This model is "just-identified" so that no overall model test of fit is available. You can test if there is gender equality. The way your model is now written, you let males and females have different estimates.
Dr. Muthen, Thank you for your response. I am interested specifically in the path y1 ON x78. x1-x5 are control variables in the analysis and I do not have any theoretical reason as to why they should be unconstrained. Should I then, in service of having a more parsimonious model, have the paths y1 ON x1-x5 constrained, and then compare the model that also constrains the y1 on x78 path? I disagree with a colleague on this topic. I believe that I should constrain the control variable path but they believe I should leave it unconstrained and only try constraining the path I am interested in and test the difference. Is there a good article/book that would walk through this sort of decision?
I think you could argue both ways depending on the situation. You want to test gender invariance for one of the paths. The best way to do that is in a model that is close to the correct model so that other sources of misfit don't play in. So if you really think/have evidence that the control variable influences are gender invariant, you should hold them invariant. If you don't, holding them invariant starts the testing of what you are interested in using a model that is too far from the correct one.