

Causal effects for 4category nominal... 

Message/Author 


I've been considering Muthen(2011), but is this syntax on the right track for a 4category 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; !p10p21 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) 


See the book example Table 8.35 at http://www.statmodel.com/Mplus_Book_Tables.shtml 


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 m1 effects (i.e., a TNIE, PNDE etc. for each of the target categories vs. the referent category of the nominal variable, so for a 4category 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? 


The "causal effect" principle is to collapse/integrate over M so I don't know what the m1 effects would mean. 


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! 


You can discuss the various effects from M to Y. Yes, it looks like you generalized the 3class input correctly to a 4class input. 


Many thanks, Dr. Muthén, much appreciated! 

Back to top 

