DSEM, VAR(1)>1
Message/Author
 AKH posted on Wednesday, January 22, 2020 - 3:10 am
Hi Drs. Muthen and Dr. Asparouhov,

I am currently applying DSEM for a 40 years time series. I estimate a twolevel (random intercept/slope) model, where the within-person level contains the simplest form of a VAR(1) effect.

I expect the VAR(1) effect to exceed 1 for many people, because of an exponential data-generating process. How well can DSEM in MPlus estimate these kinds of processes?

Thank you very much in advance!
 Tihomir Asparouhov posted on Wednesday, January 22, 2020 - 9:10 am
I would recommend that you model Log(Y) instead of Y and if there is a substantial trend you should model the trend and switch to RDSEM where
Y = Trend +Yres
where
Yres(t)=r*Yres(t-1)+e
and
Trend= a+b*t+c*Exp(t) (or something similar)

To do that kind of model in Mplus you would use
Y^ on Y^1;
Y on T ExpT;
where
define: ExpT=Exp(t)

You might find this useful

All of the regression coefficients can be random /cluster specific in the two-level settings.
 AKH posted on Thursday, January 23, 2020 - 8:55 am
Dear Timohir,

great, thank you very much! That helps.
 AH posted on Sunday, May 24, 2020 - 4:53 am
Dear Drs Muthén and Asparouhov,

a related question. I calculated a two level DSEM for a time series of about 30 years. The lagged variable was log-transformed beforehand. The model converged, and I looked at the distribution of the individual estimates of phi (my random AR coefficient). About two percent of all 3500 individuals in the sample displayed a random AR coefficient > 1, which I expected.

In Appendix D of your paper (Asparouhov, Hamaker, Muthen, 2018) you said that non-stationarity can yield biased subject-specific mean and variance estimates. Is this the matter only on the individual level, in this case for the 2 percent with AR>1, or does it also influence the average AR estimate for my entire sample in a way that I cannot trust the results anymore?

Hence, my question. At which expected proportion of AR>1 in the random effects should I switch to RDSEM? If I think there might be any person displaying it? Or 2%, 10%, 50% of persons in the sample? I am somewhat confused about what counts as a 'substantial' trend that then needs to be modelled in RDSEM instead of DSEM.

Thank you very much.
 Tihomir Asparouhov posted on Tuesday, May 26, 2020 - 11:17 am
The DIC criterion can be used to compare the RDSEM and DSEM models (and even the standard two-level model when it is setup as DSEM/RDSEM model with AR fixed to 0, see Table 5).

If the trend model doesn't have random effects you can try adding random effects for the trend. Another possibility is to add a quadratic term for trend. You might want to do all that in a two-level setup first (no ar coefficients). We generally try to resolve large AR coefficients. One thing to keep in mind is that sometimes the posterior distribution of the AR coefficient exceeds 1, while the actual point estimate is less than 1 - we don't really consider that a major problem and it does tend to happen fairly often as the models get more flexible and the posterior distributions of the random effects get wider.
 AH posted on Thursday, May 28, 2020 - 2:32 am
Dear Dr. Asparouhov,

thank you very much for your help!