Hello Winifred,

you imposing new constraints on the structural level and this causes (further?) misfit. There is no easy solution. You have to understand path tracing and the concept of testable implications. A misfit means that one or more testable implications are not met and unfortunately, there will be diffferent (causal) scenarios that lead to the same misfit.

Here are some threads with more background:

https://www.researchgate.net/post/Why_when_I_group_all_my_10_constructs_my_hypothesis_are_rejected#view=5d35556ed7141b6859527bcf

https://www.researchgate.net/post/Dear_scholars_how_to_design_a_Structural_Equation_Modeling_surveys#view=5c0cdaf3c7d8ab762f591a75

https://www.researchgate.net/post/Dear_scholars_how_to_design_a_Structural_Equation_Modeling_surveys

HTH

Holger

Your question is not quite clear to me. Do you mean that for the same set of variables, your fit indices look better for the structural equation model than for a confirmatory factor analysis with unrestricted latent covariance structure (freely estimated latent covariances/correlations)?