Preliminary notes:

The code below assumes that

• The primary IV (variable X) is continuous or dichotomous.
• Any moderators (variables W, V, Q, Z) are continuous, though the only adaptation required to handle dichotomous moderators is in the MODEL CONSTRAINT: and loop plot code - an example of how to do this is given in model 1b. Handling categorical moderators with > 2 categories is demonstrated in model 1d.
• Any mediators (variable M, or M1, M2, etc.) are continuous and satisfy the assumptions of standard multiple regression. An example of how to handle a dichotomous mediator is given in model 4c.
• The DV (variable Y) is continuous and satisfies the assumptions of standard multiple regression - an example of how to handle a dichotomous DV is given in model 1e (i.e. a moderated logistic regression) and in model 4d (i.e. an indirect effect in a logistic regression).

Model Diagram:

Statistical Diagram:

Model Equation(s):

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

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

Y = b0 + b1M + b2V + b3MV + c'X
M = a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ

Hence... substituting in equation for M

Y = b0 + b1(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ) + b2V + b3(a0 + a1X + a2W + a3Z + a4XW + a5XZ + a6WZ + a7XWZ)V + c'X

Hence... multiplying out brackets

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c'X

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

Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c')X

Hence...

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

a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV = (a1 + a4W + a5Z + a7WZ)(b1 + b3V)

One direct effect of X on Y:

c'

Mplus code for the model:

! Predictor variable - X
! Mediator variable(s) – M
! Moderator variable(s) – W, Z, V
! Outcome variable - Y

USEVARIABLES = X M W Z V Y XW XZ WZ MV XWZ;

! Create interaction terms
! Note that they have to be placed at end of USEVARIABLES subcommand above

DEFINE:
   MV = M*V;
   XW = X*W;
   XZ = X*Z;
   WZ = W*Z;
   XWZ = X*W*Z;

ANALYSIS:
   TYPE = GENERAL;
   ESTIMATOR = ML;
   BOOTSTRAP = 10000;

! In model statement name each path and intercept using parentheses

MODEL:
   [Y] (b0);
   Y ON M (b1);
   Y ON V (b2);
   Y ON MV (b3);

   Y ON X (cdash);

   [M] (a0);
   M ON X (a1);
   M ON W (a2);
   M ON Z (a3);
   M ON XW (a4);
   M ON XZ (a5);
   M ON WZ (a6);
   M ON XWZ (a7);

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

! 3 moderators, 3 values for each, gives 27 combinations
! arbitrary naming convention for conditional indirect and total effects used below:
! HWMVLQ = high value of W, medium value of V and low value of Q, etc.

MODEL CONSTRAINT:
    NEW(LOW_W MED_W HIGH_W LOW_Z MED_Z HIGH_Z LOW_V MED_V HIGH_V
    ILWLZLV IMWLZLV IHWLZLV ILWMZLV IMWMZLV IHWMZLV
    ILWHZLV IMWHZLV IHWHZLV
    ILWLZMV IMWLZMV IHWLZMV ILWMZMV IMWMZMV IHWMZMV
    ILWHZMV IMWHZMV IHWHZMV
    ILWLZHV IMWLZHV IHWLZHV ILWMZHV IMWMZHV IHWMZHV
    ILWHZHV IMWHZHV IHWHZHV
    TLWLZLV TMWLZLV THWLZLV TLWMZLV TMWMZLV THWMZLV
    TLWHZLV TMWHZLV THWHZLV
    TLWLZMV TMWLZMV THWLZMV TLWMZMV TMWMZMV THWMZMV
    TLWHZMV TMWHZMV THWHZMV
    TLWLZHV TMWLZHV THWLZHV TLWMZHV TMWMZHV THWMZHV
    TLWHZHV TMWHZHV THWHZHV);

    LOW_W = #LOWW;   ! replace #LOWW in the code with your chosen low value of W
    MED_W = #MEDW;   ! replace #MEDW in the code with your chosen medium value of W
    HIGH_W = #HIGHW;   ! replace #HIGHW in the code with your chosen high value of W

