 ## Mplus code for the mediation, moderation, and moderated mediation model templates from Andrew Hayes' PROCESS analysis examples

Model 1d: 1 moderator [BASIC MODERATION], categorical moderator with > 2 categories

Example Variables: 1 predictor X, 2 dummy variables WD1 and WD2 representing 3 category moderator W, 1 outcome Y

Preliminary notes:

The code below assumes that

• The primary IV (variable X) is continuous or dichotomous
• The moderator (variable W) has 3 categories (1-3), and is therefore represented by two dummy variables WD1, WD2, coded such that when W = 1, then WD1 = 1, WD2 = 0; when W = 2, then WD1 = 0, WD2 = 1; when W = 3 (the reference category), then WD1 = 0, WD2 = 0.
• 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 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2

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

Y = b0 + b1X + b2WD1 + b3WD2 + b4XWD1 + b5XWD2

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

Y = (b0 + b2WD1 + b3WD2) + (b1 + b4WD1 + b5WD2)X

Hence...

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

b1 + b4WD1 + b5WD2

so inserting the values of 0 and 1 for moderator W gives....

when W = 1, then WD1 = 1, WD2 = 0, hence Y = (b0 + b2) + (b1 + b4)X
when W = 2, then WD1 = 0, WD2 = 1, hence Y = (b0 + b3) + (b1 + b5)X
when W = 3, then WD1 = 0, WD2 = 0, hence Y = b0 + b1X

Mplus code for the model:

! Predictor variable - X
! Mediator variable(s) – (not applicable)
! Moderator variable(s) - W, 3 categories, represented by dichotomous 0/1 dummy variables WD1, WD2
! Outcome variable - Y

USEVARIABLES = X WD1 WD2 Y XWD1 XWD2;

! Create interaction term
! Note that it has to be placed at end of USEVARIABLES subcommand above

DEFINE:
XWD1 = X*WD1;
XWD2 = X*WD2;

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

! In model statement name each path and intercept using parentheses

MODEL:
[Y] (b0);
Y ON X (b1);
Y ON WD1 (b2);
Y ON WD2 (b3);
Y ON XWD1 (b4);
Y ON XWD2 (b5);

! Use model constraint subcommand to test simple slopes
! You need to insert your respective dummy variable values, 0 and 1, for each group of W

MODEL CONSTRAINT:
NEW(SIMP_W1 SIMP_W2 SIMP_W3);

! Now calc simple slopes for each group of W

SIMP_W1 = b1 + b4;
SIMP_W2 = b1 + b5;
SIMP_W3 = b1;

! Use loop plot to plot model for values of W = 0, W = 1
! 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(LINE_W1 LINE_W2 LINE_W3);
LOOP(XVAL,1,5,0.1);

LINE_W1 = (b0 + b2) + (b1 + b4)*XVAL;
LINE_W2 = (b0 + b3) + (b1 + b5)*XVAL;
LINE_W3 = b0 + b1*XVAL;

PLOT:
TYPE = plot2;

OUTPUT:
STAND CINT(bcbootstrap);