Conditional prob. function and regres...
Message/Author
 Alex Chavez posted on Monday, June 21, 2010 - 10:58 am
I am trying to understand how a regression of a categorical variable which is also a predictor of a latent variable is modeled. Letting Y be the latent variable formed by LS1-LS5, if I include the autoregression “LS2 ON LS1” with parameter beta, does Mplus include it in the model as follows?

LS2* = lambda2 nu + beta LS1 + epsilon2, such that
Pr(LS2 >= k | nu, LS1) = F[-(tau_ik – beta LS1 – lambda2 nu)theta_2^{-1/2}]

In particular I’m concerned about whether beta*LS1 enters into the probability function, because the predicted factor scores do not change when I change the fixed value of beta (“LS2 ON LS1@1” vs. “LS2 ON LS1@3” holding all other parameters constant).

ANALYSIS:
ESTIMATOR IS WLSMV; PARAMETERIZATION = THETA;
MODEL:
Y by LS1-LS5 @1;
LS2 ON LS1 @ 1;
! LS2 ON LS1 @ 3;
[LS1\$1-LS5\$1 @ -3];
[LS1\$2-LS5\$2 @ -2];
[LS1\$3-LS5\$3 @ -1];
[LS1\$4-LS5\$4 @ 0];
[LS1\$5-LS5\$5 @ 1];
[LS1\$6-LS5\$6 @ 2];|
[Y@0];
Y@1;
 Bengt O. Muthen posted on Tuesday, June 22, 2010 - 10:35 am
You are correct in your assumption of the modeling when your estimator is ML. In contrast, with WLSMV "LS1" is replaced by its latent response variable "LS1*". I assume your "nu" is the factor (eta).

Regarding the factor scores, Appendix 11 of the Tech appendix for Version 2 (see our web site) shows that conditional independence of y | eta is assumed. Therefore the factor scores cannot be computed correctly for your model using WLSMV. You can try ML or you can rewrite the model by letting a new factor influence the two items that you want to have related beyond the original factor.