I have limited training in SEM and have a couple of questions about a somewhat complicated model decision. I have three continuous variables that each measure an attribute of an institution that exists in 1,400 municipalities, measured annually from 2013-2019 (nearly balanced but not perfectly). Attributes "a" and "d" are institutional outcomes of interest that the municipal government has limited, indirect control over. Attribute "r" measures how much material/administrative support the institution gets from the municipal government. I want to test the hypothesis that changes the government makes to "r" result in changes to both "a" and "d". I'm interested in seeing the other relationships among "a", "d", and "r" in an exploratory way but do not have hypotheses about them.

Both the synchronous and cross-lagged models produce acceptable GOF stats, and both models provide clear evidence that "r" affects "a" and "d" at t = 0 and t + 1, respectively. I placed constraints on all repeated relationships to simplify output and added correlations on error at t = 0. The models are below (I can provide the code or output, but each is quite long).

My issues:

1. Is there any special issue with doing a cross-lagged and/or synchronous SEM model with three variables (I can only find examples with two). Do these first two below look correctly specified?

2. Both models have good fit, so I tried the cross-lagged with synchronous (third model). This model fails to converge unless I use MLE with missing values. The GOF is similar but the results are completely different. All p-values (except t-1 lags) are now > 0.95. Could this be correct or is there something incorrectly specified in the third model? Does this result invalidate the results from the first two models? Array
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