doubt with univariate moderation result

(3）"You could try making the variance components linear in the moderator and in their free parameters". Sorry, I'm quite new for SEM. Do you mean that the moderator directly moderates the variance components(ie, A C E), not through the path coefficient(a, c, e)?

Basically, yes. Consider the additive-genetic variance component. Currently, it's equal to (a + βₐx)², or a² + 2aβₐx + βₐ²x², where x represents the moderator. If x is 0, then the variance component is just a². If x is 1, then the variance component is a² + 2aβₐ + βₐ². Since the moderator only has two possible values, the variance component only has two possible values, and you don't really gain anything from having the variance component be quadratic in the moderator or coefficients. You could just instead define the variance component as a + βₐx.

I have seen the discussion about the bivariate moderation model for the binary variables from the forums. And, I also saw your reply to Mr iloo with the word that "it appears to be inherently difficult to use finite-differences gradient-based optimization with likelihood functions that are defined in terms of the multivariate-normal (and multivariate-t!) probability integral, applied to low-prevalence dichotomous variables." So, I'm wondering whether my binary data fits the bivariate moderation model or not. Is the result of bivariate moderation model with my data reliable?

iloo's difficulty was computational, not statistical. I would not conclude that the full bivariate moderation model fits your data poorly merely because of similar computational difficulties. If you want, you could try using a custom compute plan with Nelder-Mead, as I describe in iloo's thread.

Hello professor Robert, thanks for your reply.
(1) The upper limit of -0.73 seems OK. Here is the result:
base comparison ep minus2LL df AIC diffLL diffdf p
1 NaMEffects 9 4294.340 34022 -63749.66 NA NA NA
2 NaMEffects NaMEffects2 8 4297.926 34023 -63748.07 3.586121 1 0.05826409

So something interesting IS happening here. The comparison of ACE_YZ with ACE_Y makes it clear that the data are not consistent with zero moderation of _E_. And yet, there are valid upper 95% confidence limits on opposite sides of zero! T̶h̶e̶ ̶w̶e̶i̶r̶d̶ ̶t̶h̶i̶n̶g̶ ̶i̶s̶,̶ ̶t̶h̶o̶u̶g̶h̶,̶ ̶I̶ ̶c̶a̶l̶c̶u̶l̶a̶t̶e̶ ̶f̶r̶o̶m̶ ̶t̶h̶e̶ ̶i̶n̶f̶o̶r̶m̶a̶t̶i̶o̶n̶ ̶i̶n̶ ̶t̶h̶e̶ ̶'̶C̶I̶ ̶d̶e̶t̶a̶i̶l̶s̶'̶ ̶t̶a̶b̶l̶e̶s̶ ̶t̶h̶a̶t̶ ̶t̶h̶e̶ ̶m̶o̶d̶e̶l̶ ̶w̶o̶u̶l̶d̶ ̶p̶r̶e̶d̶i̶c̶t̶ ̶a̶ ̶*̶n̶e̶g̶a̶t̶i̶v̶e̶*̶ ̶_̶E̶_̶ ̶v̶a̶r̶i̶a̶n̶c̶e̶ ̶a̶t̶ ̶N̶P̶S̶O̶L̶'̶s̶ ̶s̶o̶l̶u̶t̶i̶o̶n̶ ̶o̶f̶ ̶-̶0̶.̶7̶3̶,̶ ̶b̶u̶t̶ ̶n̶o̶t̶ ̶a̶t̶ ̶S̶L̶S̶Q̶P̶'̶s̶ ̶s̶o̶l̶u̶t̶i̶o̶n̶ ̶o̶f̶ ̶0̶.̶4̶2̶:̶

ee <- function(a,b){
out <- c(NA_real_,NA_real_)
out[1] <- (a^2) #<--E variance component for non-smokers
out[2] <- (a+b)^2 #<--E variance component for smokers
return(out)
}
ee(0.30,-0.73)
ee(0.29,0.42)

That leads me to ask, how do you have your moderator variable coded? As 0 for non-smoker and 1 for smoker? And, what type of data is it; did you convert it into an MxFactor? Try running `str()` on your dataset.

Edit: syntax