bmuthen posted on Wednesday, October 16, 2002 - 5:59 am
Here is how Mplus gets the LCA s.e.'s for the binary item parameters conditional on class in the probability scale.
After the ML solution in the usual logit scale has been obtained, the s.e.'s for the corresponding probabilities are computed using the Delta Method. This method draws on a Taylor expansion, boiling down to the following.
Note that with binary outcomes you get the probability from the logit by
(1) P = 1/(1+exp(-L)).
The variance, that is the squared s.e., is obtained by the Delta Method via the first-order derivatives as
(2) V(P) = dP/dL * V(L)* dP/dL,
where V(L) is the square of the s.e. for the regular Mplus estimates inlogit scale.