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 yao lu posted on Wednesday, February 22, 2012 - 3:24 pm
Hi, I have a question regarded using CFA on repeated measures within the same group. I have a causal model described as:
F1 by x1, x2, x3
F2 by x4, x5, x6
F3 by x7, x8, x9

F4 by y1, y2, y3
F5 by y4, y4, y5
F6 by y6, y7, y8

F4 on F1
F5 on F2
F6 on F3

F1 and F4 are based on the repeated measures (e.g., x1 asks about the quality of product A, and x4 asks about the quality of product B). Similarly, F5 and F2, and F6 and F3 use repeated measures.

My question is that can I still conduct a CFA? My concern is that given repeated measures, the residual of each factor indicator needs to be correlated with that of the correspondent repeated indicator. For example, there are 9 residual correlations of factor indicators in this case. Would this cause too many complications in running and evaluating the model?

I am still at the study design stage, so do not have the actual date to run the test myself. I would highly appreciate your insight, and make appropriate changes to my study if necessary.
 Linda K. Muthen posted on Wednesday, February 22, 2012 - 6:50 pm
You can do a longitudinal factor analysis as you show. Because the analysis is multivariate, it takes care of any non-independence of observations due to the repeated measures.
 yao lu posted on Wednesday, February 22, 2012 - 8:45 pm
Hi Dr.Muthen,

Thanks for your reply. Following up my last post, the study also needs to consider two continuous moderator: F7 and F8. F8 and F7 will moderate each of the three direct effects.

I will conduct structural regression for testing the model, three direct effects with three moderating effects.

My question is for the first step of testing measurement model, should the measurement model include F1-F6, or include F1-F8? I am confused as I saw both examples in existing studies.

Thank you for your help in advance.
 yao lu posted on Wednesday, February 22, 2012 - 8:52 pm
This post is to complete my last post. Sorry I did not make it clear earlier.

For testing the moderating effect, I will run a simultaneous SEM on two groups. The SEM will use the interaction term , and compare the path coefficients of each interaction term.

e.g., for the moderating effect of F1 on the relationship between F2 and F1:

Define M1=F7*F1;
F2 on M1
 Bengt O. Muthen posted on Wednesday, February 22, 2012 - 9:11 pm
You should not use Define to create interactions involving latent variables, but instead use XWITH in the Model command. See UG ex 5.13.
 yao lu posted on Wednesday, February 22, 2012 - 9:24 pm
Hi Bengt,

Thank you for the correction.

Can you please also comment on my earlier question regarding what to include in the measurement model? (posted at 2:45pm)

Thank you in advance.
 Bengt O. Muthen posted on Wednesday, February 22, 2012 - 9:36 pm
Please see the UG example.
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