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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. |
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By specifities do you mean residual variances? |
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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? |
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bmuthen posted on Thursday, December 08, 2005 - 6:35 am
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You can get a between-level 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. |
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Actually I don't obtain any residual variances but I can compute the total specifities via 1-R² 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 R²-value as well for the between-level? So in any case I'll obtain "standardized" residual variances (1-R²)? 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? |
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bmuthen posted on Monday, December 19, 2005 - 9:28 am
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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 |
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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) R-SQUARE: - 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. |
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bmuthen posted on Monday, December 19, 2005 - 11:24 am
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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. |
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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 ;-) |
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bmuthen posted on Monday, December 19, 2005 - 11:47 am
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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. |
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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)? |
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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. |
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bmuthen posted on Monday, December 19, 2005 - 6:39 pm
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That's right. |
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