I have questions regarding 2 autoregressive models. The first is a 2-lag model with 2 latent constructs. The second is 2-lag mediator model with 3 latent constructs. In consulting my Mplus manual and other postings on this discussion board, I learned that, as a default, Mplus estimates covariances between exogenous variables (my Time 1 variables) and residual covariances between endogenous variables that do not influence any other variables (my Time 3 variables).
My first question is, should I estimate covariances between my Time 2 constructs? If so, why (i.e., why is this not the default in Mplus)?
Second, if the covariances/residual covariances at any time point are non-significant, do you recommend deleting them from the model?
Third, when I do not include covariances between my Time 2 constructs in the mediation model, my 'a' and 'b' paths are significant (p<.001) and mediation is significant (p<.001) according to both bc bootstrap confidence intervals and Dave MacKinnon's distribution of the product confidence interval method. When I allow my time 2 constructs to covary, however, my 'a' path becomes non-significant, and mediation is no longer significant (2 of the 3 covariances are non-significant). Can you offer any insight into this issue? Thanks in advance for your help.
Yes, if it is identified, on the first question. Mplus can't easily see that this is an identified model, so it doesn't free it.
No on the second question. You specify a model you believe in and keep insignificant portions of it.
For the third question, that insignificance is more trustworthy that the significance when leaving out the time 2 residual covariance. There may be remaining misspecifications that would save the day in terms of mediation - look at the modification indices.