kloud posted on Tuesday, February 26, 2019 - 3:23 pm
I¡¯m planning a simulation dealing with 2 continuous(exogenous) covariates X1 & X2, 2-binary mediators T1 & T2, and continuous outcomes Y1 & Y2. (no latent variable). To make binary mediators, I generated 2 underlying latent variables (T1*, T2*) ~ MVN(0, SIGMA). then, dichotomized these into binary ones. Variances of X1, X2, T1*, T2*, Y1, Y2 were set to be 1.
X1 with X2 T1* on X1 (then, dichotomize T1* into T1) Y1 on T1 X1 T2* on X2 T1 Y1 (then, dichotomize T2* into T2)
1. When generating T2, there are 2 options. One is to regress T2* on X2 T1* Y1(T1* : continuous latent), and the other is to regress T2* on X2 T1 Y1(T1 : dichotomized observed). I¡¯m wondering which one is correct.
2. (applying WLSMV) I think it's necessary to decompose the covariance matrix with parameters.
It is a substantive choice whether the mediator used as a predictor of Y should be treated as binary or as the corresponding continuous latent response variable. ML can handle only the case where the mediator is treated as observed binary, WLSMV only the case where it is latent, and Bayes both. So depending on which estimator you want to use, you have to make a choice.
I¡¯m going to apply WLSMV estimator. In this case, as you said, I think I could treat a binary mediator as latent variable. But in case of simulation, I had to generate underlying latent variable(normal), then dichotomize it into binary one. In this case, I can not understand how I decompose covariance.
As I have seen, most papers generated a latent continuous variable, and dichotomized it into a binary variable.
When generating T2, there seem to be 2 options. One is to regress T2* on X2 T1* Y1(T1* : continuous latent), and the other is to regress T2* on X2 T1 Y1(T1 : dichotomized observed). I¡¯m wondering which one is correct.
But I'm not sure which is correct...
and moreover, I think I have to decompose var(Y1) with parameters to assign a specific number as true value. but in this case, I don't figure out what the cov(corr) changed by dichotomization. that is, cov(T1*, X1) and cov(T1, X1)
Is this way correct to reflect the process of WLSMV?