    LOW_Z = #LOWZ;   ! replace #LOWZ in the code with your chosen low value of Z
    MED_Z = #MEDZ;   ! replace #MEDZ in the code with your chosen medium value of Z
    HIGH_Z = #HIGHZ;   ! replace #HIGHZ in the code with your chosen high value of Z

    LOW_V = #LOWV;   ! replace #LOWV in the code with your chosen low value of V
    MED_V = #MEDV;   ! replace #MEDV in the code with your chosen medium value of V
    HIGH_V = #HIGHV;   ! replace #HIGHV in the code with your chosen high value of V

! Calc conditional indirect effects for each combination of moderator values

    ILWLZLV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z +
     a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*LOW_Z*LOW_V +
     a7*b3*LOW_W*LOW_Z*LOW_V;
    IMWLZLV = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a7*b1*MED_W*LOW_Z +
     a1*b3*LOW_V + a4*b3*MED_W*LOW_V + a5*b3*LOW_Z*LOW_V +
     a7*b3*MED_W*LOW_Z*LOW_V;
    IHWLZLV = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a7*b1*HIGH_W*LOW_Z +
     a1*b3*LOW_V + a4*b3*HIGH_W*LOW_V + a5*b3*LOW_Z*LOW_V +
     a7*b3*HIGH_W*LOW_Z*LOW_V;

    ILWMZLV = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a7*b1*LOW_W*MED_Z +
     a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*MED_Z*LOW_V +
     a7*b3*LOW_W*MED_Z*LOW_V;
    IMWMZLV = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a7*b1*MED_W*MED_Z +
     a1*b3*LOW_V + a4*b3*MED_W*LOW_V + a5*b3*MED_Z*LOW_V +
     a7*b3*MED_W*MED_Z*LOW_V;
    IHWMZLV = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a7*b1*HIGH_W*MED_Z +
     a1*b3*LOW_V + a4*b3*HIGH_W*LOW_V + a5*b3*MED_Z*LOW_V +
     a7*b3*HIGH_W*MED_Z*LOW_V;

    ILWHZLV = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a7*b1*LOW_W*HIGH_Z +
     a1*b3*LOW_V + a4*b3*LOW_W*LOW_V + a5*b3*HIGH_Z*LOW_V +
     a7*b3*LOW_W*HIGH_Z*LOW_V;
    IMWHZLV = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a7*b1*MED_W*HIGH_Z +
     a1*b3*LOW_V + a4*b3*MED_W*LOW_V + a5*b3*HIGH_Z*LOW_V +
     a7*b3*MED_W*HIGH_Z*LOW_V;
    IHWHZLV = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a7*b1*HIGH_W*HIGH_Z +
     a1*b3*LOW_V + a4*b3*HIGH_W*LOW_V + a5*b3*HIGH_Z*LOW_V +
     a7*b3*HIGH_W*HIGH_Z*LOW_V;

    ILWLZMV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z +
     a1*b3*MED_V + a4*b3*LOW_W*MED_V + a5*b3*LOW_Z*MED_V +
     a7*b3*LOW_W*LOW_Z*MED_V;
    IMWLZMV = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a7*b1*MED_W*LOW_Z +
     a1*b3*MED_V + a4*b3*MED_W*MED_V + a5*b3*LOW_Z*MED_V +
     a7*b3*MED_W*LOW_Z*MED_V;
    IHWLZMV = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a7*b1*HIGH_W*LOW_Z +
     a1*b3*MED_V + a4*b3*HIGH_W*MED_V + a5*b3*LOW_Z*MED_V +
     a7*b3*HIGH_W*LOW_Z*MED_V;

    ILWMZMV = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a7*b1*LOW_W*MED_Z +
     a1*b3*MED_V + a4*b3*LOW_W*MED_V + a5*b3*MED_Z*MED_V +
     a7*b3*LOW_W*MED_Z*MED_V;
    IMWMZMV = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a7*b1*MED_W*MED_Z +
     a1*b3*MED_V + a4*b3*MED_W*MED_V + a5*b3*MED_Z*MED_V +
     a7*b3*MED_W*MED_Z*MED_V;
    IHWMZMV = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a7*b1*HIGH_W*MED_Z +
     a1*b3*MED_V + a4*b3*HIGH_W*MED_V + a5*b3*MED_Z*MED_V +
     a7*b3*HIGH_W*MED_Z*MED_V;

