When you are using type=complex twolevel mixture; both IDSCHOOL and IDCLASS are accounted for. IDCLASS is accounted for through the between level random effects. IDSCHOOL is accounted for through the robust ML estimation that accounts for the non-independence of classrooms in the same school.
Sara Suzuki posted on Saturday, January 19, 2019 - 1:42 pm
In Mplus, is there a way to use IDSCHOOL and IDCLASS both for the robust ML estimation, in the way that Stata can account for multiple levels in the Taylor linearized variance estimator?
Using finite population correction and Taylor linearized variance estimator Mplus uses only the first order correction. https://www.statmodel.com/download/SurveyJSM1.pdf page 2720 only the first term V1 is included but V2 is not included. As you can see there V2 contributes to the estimation only when fs is large, i.e., only when nearly all schools are sampled, which is not a realistic assumption. Once you assume infinite school population V2=0.