Factor scores in multilevel analysis
Message/Author
 Sharyn L. Rosenberg posted on Monday, July 03, 2006 - 5:41 am
I am wondering whether Mplus can save factor scores and standard errors from a level 2 (between level) factor.
 Thuy Nguyen posted on Monday, July 03, 2006 - 11:48 am
With SAVEDATA and the option SAVE=FSCORES, Mplus can save factor scores for a between level factor. Mplus does not compute the standard errors for the factor scores.
 Melvin C Y posted on Monday, February 06, 2012 - 10:10 pm
I am comparing the output using observed score obtained via summative score (1-5) and factor score method. In the factor score method, I ran an initial CFA with WLSMV estimator and saved the factor scores. I believe this is similar to the recomputing of raw scores into normalized scores procedure in Prelis.
Both models had identical set up for within and between model commands. The model using summative observed scores converged. However, the model with factor scores could not converge with a long message that the estimated within covariance matrix is not positive definite as it should be. Did I miss something?

Thanks,
Melvin
 Linda K. Muthen posted on Tuesday, February 07, 2012 - 5:36 pm
 Erik Sengewald posted on Friday, March 14, 2014 - 2:08 am
Dear Mplus team,
I conducted a multilevel factor analysis model for students’ evaluation of teaching with students as level one and courses at level 2. One version uses categorical indicators and another one assumes the indicators to be continuous. I estimated factor scores of the level two latent variables and observed a zero correlation between the factor scores of the first and second model. The models have seven latent variables on within and between with no restrictions on loadings, intercepts, mean and thresholds. The estimator is always Bayes and the modelfit is fine. I estimate 50 plausible values (psv) and obtained a nonzero mean for the psv when I use categorical indicators although the mean of the latent variable is zero. However, correlating only the psv value of the first imputation of this model with the psv of the model using continuous indicators the correlation is reasonable high (.85). Additionally the distribution of this first imputation differs significant from the 49 other imputations. I would like to use the factor scores of the model with categorical indicators for further analysis. What am I doing wrong? Do I need to fix model parameters such as thresholds for the categorical indicator model?
 Bengt O. Muthen posted on Friday, March 14, 2014 - 9:03 am

Support@statmodel.com.
 Susanne Schmidt posted on Thursday, March 10, 2016 - 6:30 am
Hi Mplus team,

I estimated within and between factor scores in a multilevel CFA model. I am wondering now how to use these factor scores as explanatory variables for further analysis. For one factor, a group mean centering is needed. Is it in this case appropriate to use the factor score of the between factor? Or should I use the aggregation of the within and between factor score and calculating the group mean of this aggregate?
And for a second factor, I need the individual score for each subject in the cluster. So, should I use only the within factor score or should I aggregate within and between factor scores? Actually, I thought just to use the within score but compared to the manifest scores it seems more realistic to sum within and between scores. However, if this is true, I did not find an explanation.

I was looking for a reference on the Mplus website or in a research paper but without sucess. Do you have any recommendations?

Thanks!
 Tihomir Asparouhov posted on Friday, March 11, 2016 - 10:05 am
The aggregation of the within and between is more robust to model misspecifications.

For the individual score I would use the aggregation of within and between.

This paper has some discussion on two-level factor scores
 Diep Nguyen posted on Friday, March 31, 2017 - 10:36 am
Hello Dr. Asparouhov,
I am also interested in finding a research paper that provides guidelines for using factor score in multilevel data but couldn’t find the discussion on two-level factor scores you mentioned in the NCME paper you sent the link (i.e.”general random effect latent variable modeling: random subjects, items, contexts and parameters”). I am very grateful if you could let me know which section or pages of this paper the discussion was taken place.
Thank you very much for your help!
Diep
 Tihomir Asparouhov posted on Monday, April 03, 2017 - 9:39 am
Equation (24) has two-level factor score
 Diep Nguyen posted on Tuesday, April 04, 2017 - 8:29 am
Thank you so much for your response and information, Dr. Asparouhov. I will check it out.
 Marja Holm posted on Saturday, January 27, 2018 - 2:29 am
Hello.

In my multi-level regression models, dependent variables were determined show that emotion scales loaded on the latent factors at the within level (students), and cluster_mean (classroom mean) of these scales loaded on the latent factors at the between level (classroom).

Regarding independent variables, SE groups (dummy variables) and skills (controlled variable) were predictors at the individual level.
SE group ratios and mean class scores of the skills were determined as predictor at the classroom level (cluster_mean). The controlled variable (skill) was grand-mean centered and SE groups (dummy variable) were not centered.

1. Can I used cluster_mean also dependent variables at the between level? Is this right?

2. Is the contextual effect present if the between regression coefficient is significantly different from the within regression coefficient (I used model constraint) or directly the effect of the between level ? (noted that latent dependent variables are also aggregated)
 Bengt O. Muthen posted on Saturday, January 27, 2018 - 4:55 pm
1. Yes.

2. For contextual effects, see the Raudenbush-Bryk multilevel book on page 140, and Table 5.11.
 Marja Holm posted on Sunday, January 28, 2018 - 6:54 am
Thank you very much!
 Marja Holm posted on Monday, February 05, 2018 - 6:02 am
Applies to my previous message above.

Because the dependent factor indicators are different within and between level (cluster_mean at the between, not same latent constructs)

1. Are the effects of the SE group ratios (not centered dummy variable) independent between effect on average emotions at the between level (not contextual)?

2. Can I determine contextual effect in this way: regression coefficient_between-regression coefficient_within (model constraint in MPLUS)?

3. Do you know any reference that would use this cluster mean of the dependent variables. I've just come across literature, in which the latent dependent variables are the same at the within and between levels. This did not work in my model.
 Bengt O. Muthen posted on Monday, February 05, 2018 - 9:05 am
See the book by Raudenbush-Bryk, page 140, Table 5.11. You may want to ask your questions on SEMNET.