Causal effects for 4-category nominal... PreviousNext
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 Matt McLarnon posted on Thursday, November 09, 2017 - 1:40 pm
I've been considering Muthen(2011), but is this syntax on the right track for a 4-category nominal mediator (continuous X and Y)?

%OVERALL%
[c#1] (g01); c#1 ON x (g11);
[c#2] (g02); c#2 ON x (g12);
[c#3] (g03); c#3 ON x (g13);
y ON x; y;

!c#1 and c#2 as in Muthen (2011)

%c#3%
[y] (b03); y ON x (b13);
%c#4%
[y] (b04); y ON x (b14);

MODEL CONSTRAINT:
NEW(d0 d1 p10 p11 p20 p21 p30 p31 p40 p41
t11 t10 t01 t00 DE TIE TOT PIE);

d0=exp(g01)+exp(g02)+exp(g03)+1;
d1=exp(g01+g11)+exp(g02+g12)+exp(g03+g13)+1;
!p10-p21 as in Muthen (2011)

p30=exp(g03)/d0;
p31=exp(g03+g13)/d1;
p40=1/d0;
p41=1/d1;

t11=(b01+b11)*p11+(b02+b12)*p21+(b03+b13)*p31+(b04+b14)*p41;
t10=(b01+b11)*p10+(b02+b12)*p20+(b03+b13)*p30+(b04+b14)*p40;
t01=(b01)*p11+(b02)*p21+(b03)*p31+(b04)*p41;
t00=(b01)*p10+(b02)*p20+(b03)*p30+(b04)*p40;

!DE TIE TOT PIE as in Muthen (2011)
 Bengt O. Muthen posted on Friday, November 10, 2017 - 4:39 pm
See the book example Table 8.35 at

http://www.statmodel.com/Mplus_Book_Tables.shtml
 Matt McLarnon posted on Sunday, November 12, 2017 - 12:58 pm
Thank you - both the book and 2011 paper are excellent resources that have been extremely useful in this and other projects

I had considered the 2011 example closer to my purpose because of continuous Y, whereas the example in the book and Table 8.35 focused on a binary Y

1) instead of the above, would there be value added in estimating causal effects for each of the m-1 effects (i.e., a TNIE, PNDE etc. for each of the target categories vs. the referent category of the nominal variable, so for a 4-category nominal variable there would be three TNIEs and sets of causal effects)?

If so,

2) is inclusion of the "exp(g03+g13)" terms to the calculation of d0 and d1 (the denominator from the book/2011 formulae) correct?

3) is inclusion of the "(b04+b14)*p41" terms to the calculation of t11 and t01 (the terms representing the expectation values from the book/2011 formulae) correct?

4) is inclusion of the "(b04)*p41" terms to the calculation of t01 and t00 (expectation values) correct?
 Bengt O. Muthen posted on Sunday, November 12, 2017 - 5:38 pm
The "causal effect" principle is to collapse/integrate over M so I don't know what the m-1 effects would mean.
 Matt McLarnon posted on Monday, November 13, 2017 - 5:38 am
I was thinking that there would be "causal effects" for each comparison, between a target and a referent category, such that it would be meaningful to estimate whether choosing one response option of the nominal mediator vs. a referent category would transmit the effect of X on Y
But this makes sense, thank you.

May I ask then, are calculations for the d0, d1, t11, t10, t01, and t00 from the first post appropriate?

Thank you!
 Bengt O. Muthen posted on Monday, November 13, 2017 - 3:56 pm
You can discuss the various effects from M to Y.

Yes, it looks like you generalized the 3-class input correctly to a 4-class input.
 Matt McLarnon posted on Tuesday, November 14, 2017 - 4:47 am
Many thanks, Dr. Muthén, much appreciated!
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