I want to know if it is appropriate to combine different tests with SEM in the same study. Lets say I have four hypotheses and a hypothesized model. Can I use different tests for each of the hypothesis and the SEM for the hypothesized model?
Yes, as long as the assumptions of the different models are satisfied. If there are a large number of t-tests you will need to adjust for the experimentwise error rate.
The way I see it, comparing groups (e.g. men & women) only makes sense if your SEM tells you that this exogenous variable has an influence on variables you wish to explain or is correlated with other in a significant way. On a more general note, I see no reasons why you should not incorporate these analyses in the same study.
Kind Regards
Marcel
Yes you can. As people said, just watch out for assumptions. Another point is that some of your hypothesis will have to be tested in the form of a multiple groups SEM, which is kind of complex with a large amount of groups. Also, you need to be very careful about sample sizes as each group estimation will be calculated separately from the other groups. That's why it might not be as feasible as working with anovas, t-tests, etc.
Why not but don't make it more complicated. CFA and SEM can describe the relationships in a single frame that might be more effective.
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