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I have a data that is hierarchically nested. Patients nested within treating clinicians, and clinicians nested within clinics. Using univariate ordinal random intercept models I estimate my ICCs for my 10 items to be in the range of: Level 2 ICCs range from .150  .260. Level 3 ICCs range from .001  .088. Level 2 group sizes range from 1100. Level 3 group sizes have as many as 100 level 2 clinicians in them with some clinics treating over 1000 patients. My model is a twolevel CFA with WLSMV and categorical data however my data structure 'may' have 3 levels I appreciate that threelevel factor models are not possible in Mplus but I wonder if the level 3 ICCs for some items may be nontrivial (the largest is .088) and given the level 3 group sizes I wondered if there is any way in Mplus in which a clustered sampling correction for level 3 can be used simultaneously with the 2level CFA to correct the chisquare and standard errors to accommodate the level 3 dependency. 


You can use TYPE = COMPLEX TWOLEVEL and use 2 cluster variables: CLUSTER = clinic doctor; COMPLEX corrects chi2 and SEs for the nesting in the clinic level and TWOLEVEL models the patient and doctor variation. 


Thanks Bengt, I notice that this method only provides a loglikelihood (as shown below) however the manual on p.234 and p.501 seems to suggest that the a corrected chisquare is provided. Am I to assume therefore that this loglikelihood is intended to be used for nested model comparisons only? Is there anyway to get a chisquare for use in a CFI or RMSEA for example? MODEL FIT INFORMATION Number of Free Parameters 74 Loglikelihood H0 Value 213462.813 H0 Scaling Correction Factor 4.381 for MLR Information Criteria Akaike (AIC) 427073.626 Bayesian (BIC) 427659.151 SampleSize Adjusted BIC 427423.982 (n* = (n + 2) / 24) 


If chisquare and related fit statistics are not given, they are not available because means, variances, and covariances are not sufficient statistics for model estimation. In this case, nested models can be compared using 2 times the loglikelihood difference which is distributed as chisquare. 

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