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 + c1'X + c2'W + c3'XW
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 + c1'X + c2'W + c3'XW
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 + c1'X + c2'W + c3'XW

Hence... multiplying out brackets

Y = b0 + a0b1 + a1b1X + a2b1W + a3b1Z + a4b1XW + a5b1XZ + a6b1WZ + a7b1XWZ + b2V + a0b3V + a1b3XV + a2b3WV + a3b3ZV + a4b3XWV + a5b3XZV + a6b3WZV + a7b3XWZV + c1'X + c2'W + c3'XW

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

Y = (b0 + a0b1 + a2b1W + a3b1Z + a6b1WZ + b2V + a0b3V + a2b3WV + a3b3ZV + a6b3WZV + c2'W) + (a1b1 + a4b1W + a5b1Z + a7b1WZ + a1b3V + a4b3WV + a5b3ZV + a7b3WZV + c1' + c3'W)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, conditional on W:

c1' + c3'W

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 (cdash1);
   Y ON W (cdash2);
   Y ON XW (cdash3);

   [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
    DIR_LOWW DIR_MEDW DIR_HIW
    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 direct effects for each combination of moderator values

    DIR_LOWW = cdash1 + cdash3*LOW_W;
    DIR_MEDW = cdash1 + cdash3*MED_W;
    DIR_HIW = cdash1 + cdash3*HIGH_W;

! Calc conditional total effects for each combination of moderator values

    TLWLZLV = ILWLZLV + DIR_LOWW;
    TMWLZLV = IMWLZLV + DIR_MEDW;
    THWLZLV = IHWLZLV + DIR_HIW;

    TLWMZLV = ILWMZLV + DIR_LOWW;
    TMWMZLV = IMWMZLV + DIR_MEDW;
    THWMZLV = IHWMZLV + DIR_HIW;

    TLWHZLV = ILWHZLV + DIR_LOWW;
    TMWHZLV = IMWHZLV + DIR_MEDW;
    THWHZLV = IHWHZLV + DIR_HIW;

    TLWLZMV = ILWLZMV + DIR_LOWW;
    TMWLZMV = IMWLZMV + DIR_MEDW;
    THWLZMV = IHWLZMV + DIR_HIW;

    TLWMZMV = ILWMZMV + DIR_LOWW;
    TMWMZMV = IMWMZMV + DIR_MEDW;
    THWMZMV = IHWMZMV + DIR_HIW;

    TLWHZMV = ILWHZMV + DIR_LOWW;
    TMWHZMV = IMWHZMV + DIR_MEDW;
    THWHZMV = IHWHZMV + DIR_HIW;

    TLWLZHV = ILWLZHV + DIR_LOWW;
    TMWLZHV = IMWLZHV + DIR_MEDW;
    THWLZHV = IHWLZHV + DIR_HIW;

    TLWMZHV = ILWMZHV + DIR_LOWW;
    TMWMZHV = IMWMZHV + DIR_MEDW;
    THWMZHV = IHWMZHV + DIR_HIW;

    TLWHZHV = ILWHZHV + DIR_LOWW;
    TMWHZHV = IMWHZHV + DIR_MEDW;
    THWHZHV = IHWHZHV + DIR_HIW;

! 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