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.