I am trying to write the model equation for a LCA (ordered response categories) so that it is matched with the output I recieve from running the LCA on Mplus. However, I am also writing it parallel to a latent trait formulation (Graded Response Model).
In Muthen (2002), with a binary u, the following is given:
P(u = 1 | c ) = 1 – [1/ 1+exp(-(Tau- u*))]
1) is the Tau the same (group specific) item threshold parameter that is provided from the output?
2) There is no slope parameter equivalent to lambda (factor loading) as in included in GRM output, correct?