I assume you impose measurement invariance over the time points. You can then fix the factor mean at time 1 to zero (this is needed to set the metric of the factor) which means that the factor mean at time 2 expresses the difference.
Hello, Thank you, the above description makes sense for latent variables, when measurement invariance is imposed and time 1 factor mean is fixed to 0. If possible, I'd like to get clarification on how Mplus treats an autoregressive model versus a latent change score model, for an observed variable.
The reason is because I ran two models, an autoregressor model and latent difference score model, both yielded identical values.
MODEL 1 (autoregressor approach) XTime2 on Xtime1 AT1 BT1 CT1; (X variables are observed. A B C are three latent variables at time 1)
MODEL 2 (LDS approach) XTime2 on XTime1@1; Xdiff by XTime2@1; Xdiff on XTime1*; XTime1*; XTime2@0; Xdiff*; Xdiff on AT1 BT1 CT1
Both models yield identical values. My confusion comes from reading articles that say that autoregressive modeling evaluates inter-individual changes, whereas LDS modeling is a better approach because it evaluates both inter- and intra-individual differences. This description doesn't hold if both models are identical in Mplus. So I wonder how Mplus treats an autoregressive model, even for an observed variable (so I haven't fixed the mean to zero or imposed measurement invariance). Any insight on this is greatly appreciated!