SE for factor scores from EFA output PreviousNext
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 Ann Haas posted on Wednesday, August 08, 2012 - 12:43 pm
Is there a way to calculate SE for the factor scores from the EFA output? We are able to calculate the factor scores themselves, and we are trying to avoid re-running a number of EFA models in CFA format.

 Linda K. Muthen posted on Wednesday, August 08, 2012 - 1:24 pm
You can run an EFA through ESEM and get factor scores and standard errors. If you remove the covariates and direct effects from Example 5.24, it is an EFA.
 Ann Haas posted on Thursday, August 09, 2012 - 6:11 am
Could you describe how Mplus calculates the SEs of factor scores, or point us to any references?

 Linda K. Muthen posted on Friday, August 10, 2012 - 10:16 am
We don't have this documented. For continuous outcomes, see a factor analysis literature. For categorical outcomes, see the IRT literature.
 Xu, Man posted on Wednesday, June 05, 2013 - 3:12 am
Is it always possible to get standard errors of the factor scores?

I exported factor scores from an EFA (binary items, bi-factor rotation, WLSMV estimator) and don't think the standard errors are given.

But in a CFA model (continuous items, ml estimator) I saw the standard errors were included in the factor score file.

On a separate note, are the factor scores obtained this way by any way comparable to the actual latent variables themselves?

I was thinking to export plausible values (which I think are random draws from the latent variables), but it seems only possible to do that through Bayes estimator. Is this true?


 Linda K. Muthen posted on Wednesday, June 05, 2013 - 12:20 pm
We don't give factor scores from EFA so I am not sure what your fist paragraph means.

Factor scores and latent variables are not the same unless factor score determinacy is one.

Yes, plausible values are available only with Bayes.
 Xu, Man posted on Wednesday, June 05, 2013 - 3:46 pm
Sorry for the confusion regarding EFA, I meant that I used ESEM set up to obtain EFA factor scores with binary items, bi-factor rotation, WLSMV estimator.

I just noticed another case where factor score standard errors were not given - it's a CFA with ordinal items and WLSMV estimator.
 Bengt O. Muthen posted on Wednesday, June 05, 2013 - 4:14 pm
We add factor score standard errors for more cases as we develop new program versions.

But if you want to focus on using factor scores, Bayes and its plausible values is a good way to go.
 Xu, Man posted on Wednesday, June 05, 2013 - 9:32 pm
Thank you - I actually am not fully aware what I should do to best take advantage of the factor score standard errors. I guess I could construct confidence intervals and see how the factor scores differ from each other at different levels?

Re focusing on factor scores, it's mainly for specific modelling situations, for example, in ESEM, sometimes the factor structure can change depending on covariate - even the covariate is not part of the model.

Another reason to use factor scores is for colleagues who do not want to go into latent variable but still want to take advantage of psycho-metrically defined variables. But apart from problems of computing factor scores itself, I found in settings such as the bi-factor CFA, the 0 correlations between factors are ignored in factor scores. Although I have not tried Bayes yet, but the idea of plausible values sound much better in general.
 Xu, Man posted on Thursday, June 06, 2013 - 8:41 am
* In second paragraph of previous post, I meant:

-even the covariate is not part of the EFA model.
 Peter Halpin posted on Wednesday, October 08, 2014 - 10:44 am

I also have some questions about factor score standard errors and their availability in Mplus 7.2

Could you please summarize the cases where SEs are (or are not) available for TYPE = GENERAL analyzes?
e.g, for which types of indicators variables (e.g., continuous, categorical, tobit, combinations thereof)?
Does this depend on the estimator used?

Also, I believe that Mplus uses "modal a' posteriori" estimates for cases in which factor scores are available (equation 231 in the technical appendices).
For Gaussian indicators, this coincides with the posterior mean of the factors, so the standard errors are available from the posterior covariance matrix. For non-continuous indictors, how are the SEs obtained for the MAP estimator? A reference here would be great.

Thank you, Peter
 Bengt O. Muthen posted on Wednesday, October 08, 2014 - 5:51 pm
For Type=General, here is the current state for factor score SEs:

SEs not given: estimators=wlsmv/wlsm/wls/ulsmv
estimate=posterior mode

SEs given: estimators=ML/MLR/MLF
estimate=posterior mean

It is not dependent on the type of indicator variables.

I believe the IRT literature has descriptions of MAP SEs for categorical outcomes.
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