Does anybody know a reference in which it is shown that the likelihood ratio test statistic converges to a Chi squared distribution for extended SEMs with definition variables?
With extended SEM I mean RAM models where the entries of A and S may be arbitrary algebras. In contrast to classical SEM where the entries of A,S are either fixed or a single parameter. With definition variables I mean that any fixed value in an SEM may be replaced by a person specific value such that it is different for every person.
In textbooks I can only find the proof for classical SEMs without definition variables. I am pretty sure that the switch from classical to extended SEM does not violate any of the assumptions used in standard proofs that the likelihood ratio test is Chi squared distribution. I am not so sure about the definition variables.