Preliminary notes:

The code below assumes that

• The latent IV (factor X) is measured by continuous observed variables X1-X4.
• Any latent moderator(s) (factors W, V, Q, Z) are measured by continuous observed variables W1-W4, Z1-Z4, V1-V4, Q1-Q4 respectively.
• Any latent mediator(s) (factor M, or factors M1, M2, etc.) are measured by continuous observed variables M1-M4 or M1_1-M1-4, M2_1-M2_4 respectively.
• The latent outcome Y is measured by continuous observed variables Y1-Y4.

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 + b2MV + c1'X + c2'V + c3'XV
M = a0 + a1X

Algebra to calculate indirect and/or conditional effects by writing model as Y = a + bX:

Y = b0 + b1M + b2MV + c1'X + c2'V + c3'XV
M = a0 + a1X

Hence... substituting in equation for M

Y = b0 + b1(a0 + a1X) + b2(a0 + a1X)V + c1'X + c2'V + c3'XV

Hence... multiplying out brackets

Y = b0 + a0b1 + a1b1X + a0b2V + a1b2XV + c1'X + c2'V + c3'XV

Hence... grouping terms into form Y = a + bX

Y = (b0 + a0b1 + c2'V + a0b2V) + (a1b1 + a1b2V + c1' + c3'V)X

Hence...

One indirect effect(s) of X on Y, conditional on V:

a1b1 + a1b2V = a1(b1 + b2V)

One direct effect of X on Y, conditional on V:

c1' + c3'V

Mplus code for the model:

! Latent predictor variable X measured by X1-X4
! Latent mediator M measured by 4 observed variables M1-M4
! Latent moderator V measured by 4 observed variables V1-V4
! Latent outcome variable Y measured by Y1-Y4

USEVARIABLES = X1 X2 X3 X4 M1 M2 M3 M4
V1 V2 V3 V4
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 factors by fixing variance = 1 (instead of first loading)
! This makes these factors standardised
   X BY X1 X2 X3 X4;
   M BY M1 M2 M3 M4;
   V BY V1* V2 V3 V4;
   Y BY Y1 Y2 Y3 Y4;

    V@1;

! Create latent interactions
   MV | M XWITH V;
   XV | X XWITH V;

! Fit structural model and name parameters
! Note that intercepts of M, Y are fixed = 0 since they are latent vars
! so no code to state and name them as parameters
   Y ON M (b1);
   Y ON MV (b2);

   Y ON X (cdash1);
   Y ON V (cdash2);
   Y ON XV (cdash3);

   M ON X (a1);

! Use model constraint subcommand to test conditional indirect effects
! You need to pick low, medium and high moderator values for V
! for example, of 1 SD below mean, mean, 1 SD above mean

! 1 moderator, 3 values for it
! arbitrary naming convention for conditional indirect and total effects used below:
! MED_Q = medium value of Q, etc.

MODEL CONSTRAINT:
    NEW(LOW_V MED_V HIGH_V
    IND_LOWV IND_MEDV IND_HIV
    IMM
    DIR_LOWV DIR_MEDV DIR_HIV
    TOT_LOWV TOT_MEDV TOT_HIV);

    LOW_V = -1;   ! -1 SD below mean value of V
    MED_V = 0;   ! mean value of V
    HIGH_V = 1;   ! +1 SD above mean value of V

! Calc conditional indirect effects for each combination of moderator values
! and index of moderated mediation

    IND_LOWV = a1*b1 + a1*b2*LOW_V;
    IND_MEDV = a1*b1 + a1*b2*MED_V;
    IND_HIV = a1*b1 + a1*b2*HIGH_V;

    IMM = a1*b3;

! Calc conditional direct effects for each combination of moderator values

    DIR_LOWV = cdash1 + cdash3*LOW_V;
    DIR_MEDV = cdash1 + cdash3*MED_V;
    DIR_HIV = cdash1 + cdash3*HIGH_V;

! Calc conditional total effects for each combination of moderator values

    TOT_LOWV = IND_LOWV + DIR_LOWV;
    TOT_MEDV = IND_MEDV + DIR_MEDV;
    TOT_HIV = IND_HIV + DIR_HIV;

! Use loop plot to plot conditional indirect effect of X on Y for each combination of low, med, high moderator values
! Could be edited to show conditional direct or conditional total effects instead
! 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 = IND_LOWV*XVAL;
    MEDMOD = IND_MEDV*XVAL;
    HIMOD = IND_HIV*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.figureitout.org.uk