    ILWHZMV = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a7*b1*LOW_W*HIGH_Z +
     a1*b3*MED_V + a4*b3*LOW_W*MED_V + a5*b3*HIGH_Z*MED_V +
     a7*b3*LOW_W*HIGH_Z*MED_V;
    IMWHZMV = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a7*b1*MED_W*HIGH_Z +
     a1*b3*MED_V + a4*b3*MED_W*MED_V + a5*b3*HIGH_Z*MED_V +
     a7*b3*MED_W*HIGH_Z*MED_V;
    IHWHZMV = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a7*b1*HIGH_W*HIGH_Z +
     a1*b3*MED_V + a4*b3*HIGH_W*MED_V + a5*b3*HIGH_Z*MED_V +
     a7*b3*HIGH_W*HIGH_Z*MED_V;

    ILWLZHV = a1*b1 + a4*b1*LOW_W + a5*b1*LOW_Z + a7*b1*LOW_W*LOW_Z +
     a1*b3*HIGH_V + a4*b3*LOW_W*HIGH_V + a5*b3*LOW_Z*HIGH_V +
     a7*b3*LOW_W*LOW_Z*HIGH_V;
    IMWLZHV = a1*b1 + a4*b1*MED_W + a5*b1*LOW_Z + a7*b1*MED_W*LOW_Z +
     a1*b3*HIGH_V + a4*b3*MED_W*HIGH_V + a5*b3*LOW_Z*HIGH_V +
     a7*b3*MED_W*LOW_Z*HIGH_V;
    IHWLZHV = a1*b1 + a4*b1*HIGH_W + a5*b1*LOW_Z + a7*b1*HIGH_W*LOW_Z +
     a1*b3*HIGH_V + a4*b3*HIGH_W*HIGH_V + a5*b3*LOW_Z*HIGH_V +
     a7*b3*HIGH_W*LOW_Z*HIGH_V;

    ILWMZHV = a1*b1 + a4*b1*LOW_W + a5*b1*MED_Z + a7*b1*LOW_W*MED_Z +
     a1*b3*HIGH_V + a4*b3*LOW_W*HIGH_V + a5*b3*MED_Z*HIGH_V +
     a7*b3*LOW_W*MED_Z*HIGH_V;
    IMWMZHV = a1*b1 + a4*b1*MED_W + a5*b1*MED_Z + a7*b1*MED_W*MED_Z +
     a1*b3*HIGH_V + a4*b3*MED_W*HIGH_V + a5*b3*MED_Z*HIGH_V +
     a7*b3*MED_W*MED_Z*HIGH_V;
    IHWMZHV = a1*b1 + a4*b1*HIGH_W + a5*b1*MED_Z + a7*b1*HIGH_W*MED_Z +
     a1*b3*HIGH_V + a4*b3*HIGH_W*HIGH_V + a5*b3*MED_Z*HIGH_V +
     a7*b3*HIGH_W*MED_Z*HIGH_V;

    ILWHZHV = a1*b1 + a4*b1*LOW_W + a5*b1*HIGH_Z + a7*b1*LOW_W*HIGH_Z +
     a1*b3*HIGH_V + a4*b3*LOW_W*HIGH_V + a5*b3*HIGH_Z*HIGH_V +
     a7*b3*LOW_W*HIGH_Z*HIGH_V;
    IMWHZHV = a1*b1 + a4*b1*MED_W + a5*b1*HIGH_Z + a7*b1*MED_W*HIGH_Z +
     a1*b3*HIGH_V + a4*b3*MED_W*HIGH_V + a5*b3*HIGH_Z*HIGH_V +
     a7*b3*MED_W*HIGH_Z*HIGH_V;
    IHWHZHV = a1*b1 + a4*b1*HIGH_W + a5*b1*HIGH_Z + a7*b1*HIGH_W*HIGH_Z +
     a1*b3*HIGH_V + a4*b3*HIGH_W*HIGH_V + a5*b3*HIGH_Z*HIGH_V +
     a7*b3*HIGH_W*HIGH_Z*HIGH_V;

