Nonlinear indirect effect in lavaan & semTools

Question

I would like to use semTools to examine several indirect effects. However, some predictors have nonlinear relationships (i.e., quadratic) with the mediators, but I found very little information online about the codes for this.

I've tried to specify the nonlinear indirect effect using the codes below.

M is the mediator; X is the predictor; X_SQ is the squared variable of X (i.e., X^2); Y is the outcome variable.

the path between the predictor and mediator (including the linear and quadratic term)

M ~ a*X + asq*X_SQ

the path between the mediator and outcome

Y ~ b * M

the indirect effect

Indirect effect := asq*b

I'm particularly unsure about the last line of codes. Can anyone please advise?

Answer 1

A quadratic term is a product of a variable with itself, analogous to an interaction (product of 2 different variables). So you can uses the same method of probing an interaction, by defining the simple effect of X at multiple levels of a moderator (see syntax example here). But in this case, X is the moderator of X's effect. So define 3 simple effects of X: at low, medium, and high levels of X. These would be the tangent line touching the curvilinear X slope at those different locations on the X axis, which is a "local linear effect" at those locations.