Latent Difference Score Model
Message/Author
 Maren Lotz posted on Thursday, November 10, 2016 - 3:49 am
Hello,

in our Survey we have two timestamps (pre- and posttest) and measure in each the economic knowledge by 30 dichotomous items.

We now want to compute the latent difference score between these two timestamps.

Is there any example syntax for a latent difference score model? I cant't find it in the user guide.

Thank you
 Bengt O. Muthen posted on Thursday, November 10, 2016 - 12:19 pm
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.
 Kyle Levesque posted on Tuesday, June 12, 2018 - 8:27 am
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!
 Bengt O. Muthen posted on Tuesday, June 12, 2018 - 5:49 pm
This question is suitable for SEMNET. See also the Grimm,Ram, Estabrook book on growth modeling.