I am working on a SEM model where i have 7 latent variables (6 exogenous and 1 endogenous). In AMOS when I co-vary the exogenous constructs, only 2 paths are coming significant out of 6. But when i do not co-vary them, 4 hypothesis are accepted. My question is "Do we really need to co-vary all the exogenous constructs?
When you do not allow the correlations between exogeneous variables but they are in fact correlated, the model would be misspecified and the regression paths to your endogenous variable may be biased (over- or underestimated). Therefore, the answer is, yes, you should include all correlations that are non-zero to avoid misfit and bias in your model.
To second Christian Geiser answer: it is a very strong assumption to omit paths or covariances. It means that you imply this associations to be zero. Any non-zero association in the data will contribute to a misfit of the model. Such strong assumptions should be backed up by theory, otherwise it is reasonable to model this possible relations.
Yes, it is necessary to covary exogenous constructs in a structural model. Structural equation modeling (SEM) involves representing how various aspects of a phenomenon causally connect to one another. In SEM, models often contain postulated causal connections among latent variables (variables that can’t be directly observed). These latent variables are connected to observed variables through equations or diagrams. The covariance between exogenous (independent) latent variables is an essential consideration in SEM1. If you’d like more details, feel free to ask!
Rainer Duesing and Chuck A Arize Thank you for the clarification. Highly appreciate.
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