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 Yang An posted on Wednesday, May 17, 2006 - 7:29 am
I am trying to use CFA to get factor scores, fixing variance of latent variables to 1. But usually, this is done in cross-sectional study. In our study, we have repeated measures for up to 10 waves. I am not sure how to handle this.
I tried two appoaches:
1. use all repeated data we have,fit one CFA model.
2. use only wave 1 data to fit the model,
and for subsequent waves use the same loading and intercepts.

Both methods above are kind of flawed. But I can not think of better way to do this.
 Boliang Guo posted on Wednesday, May 17, 2006 - 7:35 am
this should be a measurement invariance study. if you did not test the structure, I think you should test it first using each time's data, if yes, I think you could conduct the ME/I test to see the to which extent your model invariant across measurement waves. if you have strong theory about the ME/I across measurement wave, then, I think you jsut get the factor score by each time's data.
 Linda K. Muthen posted on Wednesday, May 17, 2006 - 11:47 am
I agree that you need to test for measurement invariance across time. If you have measurement invariance across time, I would do a multiple indicator growth model. I would not use factor scores.
 Yang An posted on Thursday, May 18, 2006 - 7:19 am
So when we test for measurement invariance across time, do we only test if the factor loadings are the same?
How do we deal with the intercepts of the obverved variables and the correlation between latent variables. Do we keep them the same?
Also, when we do the test, how do we control for TYPE 1 error? Is there a simutaeous test available?
Thank you very much.
 Boliang Guo posted on Thursday, May 18, 2006 - 7:35 am
pls refer paper
Vandenberg, R. J. & Lance, C. E. (2000). A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research. Organizational Research Methods, 3, 4-69.
 Linda K. Muthen posted on Thursday, May 18, 2006 - 7:58 am
See also the section on testing for measurement invariance in Chapter 13 of the Mplus User's Guide. It is described for groups but the same issues apply across time.
 Blaze Aylmer posted on Thursday, May 18, 2006 - 4:05 pm
This is a good resource page for MI

see also ref on byrne and Muthen Psy methods 1998.

You might want to look at
Vandenberg, R. J. (2002). Toward a Further Understanding of and Improvement in Measurement Invariance Methods and Procedures. Organizational Research Methods, 5(2), 139-158.
 Amery Wu posted on Monday, June 02, 2008 - 1:22 pm

I am studying measurement invariance across time. In your previous response, you mentioned that the model specification follows the measurement invariance using MG-CFA as described in Chapter 13.

I was wondering whether MG-CFA was designed for cross-sectional data assuming independence. Don't we need to deal with the dependence problem of repeated measures data when using MG-CFA? If so, how?

Thank you.
 Linda K. Muthen posted on Monday, June 02, 2008 - 3:08 pm
The lack of independence due to several variables being measured on the same person is taken care of by multivariate modeling of the data.
 Amery Wu posted on Thursday, June 05, 2008 - 3:35 pm
Hi Linda,

I am following up on Amery's question above.

When I think of measurement invariance across time I usually think of testing this with a single group model. For example, imagine I am investigating the measurement of a 10 item scale that has been administered twice to the same respondents. This single group model would then have two latent variables with item manifest varibles each; the latent variable would be correlated and particular errors would be correlated reflecting the same scale being administered twice (e.g, item 1 on time 1 correlated to item 1 on time 2).

Now, if one, however, approaches this from a multi-group approach one is not able to model the correlated errors, nor the correlated latent variables. Would this not bias the Chi-squared tests of measurement invariance? I am still thinking it through but it seems to me that treating a repeated measures measurement invariance problem as multi-groups would lead to biased results.

Any thoughts on this would be much appreciated.

Cheers, Bruno

Bruno D. Zumbo, Ph.D.
University of British Columbia
 Linda K. Muthen posted on Thursday, June 05, 2008 - 3:43 pm
Measurement invariance across time cannot be done using multiple group analysis because the groups would not be independent. Our short course handouts are available on the website. See Topic 3, multiple indicator growth for an example of testing measurement invariance across time.
 Katie Daniels posted on Wednesday, August 03, 2011 - 12:22 pm
Can you point me to any additional reading on how to handle measurement invariance over time? Specifically, I need to understand this issue of the lack of independence of the repeated measures within the CFA framework.
 Linda K. Muthen posted on Wednesday, August 03, 2011 - 3:18 pm
The lack of independence is dealt with by correlating the factors over time. By the way, the multiple indicator growth example is in the current Topic 4 course handout.
 Annie Fox posted on Friday, February 28, 2014 - 10:50 am
We are trying to run a longitudinal CFA of a 3-factor model over 3 time points using WLSMV. We are trying to test the configural model using Theta parametrization, but are encountering an non-positive definite error message and cannot seem to find any problems with the parameter mentioned in the error message. Are we using the appropriate parametrization?

The syntax we are using:

F1_0 BY U0T1-U0T5;
F2_0 BY U0T6 U0T7;
F3_0 BY U0T8-U0T12;

F1_2 BY U2T1-U2T5;
F2_2 BY U2T6 U2T7;
F3_2 BY U2T8-U2T12;

F1_3 BY U3T1-U3T5;
F2_3 BY U3T6 U3T7;
F3_3 BY U3T8-U3T12;

U0T1-U0T17@1 U2T1-U2T17@1 U3T1-U3T17@1;

F1_0 WITH F1_2* F1_3*; F1_2 WITH F1_3*;
F2_0 WITH F2_2* F2_3*; F2_2 WITH F2_3*;
F3_0 WITH F3_2* F3_3*; F3_2 WITH F3_3*;

[F1_0@0 F2_0@0 F3_0@0
F1_2@0 F2_2@0 F3_2@0
F1_3@0 F2_3@0 F3_3@0];
 Bengt O. Muthen posted on Friday, February 28, 2014 - 1:55 pm
Input looks alright. We need to see the full output, including TECH1. Please send to Support together with license number.
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