# How to explain negative residual covariance in cross-lagged SEM?

Question in short:

If I see a positive (significant) residual covariance between two endogenous variables in a cross-lagged SEM for the first lag and a negative (significant) residual covariance for the second lag, how can I explain that descriptively to the audience? I am particularly interested in describing why we see such positive and negative residual covariances from the data itself. Could you please suggest?

Details of my scenario:

I have two categorical (binary) endogenous variables emp and SA at three time points, 1, 2, and 5. I have run the following cross-lagged SEM with fixed effects age and sex:

full_clpm1 <- '

# synchronous covariances

SA1 ~~ emp1

SA2 ~~ emp2

SA5 ~~ emp5

# autoregressive + cross-lagged paths

emp1 ~ AGE + sex

SA1 ~ AGE + sex

emp2 ~ AGE + sex + emp1 + SA1

SA2 ~ AGE + sex + emp1 + SA1

emp5 ~ AGE + sex + emp1 + SA1 + emp2 + SA2

SA5 ~ AGE + sex + emp1 + SA1 + emp2 + SA2

'

# fit the model

fit1 <- sem(full_clpm1, data=dp)
summary(fit1)


I got the following results for the residual covariances and wondering why the first covariance is positive and the second one is negative (both statistically significant):

I want to know what this means and how I can show descriptively why the second time point had negative residual covariance between emp2 and SA2. I already tried separate probit regressions on emp2 and SA2 and found the correlations of the residuals from these two non-simultaneous regression models. But that correlation appears to be positive (and very small). So, could you suggest me a way to show the reason of this negative residual covariance descriptively for the sake of discussion? I am wondering there must be some way of explaining this negative residual covariance descriptively.

Disclaimer: Cross-posted from https://groups.google.com/forum/#!topic/lavaan/4H38vTlUcL4 as suggested there.