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 di phu posted on Friday, February 09, 2007 - 9:39 pm
I am new to Mplus (just learning to use it at my university) and have a question regarding factor scores and weights. I have read most of the messages and realize that Mplus won't give factor scores for an EFA with categorical data, and that it is suggested to set up a EFA in a CFA context. However, in the past when factor analyzing categorical items in SAS I'd create a tetrachoric correlation matrix and then have SAS factor analyze that matrix. My understanding is that this is basically what Mplus does. With the command "score" SAS would then give me the factor weights which I could then use to create factor scores. I am wondering if one can do this in Mplus when the ULS estimator is used (as I understand it that is the estimator used in SAS). If not is it because there is something inherently wrong in doing this or just because of how Mplus is set up. I would like to move to Mplus but don't really feel like setting up 70 some items in a CFA context.

Thanks!
 Linda K. Muthen posted on Saturday, February 10, 2007 - 10:49 am
It is incorrect to compute the factor scores for categorical outcomes by using factor weights from an analysis of a tetrachoric correlation matrix. The parameter estimates from such an analysis are correct but the necessary posterior distribution needs to take into account the categorical nature of the data. This is done by using an iterative procedure to estimate the factor scores in line with IRT. This is how Mplus estimates factor scores for categorical outcomes. Although you could analyze a tetrachoric correlation matrix in Mplus just like you do in SAS and you could use the factor loadings to create factor scores, this would not be correct.

We don't see EFA as a final analysis. We use it as part of a descriptive exploration of a data set to see if the number of factors expected is extracted and if the items behave as expected. We then turn to a CFA model where instead of estimating factor scores and doing an analysis in two steps which could lead to estimation errors, we directly estimate the relationships of factors to other variables.
 yang posted on Wednesday, November 07, 2007 - 9:56 am
Linda,

I am trying to understand how Mplus obtains factor scores for a unidimensional structure with ordinal indicators only(No covariates).

On page 48 of Mplus Technical Appendices (#11), it seems that the covariates (X) are necessary to estimate factor scores. However, in my situation, there are only indicators available to estimate the factor score.

I did obtain factors running Mplus (V4.2). However, I need your nice help to better understand how Mplus got it.

Thank you very much.
 Linda K. Muthen posted on Thursday, November 08, 2007 - 7:56 am
The formula is a general formula that includes covariates. Covariates are not required.
 yang posted on Tuesday, December 18, 2007 - 9:29 am
Linda,

Thanks for your nice instructions.

I am studying Appendix #11, and the formulas seem to be pretty brief for me. Is there any other resource (textbook, paper, etc) that can give more details? Thank you.
 Linda K. Muthen posted on Tuesday, December 18, 2007 - 1:21 pm
You can check the IRT literature. See "Expected A Posteriori" Method in these IRT refs - perhaps start with Baker & Kim:

Baker, F.B. & Kim, S.H. (2004). Item response theory. Parameter estimation
techniques. Second edition. New York: Marcel Dekker.

Bock, R.D. (1997). A brief history of item response theory. Educational Measurement: Issues and Practice, 16, 21-33.

du Toit, M. (2003). IRT from SSI. Lincolnwood, IL: Scientific Software International, Inc. (BILOG, MULTILOG, PARSCALE, TESTFACT)

Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.

Hambleton, R.K. & Swaminathan, H. (1985). Item response theory. Boston: Kluwer-Nijhoff.
 yang posted on Friday, April 25, 2008 - 12:19 pm
Linda,

For a uni-dimensional structure with binary items, is there any difference between the factor score estimates obtained from CFA in Mplus (Version 5), and the latent trait estimates obtained from an IRT software/package using the “Expected A Posteriori” (EAP) method (assuming 2-PL model)? If yes, what is the difference (in theory and/or implementation)? If no, is Mplus utilizing an IRT model/algorithm in the estimation of ‘Factor Score’?

Thank you.
 Linda K. Muthen posted on Friday, April 25, 2008 - 3:42 pm
With maximum likelihood estimation and the logit link, Mplus factors scores are the same as IRT scores.
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