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Dear MPlusteam, how can I obtain specifities on the two levels (between and within) when doing a multilevel cfa with ordinal observed variables? Do I have to change the parameterization or is it just a question of freeing parameters? If I've to change the parameterization, is there a short explanation of the differences between theta and delta parameterization? Thanks for your advice. Best regards, Florian Fiedler. 


By specifities do you mean residual variances? 


Yes. In my model I only obtain residual variances of the items on within level which can be interpreted as total specifities but I can't seperate them into two levels. Or would you suggest just to compare models to argue in favour or against a certain between level factor structure? 

bmuthen posted on Thursday, December 08, 2005  6:35 am



You can get a betweenlevel residual variance by mentioning this parameter on between, say %between% yb; Often, however, these are close to zero and can sometimes be hard to estimate. 


Actually I don't obtain any residual variances but I can compute the total specifities via 1R² for each item ... I'm not sure if I've understand it right. When mentioning a variable (factor indicator) seperately on the betweenlevel I'll obtain a R²value as well for the betweenlevel? So in any case I'll obtain "standardized" residual variances (1R²)? I tried to compute the "estimated" residual variances via: Total item variance: Vt=(L11²*F11+L12²F12)/R² Residual item variance: Vr=L11²*F11/Vt Is this the right way to go? 

bmuthen posted on Monday, December 19, 2005  9:28 am



You should get residual variances in the output if you ask for standardized in the Output command. If not, please send your output to support@statmodel.com 


Where in the output should they be found (section)? I specified the model in the following way. MODEL: %WITHIN% SK_w BY S40@1 S41*1; SK2_w BY S42@1 S43*1 S44*.9 S45*.9; SK_w WITH SK2_w*.4; %BETWEEN% SK BY S40@1 S41*1; SK2 BY S42@1 S43*1 S44*.9 S45*.9; SK WITH SK2*.4; S40@0; S41@0; S42@0; S43@0; S44@0; S45@0; MODEL RESULTS section: WITHIN  estimates for BY and WITH statements, S.E., Std StdYX  variances for latent factors BETWEEN  estimates for BY and WITH statements, S.E., Std StdYX  variances for latent factors  thresholds  residual variances (all fixed to 0) RSQUARE:  all within R²  all between R² (all fixed to 1) RESIDUAL OUTPUT section:  univariate distr. fit  bivariate distr. fit Then the technical outputs follow. That's all. 

bmuthen posted on Monday, December 19, 2005  11:24 am



Ah yes, you are doing 2level factor analysis of categorical items, which means that the WLSMV estimator is not available and you are using ML estimation which uses a logistic link (as opposed to the probit link of the WLSMV estimator). Note that with ML and logistic link, the Theta/Delta parameterization distinction is not made. In your ML run, the withinlevel residual variances are those of the logistic density, namely pisquare divided by 3 (see text books on logistic regression), where pi = 3.14. Because this is the value they always have, we don't print them, but this is the value used in the withinlevel Rsquare computations. Rsquare = 1 on between because the betweenlevel residual variances are zero by default. 


But if the residual variance is (pi^2)/3 for all items, the R² should not differ ... So does it mean, the TOTAL variance of an item equals (pi^2)/3 and the explained variance is R²*(pi^2)/3? As in a statement above, I'm interested in the computation of communalities. Via (explained by factor)/(total variance) I'd like to show the contribution of a within factor compared to a between factor. Hope it's getting clearer now ;) 

bmuthen posted on Monday, December 19, 2005  11:47 am



Rsquare varies across items as a function of the loadings varying across the items. Compare with regular regression  the slopes influence the Rsquare. 


Well, for the computation of ICCs I already used pi²/3 as total item variance, since it's the only way to obtain ICCs with ordinal variables. But there I thought it was the TOTAL variance. So when building say a factor model, the unexplained variance (which I would call residual variance then) should decrease  or is the total variance increasing by lambda*(factor variance)? 


I think, I got it. To get the total variance of the variable, I add up the factor contributions plus pi²/3, so the residual is always the same, but it's proportion in the total item variance differs and will increase with larger contributions of factors. 

bmuthen posted on Monday, December 19, 2005  6:39 pm



That's right. 

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