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

Model 4d: 1 or more mediators, in parallel if multiple (example uses 1) [BASIC MEDIATION], dichotomous outcome

Example Variables: 1 predictor X, 1 mediator M, 1 outcome Y

Preliminary notes:

The code below assumes that

• The primary IV (variable X) is continuous or dichotomous
• The mediator (variable M) is continuous. An example of how to handle a dichotomous mediator is given in model 4c.
• The DV (variable Y) is dichotomous and satisfies the assumptions of binary logistic regression.

Model Diagram: Statistical Diagram: Model Equation(s):

logit(Y) = b0 + b1M + c'X
M = a0 + a1X

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

logit(Y) = b0 + b1M + c'X
M = a0 + a1X

Hence... substituting in equations for M

logit(Y) = b0 + b1(a0 + a1X) + c'X

Hence... multiplying out brackets

logit(Y) = b0 + a0b1 + a1b1X + c'X

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

logit(Y) = (b0 + a0b1) + (a1b1 + c')X

Hence...

Indirect effect of X on Y:

a1b1 - or, if expressed as an odds ratio, exp(a1b1)

Direct effect of X on Y:

c' - or, if expressed as an odds ratio, exp(c')

Mplus code for the model:

! Predictor variable - X
! Mediator variable(s) – M
! Moderator variable(s) - none
! Outcome variable - Y

USEVARIABLES = X M Y;

CATEGORICAL = Y;

ANALYSIS:
TYPE = GENERAL;
ESTIMATOR = ML;

! In model statement name each path using parentheses

MODEL:
Y ON M (b1);

Y ON X (cdash);   ! direct effect of X on Y

M ON X (a1);

! Use model constraint to calculate indirect effect, and odds ratio

MODEL CONSTRAINT:
NEW(a1b1 ORa1b1);
a1b1 = a1*b1;   ! Indirect effect of X on Y via M
ORa1b1 = exp(a1*b1);   ! Odds ratio wrto indirect effect of X on Y via M

OUTPUT:
STAND CINT(bcbootstrap);

Editing required for testing indirect effect(s) using alternative MODEL INDIRECT: subcommand

MODEL INDIRECT: offers an alternative to MODEL CONSTRAINT: for models containing indirect effects, where these are not moderated. To use MODEL INDIRECT: instead, you would edit the code above as follows:

First, you can remove the naming of parameters using parentheses in the MODEL: command, i.e. you just need:

MODEL:
Y ON X M;
M ON X;

Second, replace the MODEL CONSTRAINT: subcommand with the following MODEL INDIRECT: subcommand:

MODEL INDIRECT:
Y IND X;

Leave the OUTPUT: command unchanged.