I am trying to run a SEM which has four latent variables in it. Let us consider these variables as A, B, C and D. All are latent. Here A and B are independent variables, C is mediator and E is dependent variable.
First I ran a CFA by taking all these 4 variables with their items and got model fit (CMIN/df, CFI etc are in recommended limits). It also give good results for AVE, convergent validity and discriminant validity. This is the first time, I have reported the model fit.
Then I come to SEM, I draw the arrows in SEM using AMOS, and made A & B as independent variable, C as mediator and D as dependent variable. Now when relationships are introduced, my CMIN/df, CFi values have changed considerably. Do I again need to check model fit now and report it with this structure? Or I just have to check the model fit at CFA level and then straight go to SEM without reporting model fit?
https://www.youtube.com/watch?v=HoZQ5rNOBDY&t=162s
https://www.youtube.com/watch?v=9jGL45NuVAA&t=4s
https://www.youtube.com/watch?v=j_yufPUjkwk
Hello Ajay,
I'm guessing that your prior check of measurement model adequacy allowed for the four latent variables to be correlated (to an unspecified degree). So, the addition of your hypothesized paths among the factors imposed a different structure, having fewer links, and which apparently yields poorer fit (based on the indices you are attending to). Which is correct? They both are, but they represent very different models (and, therefore, should be expected to differ).
People have parsed the degree of overall model-data misfit into the measurement portion and the structural portion (which could be construed as checking and reporting at two times/levels). Your observed change in fit reflects what happens when you imposed restrictions on the relationships among the latent variables via your paths.
Apologies if I've misunderstood your query.
Good luck with your work.
Prior to testing any structural model (in your case, the mediation model), you need to assess fit of the measurement model or CFA. Once you have adequate fit for the CFA, you can proceed to test the structural hypothesized model. In order to be able to interpret the model, you need to ensure that the fit statistics are adequate. So, yes, you need to interpret/report the fit indices for the CFA and your structural model.
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