Reliability of indicators
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sbremer
Joined: 11/08/2011
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Hei OpenMx-Community,
is there a way to measure the reliability of the indicators in a SEM?
Is it correct to standardise the run model by the function standardizeRAM(model) and computing the squares of the path coefficients/factor loadings (squared multiple correlation)?
I found the function standardizeRAM(model) here: http://openmx.psyc.virginia.edu/thread/1095
Thanks in advance!
These squared multiple
I'm not so sure that I would necessarily call that reliability, though others may disagree. I'd also add that you may want to keep items with lower factor loadings for any number of reasons. Removing items always lowers the factor communality (unless those items' loadings are zero). Including items with lower loadings may be necessary for representing the "whole of the factor space."
For example, say you have a measure of affect that includes three items: sad, angry and upset. Ignore the fact that there are only three items: it's an example. You'd probably expect relatively high loadings for the angry and upset items, and a lower one for sadness, because angry and upset probably have more in common with each other than they do with sadness. However, how you interpret the factor greatly depends on whether the sad item is included. With it, you're measuring what sadness and anger have in common. Without it, your factor represents just anger.
Why do you want to know how reliable your items are? What does reliability mean for your research?
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In reply to These squared multiple by Ryne
I see your point. Your answer
But I don't want to remove any indicators. My adviser said that those squared correlations would help identifying errors I made, e.g. when squared correlations are negativ I probably specified something incorrect. Furthermore it seems to me, that interpreting communalities is standard procedure.
My starting point was to compute the explained variance of an indicator by a latent variable. In the case of standardised indicators this is the square of the estimated path coefficient. That is the same a computing the reliability/communality, correct?
Can I compute this with non-standardised indicators? Is the way I suggested is the previous post correct?
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In reply to I see your point. Your answer by sbremer
The explained variance of an
rho^2 = lambda %*% solve(sigma) %*% t(lambda)
where solve() is inversion, t() is transposition.
I'll add again that this is not exactly reliability, though it is a very good estimate of the reliability of factor scores.
Finally, you don't need standardized data to get the R^2 for an indicator. loading^2 divided by (loading^2 + residual variance) will yield the explained variance regardless of the scaling/standardization.
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Reliability in SEM
There is material about this in Graham Dunn's book Statistics in Psychiatry which you may find helpful. Not much knowledge of psychiatry, if any, is needed.
Michael
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