DSEM/Discrete ctSEM vs. Continuous ctSEM

[follhim]

Hello @cdriveraus!

I work in a lab with access to some daily diary data (several standardized prompts within a day, for 30 days). My understanding is that DSEM (Asparahouv) is the gold standard to estimate within-person effects. While I do have access to Mplus, I'm not the biggest fan, as it hinders reproducibility, compared to R (free/open-source).

While looking for DSEM alternatives, I stumbled across ctsem, which has predominantly been used to model temporal intervals as continuous. I've read (briefly) your papers, and most are centered around continuous modeling, but to my understanding, it appears you can treat intervals as discrete in a manner very similar to DSEM.

So I have some questions:

1. Is the discrete modeling approach in ctsem largely equivalent to DSEM in Mplus?
2. Based on my read with your posts on stan discourse and otherwise, I perceive you to advocate for continuous modeling even when timepoints are measured at regular intervals?

Thank you!

[cdriveraus]

dsem in mplus is a common standard in some areas because people are familiar with the way it works and for what it does it does it well. There are things mplus can't do, some of which ctsem can do. There are things ctsem can't do, which mplus can do. 'gold standard' would be to have an appropriate model fitted :) If you a) think your processes continuously interact and exist (rather than suddenly 'jumping' in value at the specific moments you choose to observe) and b) you want to interpret parameter estimates and not just make predictions, then some kind of continuous time approach generally seems more sensible. mplus can, I believe, approximate this by inserting lots of missingness.

the discrete time approach in ctsem is, generally speaking, very similar to what is done in mplus. measurement error often seems ignored when people use mplus (it is modelled by default with ctsem) but I assume you could include this.

[follhim]

Super helpful. I think there is something more appealing, conceptually, about understanding what these panel data represent (which are continuous dynamic processes. So continuous makes sense.

SECOND question:

1. I was approaching using ctsem for daily diary studies, but can it be used for larger panel studies (3 timepoints)?
   I guess in other words, what is the minimum recommended timepoints for ctsem? For DSEM, I know the absolute minimum is 10.

[cdriveraus]

You 'can' fit models to data with only 1 timepoint, if the ctsem model is structured appropriately (i.e., lots of restrictions). In most cases 3 is the bare minimum where it makes any sense, but for 'typical' use cases people want at least 4 to be able to estimate random intercepts, cross effects, system noise etc.

[follhim]

Sorry last question! Is ctsem, then, largely equivalent to the continuous-time residual dynamic structural equation modeling approach in Mplus?

[cdriveraus]

That would be one specific model you can create in ctsem, but the default ctsem model is better thought of as a ct random effects cross lagged panel model with measurement error.

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