters
! Note that intercept of Y is fixed = 0 since they are latent vars
! so no code to state and name them as parameters
Y ON X (b1);
Y ON W (b2);
Y ON XW (b3);
! Use model constraint subcommand to test simple slopes
! You need to pick low, medium and high moderator values,
! for example, of 1 SD below mean, mean, 1 SD above mean
! Since we have standardised factors, this is simple  use moderator values of 1, 0, 1 !
MODEL CONSTRAINT:
NEW(LOW_W MED_W HIGH_W SIMP_LO SIMP_MED SIMP_HI);
LOW_W = 1; ! 1 SD below mean of W
MED_W = 0; ! mean of W
HIGH_W = 1; ! +1 SD below mean of W
! Now calc simple slopes for each value of W
SIMP_LO = b1 + b3*LOW_W;
SIMP_MED = b1 + b3*MED_W;
SIMP_HI = b1 + b3*HIGH_W;
! Use loop plot to plot total effects of X on Y for low, med, high values of W
! NOTE  values from 3 to 3 in LOOP() statement since
! X is factor with mean set at default of 0
PLOT(LOMOD MEDMOD HIMOD);
LOOP(XVAL,3,3,0.1);
LOMOD = (b1 + b3*LOW_W)*XVAL;
MEDMOD = (b1 + b3*MED_W)*XVAL;
HIMOD = (b1 + b3*HIGH_W)*XVAL;
PLOT:
TYPE = plot2;
OUTPUT:
CINT;
Return to Model Template index.
To cite this page and/or any code used, please use:
Stride, C.B., Gardner, S., Catley, N. & Thomas, F.(2015) 'Mplus code for the mediation, moderation, and moderated mediation model templates from Andrew Hayes' PROCESS analysis examples', http://www.offbeat.group.shef.ac.uk/FIO/mplusmedmod.htm
