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 Florian Fiedler posted on Wednesday, December 07, 2005 - 7:48 am
Dear MPlus-team,

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.
 Linda K. Muthen posted on Wednesday, December 07, 2005 - 8:24 am
By specifities do you mean residual variances?
 Florian Fiedler posted on Thursday, December 08, 2005 - 3:18 am
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 between-level residual variance by mentioning this parameter on between, say


Often, however, these are close to zero and can sometimes be hard to estimate.
 Florian Fiedler posted on Monday, December 19, 2005 - 6:21 am
Actually I don't obtain any residual variances but I can compute the total specifities via 1-R for each item ...

I'm not sure if I've understand it right.

When mentioning a variable (factor indicator) seperately on the between-level I'll obtain a R-value as well for the between-level? So in any case I'll obtain "standardized" residual variances (1-R)?

I tried to compute the "estimated" residual variances via:

Total item variance: Vt=(L11*F11+L12F12)/R

Residual item variance: Vr=L11*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
 Florian Fiedler posted on Monday, December 19, 2005 - 10:07 am
Where in the output should they be found (section)?

I specified the model in the following way.


SK_w BY S40@1 S41*1;
SK2_w BY S42@1 S43*1 S44*.9 S45*.9;
SK_w WITH SK2_w*.4;


SK BY S40@1 S41*1;
SK2 BY S42@1 S43*1 S44*.9 S45*.9;
S40@0; S41@0; S42@0; S43@0; S44@0; S45@0;

- estimates for BY and WITH statements, S.E., Std StdYX
- variances for latent factors
- estimates for BY and WITH statements, S.E., Std StdYX
- variances for latent factors
- thresholds
- residual variances (all fixed to 0)

- all within R
- all between R (all fixed to 1)

- 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 2-level 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 within-level residual variances are those of the logistic density, namely pi-square 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 within-level R-square computations. R-square = 1 on between because the between-level residual variances are zero by default.
 Florian Fiedler posted on Monday, December 19, 2005 - 11:36 am
But if the residual variance is (pi^2)/3 for all items, the R should not differ ...

So does it mean, the TOTAL variance of an item equals (pi^2)/3 and the explained variance is R*(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
R-square varies across items as a function of the loadings varying across the items. Compare with regular regression - the slopes influence the R-square.
 Florian Fiedler posted on Monday, December 19, 2005 - 12:07 pm
Well, for the computation of ICCs I already used pi/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)?
 Florian Fiedler posted on Monday, December 19, 2005 - 1:11 pm
I think, I got it. To get the total variance of the variable, I add up the factor contributions plus pi/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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