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 Maria Rueda posted on Thursday, December 01, 2011 - 10:00 am
Hi, I'm using CFA to estimate jointly a set of latent variables. I save the factor scores and I have the following questions.
1. I have read that factor scores are predicted using regression method. Where I can find references that explain the estimation approach and assumptions.
2. Are the scores unbiased and do you have some references that help me support that?
3. I'm using them as explanatory variables but I also would like to use them as dependent variables. I read in another post that I can not and that I would need other method for estimating the scores. Can I choose another method in mplus or does it means that I need to use another program?
Thanks for all your help
 Maria Rueda posted on Thursday, December 01, 2011 - 11:11 am
I would like to add something. I'm estimating three latent factors jointly. Even in that case, can I use them as dependent variables?.
Thanks again
 Linda K. Muthen posted on Thursday, December 01, 2011 - 2:56 pm
1. See Technical Appendix 11 on the website.
2. No, the scores are not unbiased.
3. They should be used as independent variables. They should not be used as dependent variables in any case.

You would need to use another program if you want different factor scores.
 Maria Rueda posted on Friday, December 02, 2011 - 9:03 am
Dear Linda,
Thanks for your answers. I would like to follow up on my second question. If mplus factor scores are used as independent variables, can I consider them unbiased?

Thanks again
 Linda K. Muthen posted on Friday, December 02, 2011 - 11:17 am
They are biased but when used as independent variables, the bias cancels out so the regression slopes are not biased.
 Maria Rueda posted on Saturday, December 03, 2011 - 1:35 pm
Thanks again. Lastly, Do you know any reference I can read to support the idea that the bias cancels when using them as independent variables.

 Bengt O. Muthen posted on Saturday, December 03, 2011 - 1:56 pm
I think you find it in

Skrondal, A. and Laake, P. (2001). Regression among factor scores. Psychometrika 66, 563-575.

Or in Tucker's P-a article (probably referred to in there).

Actually, I mention it in my 1993 BJMSP article and refer to Tucker (1971); see

 Maria Rueda posted on Saturday, December 10, 2011 - 10:39 pm
Dear Bengt,
Thanks for the reference.
One more question. When predicting factor scores, how mplus handle missing items?
I'm doing a CFA (ML). It seems that for the persons that have missing in some items, it still predicts a factor score. Is it using the covariance matrix between the latent factors?
 Linda K. Muthen posted on Sunday, December 11, 2011 - 3:12 pm
Factor scores are estimated using all available information on the observed variables for each person together with the parameter estimates for everyone.
 Beth Bynum posted on Wednesday, March 14, 2012 - 12:36 pm

I have running CFA analyses to determine the factor structure of a set of scales. My model includes 30 observed variables, 13 first-order factors (8 Trait factors and 5 Method factors), and a second-order factor that the 8 trait factors load on to. I have saved the factor scores using the SAVE=FSCORES option. I would like to use the trait factor scores as independent variables in regression analyses. I understand that using factor scores can be problematic if the determinacy is low. I've specified the FSDETERMINACY option. The output provides determinacy estimates and factor score information for 114 different patterns.

1) What is the difference in the output for the different patterns? Is there one pattern I should look at over another?

2) Does the use of factor scores in the context I have described seem reasonable?

 Linda K. Muthen posted on Wednesday, March 14, 2012 - 5:48 pm
1. I think the factor score information is simply descriptive statistics for the factor scores. The factor score determinacy is a single number.

2. If you have continuous factor indicators, using the factor scores as an independent variable is okay.
 Dmitriy Poznyak posted on Friday, August 02, 2013 - 6:45 am
Dear Mplus team,

I have a question about comparability of the latent factor scores in two related models. Specifically, if I were to run the factor model for Data A and then use unstandardized loadings in estimating the same model for Data B (by fixing the loadings to be the same between two models) would the factor scores be computed in an essentially comparable way, since fixing loadings seem to be forcing the variance-covariance matrices to be the same? It is our understanding is that unstandardized factor loadings are used for the factor scores’ computation, but we are not sure whether other parameters, such as item intercepts are also used in calculating the scores in Mplus?

Thank you,
 Linda K. Muthen posted on Friday, August 02, 2013 - 8:29 am
You should fix all of the parameters to use the model for prediction. You can use the SVALUES option of the OUTPUT command to get input with ending values as starting values and change the * symbol to @. Note that when you do this you make the assumption that both samples come from the same population.
 Dmitriy Poznyak posted on Friday, August 02, 2013 - 12:45 pm
Many thanks for your very prompt reply, Linda. This makes perfect sense.
 Kara Thompson posted on Thursday, September 26, 2013 - 2:15 pm
Is it ok to save out factor scores from a LGM model (i,s) and use them as independent variables in a regression model?

How would this model differ from simply doing the regression in mplus?

 Bengt O. Muthen posted on Thursday, September 26, 2013 - 3:42 pm
If the factor scores are well estimated you can use them as IVs. By simply doing the regression, do perhaps you mean summing up the items - that assumes that the items are equivalent.
 Kara Thompson posted on Thursday, September 26, 2013 - 4:14 pm
Thank you!

What I meant was simultaneously doing the LGM and the regression in the same model?

I s | ......

Z on I s;

Does this make a difference?
 Linda K. Muthen posted on Thursday, September 26, 2013 - 6:26 pm
This is best way to do this.
 John Woo posted on Thursday, August 06, 2015 - 4:03 pm
Hi, this is related to the question above. Is there a reference that shows why the latter way is better than the two-step regression approach (i.e., using factor scores as IV)?
 Bengt O. Muthen posted on Friday, August 07, 2015 - 5:23 pm
See the FAQ on our web site called "Factor scores".
 John Woo posted on Saturday, August 08, 2015 - 12:32 pm
Thank you. I have a couple more beginners-level questions..

(1) when Mplus does any kinds of latent variable regressions (e.g., UG Ex 6.12, Ex 6.13, etc), is it essentially using the Revised factor score regression method (as specified in Skrondal & Laake)? I had thought that Mplus estimates all measurement and structural parameters simultaneously, as opposed to using sequential regression approach? I might be confused here with the term "simultaneous"..

(2) I've read that factor scores cannot be used as DV because of biased estimations. Does this apply only to a crude way of factor score regression? Does Mplus make correction for this (for example, UG Ex 6.12) -- by, for example, using the Bartlett FSR? Bottom line: in UG 6.12, can we interpret the regression of the latent growth factors on x as producing unbiased estimates?
 Bengt O. Muthen posted on Sunday, August 09, 2015 - 7:19 pm
(1). No, the standard approach of Mplus is to not take the intermediate step of estimating factor scores. Using that intermediate step was what was done before SEM was developed.

(2) UG ex 6.12 also does not use the intermediate step of estimating factor scores. So estimates are fine.
 Michael Strambler posted on Monday, March 12, 2018 - 7:34 am
I am generating factor scores from a CFA with categorial indicators (likert scale) and plan to use the mean values as predictors. Is it also advisable to use the standard deviation for each factor score as part of this measure? For instance, I believe I saw an example elsewhere where the factor scores were divided by the SD and the resulting values were used as predictors.
 Bengt O. Muthen posted on Monday, March 12, 2018 - 3:32 pm
I can think of no particular reason that necessitates that factor scores be divided by their SDs.
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