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Dear MPlusteam, I'm conducting a CFA on school data (ordinal variables), so I'd like to take clustering into account. Only part of the variables within the scales have substantial ICCs. Is it wise to fit a "full" factor model on the withinlevel and a "partial" model on the betweenlevel, so the loadings of variables with low ICCs would be 0 on the between factors. How would you interpret those findings and the loadings on the within and between factors? 

bmuthen posted on Thursday, November 24, 2005  8:14 am



Yes, you can fit a 2level factor model where the loading estimates will then most likely be small for the variables with small iccs. Note that you can have zero between residual variances and that is ok. The items with substantial between loadings then represent the schoollevel factor  for example, with achievement data you may find that only reading variables and not math variables measure school excellence. 


So you would say, it's also a kind of model selection strategy to "exclude" variables from between level loadings because of small or neglectable ICCs? Thank you very much fpr your comments. Florian Fiedler. 

bmuthen posted on Friday, November 25, 2005  8:22 am



Yes, you can do that type of exploration. 

MReis posted on Tuesday, December 06, 2005  3:31 am



Hello, I have two related questions to the above topic:  The ICC is an index of the proportional amount of betweenlevelvariance, but is there a rule of thumb about how many variance in absolut terms is "necessary" for successfull twolevelmodeling (robust estimates, etc.)?  Regarding the discussed selection strategy of excluding items with low ICC/variance from the betweenlevel: Are two models nested, that simply differ in the number of betweenlevelitems (i.e. fixing their betweenlevelvariance to zero) and therefore could be used in a logdifftest? Thanks for any suggestions. 


I know of no such rule of thumb. For models to be nested, they must share the same set of observed variables. 

MReis posted on Tuesday, December 06, 2005  9:38 am



Many thanks. Regarding your second answer, does that mean that eliminating items from the betweenmodel due to low ICC could only be based on the overall fit indices (CFI, etc.)? 


If you want to test nested models, you could use the loglikelihoods or chisquare if it is available. I don't know of any other type of difference testing. 

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