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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! 

Adam Garber posted on Sunday, November 25, 2018  10:43 pm



I have a similar question to the one mentioned above  Is it possible to estimate classspecific indirect effects in the context of a nominal latent class variable as mediator? (i.e. conditional mediation) In Muthen (2011), I have read that the indirect effect is summed over the levels of the mediator. Why is this? It seems like a natural extension to consider how indirect effects vary across levels of the categorical mediator. 4class example: t11_1= (b01+b11)*p11; t11_2= (b02+b12)*p21; t11_3= (b03+b13)*p31; t11_4= (b04+b14)*p41; t10_1= (b01+b11)*p10; t10_2= (b02+b12)*p20; t10_3= (b03+b13)*p30; t10_4= (b04+b14)*p40; t01_1= (b01)*p11; t01_2= (b02)*p21; t01_3= (b03)*p31; t01_4= (b04)*p41; t00_1= (b01)*p10; t00_2= (b02)*p20; t00_3= (b03)*p30; t00_4= (b04)*p40; 


The indirect effects are summed over the nominal mediator because that is the definition of the counterfactuallydefined "causal" indirect effect. That same summing (or integration for continuous mediator) is used for all types of M and Y variables. I don't know under which indirect effect definition effects for each category of the mediator would be appropriate  but maybe it is a useful descriptive statistic. 

Adam Garber posted on Monday, November 26, 2018  11:10 pm



Thanks Dr. Muthen your response is greatly appreciated. In the specification of a mediation model with the nominal latent class variable as mediator, separate Y on X regressions are estimated for each class. Therefore, in specific research contexts may the latent class variable be conceived and reported to act both as a mediator and moderator simultaneously? Such an analysis, could report the summed/integrated indirect effect and also report the moderation effect. T. Beauchaine (2005), has suggested such a modeling situation in which a variable concurrently has moderating and mediating effects. 


Yes, separate Y on X regressions for each class represents moderation, that is, an X*M interaction. But you don't need to let Y on X be class varying. If you mention this regression in only the Overall part of the model, the slope will be equal across the classes  no moderation. 

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