 QUADRATIC NONLINEAR EFFECT    Message/Author  crystal posted on Sunday, December 07, 2014 - 12:45 pm
Hi I am trying to create a SEM model with a quadratic effect between my mediating variable and my outcome variable
(X1, X2 AND X3) all predict mediating variable and the mediating variable predicts Y1
X1------
X2----- mediating variable ------ Y1
X3-----

i want to model a quadratic relationship between mediating variable and y1. do i just add a power term of mediating variable (squared) and have it predict Y1? Also, do i need my exogenous variables predicting the squared term?  Bengt O. Muthen posted on Tuesday, December 09, 2014 - 11:57 am
Create m2 in Define:

Define:
m2 = (m-mbar)*(m-mbar); !mbar = mean

Then use

Model:
y on m m2;
m on x1-x3;

Here, m2 will be a covariate and automatically correlated with x1-x3.

Because of the non-linearity I would ignore the chi-square testing.  Bengt O. Muthen posted on Tuesday, December 09, 2014 - 11:59 am
Also, the indirect effect estimation is not straightforward in this case. Perhaps it could be derived from my paper on our website:

Muth�n, B. (2011). Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus.  Cheng-Lung Wang posted on Thursday, November 08, 2018 - 11:47 pm
Dear Mplus team,

I got huge lessons from your suggestion on the issue of handing the meditation model with a quadratic factor in the section "nonlinear factor analysis"

The model depiction follows (variables are latent and continuous except for outcome which is continuous but observed).
Y on X, X-squared, M
Y IND X;
Y IND X M;
The syntax with not this one. This describes what the model looks like.

However, I thought that the meaning of the coefficient of (X) in the model which quadratic term included is different from a model without the quadratic term (Tradition linear mediation model), due to the fact that the coefficient (c1b1+c2) represents the slope at X=0 rather than the slope of whole data.
A brief description of the quations of my model
M = b0 + b1(X) -- (1)
Y = c0 + c1(M) + c2(X) + c3 (X-squared) -- (2)
Y = c0 + b0c1 + (c1b1+c2)(X) + c3(X-squared) -- (3)

Hence, I am asking that if I can't express a linearly indirect effect and curvilinear relationships between X and Y at the same time. I found out a paper discussing a quadratic indirect effect but not in the case of my mine.

Thank you to respond to my question.  Bengt O. Muthen posted on Friday, November 09, 2018 - 1:07 pm
I don't understand how you can have both equations (2) and (3) in the same model. The model of (1) and (2) is expressed as

m on x;
y on m x x2;

where x2 is defined as x squared using XWITH.  Back to top
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