! Calc conditional total effects for each combination of moderator values

    TLWLZLV = ILWLZLV + cdash;
    TMWLZLV = IMWLZLV + cdash;
    THWLZLV = IHWLZLV + cdash;

    TLWMZLV = ILWMZLV + cdash;
    TMWMZLV = IMWMZLV + cdash;
    THWMZLV = IHWMZLV + cdash;

    TLWHZLV = ILWHZLV + cdash;
    TMWHZLV = IMWHZLV + cdash;
    THWHZLV = IHWHZLV + cdash;

    TLWLZMV = ILWLZMV + cdash;
    TMWLZMV = IMWLZMV + cdash;
    THWLZMV = IHWLZMV + cdash;

    TLWMZMV = ILWMZMV + cdash;
    TMWMZMV = IMWMZMV + cdash;
    THWMZMV = IHWMZMV + cdash;

    TLWHZMV = ILWHZMV + cdash;
    TMWHZMV = IMWHZMV + cdash;
    THWHZMV = IHWHZMV + cdash;

    TLWLZHV = ILWLZHV + cdash;
    TMWLZHV = IMWLZHV + cdash;
    THWLZHV = IHWLZHV + cdash;

    TLWMZHV = ILWMZHV + cdash;
    TMWMZHV = IMWMZHV + cdash;
    THWMZHV = IHWMZHV + cdash;

    TLWHZHV = ILWHZHV + cdash;
    TMWHZHV = IMWHZHV + cdash;
    THWHZHV = IHWHZHV + cdash;

! 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 of 1,5 in LOOP() statement need to be replaced by
! logical min and max limits of predictor X used in analysis

    PLOT(PLWLZLV PMWLZLV PHWLZLV PLWMZLV PMWMZLV PHWMZLV
    PLWHZLV PMWHZLV PHWHZLV
    PLWLZMV PMWLZMV PHWLZMV PLWMZMV PMWMZMV PHWMZMV
    PLWHZMV PMWHZMV PHWHZMV
    PLWLZHV PMWLZHV PHWLZHV PLWMZHV PMWMZHV PHWMZHV
    PLWHZHV PMWHZHV PHWHZHV);

    LOOP(XVAL,1,5,0.1);

    PLWLZLV = ILWLZLV*XVAL;
    PMWLZLV = IMWLZLV*XVAL;
    PHWLZLV = IHWLZLV*XVAL;

    PLWMZLV = ILWMZLV*XVAL;
    PMWMZLV = IMWMZLV*XVAL;
    PHWMZLV = IHWMZLV*XVAL;

    PLWHZLV = ILWHZLV*XVAL;
    PMWHZLV = IMWHZLV*XVAL;
    PHWHZLV = IHWHZLV*XVAL;

    PLWLZMV = ILWLZMV*XVAL;
    PMWLZMV = IMWLZMV*XVAL;
    PHWLZMV = IHWLZMV*XVAL;

    PLWMZMV = ILWMZMV*XVAL;
    PMWMZMV = IMWMZMV*XVAL;
    PHWMZMV = IHWMZMV*XVAL;

    PLWHZMV = ILWHZMV*XVAL;
    PMWHZMV = IMWHZMV*XVAL;
    PHWHZMV = IHWHZMV*XVAL;

    PLWLZHV = ILWLZHV*XVAL;
    PMWLZHV = IMWLZHV*XVAL;
    PHWLZHV = IHWLZHV*XVAL;

    PLWMZHV = ILWMZHV*XVAL;
    PMWMZHV = IMWMZHV*XVAL;
    PHWMZHV = IHWMZHV*XVAL;

    PLWHZHV = ILWHZHV*XVAL;
    PMWHZHV = IMWHZHV*XVAL;
    PHWHZHV = IHWHZHV*XVAL;

PLOT:
   TYPE = plot2;

OUTPUT:
   STAND CINT(bcbootstrap);

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