Identifiability in bivariate process models

[derekasimon]

Hi!

I am currently examining the influence of the situation on personality state changes. Specifically, I am trying to ascertain how best to model situational influences on personality states with two types of models: 1) With the situation as a time dependent predictor influencing personality state dynamics contemporaneously and 2) With the situation as an additional, latent process influencing changes in personality states through cross-effects. Both personality states (i.e., BFI-2) and situation characteristics (i.e., DIAMONDS) are assessed in the same manner on each ESM survey.

From what I have seen so far, the univariate model with the situation as a time dependent predictor is largely outperforming the bivariate model. With this in mind, I was curious if it is possible to also include the same situation variable as a time dependent predictor in the bivariate model to incorporate the contemporaneous effects. So far, this model has not converged (I am using Bayesian, HMC estimation), assumably due to identifiability issues with including the same situation variable as both a latent process and a manifest variable.

If this is not doable, then I think this model-comparison approach between univariate and bivariate models is the correct avenue, but it would be cool to have an even playing field of bivariate models with and without contemporaneous effects operating alongside cross-effects.

P.S. Thank you so much, Charles, for creating this package and for the plethora of papers I have read to help me understand SDE modeling through an SEM framework!

[cdriveraus]

I don't know how you are comparing the models but suspect it's not right. Time dependent predictors are inpulses that influence the latent processes at the moment they are observed, and they do not directly enter the likelihood for the model. In other words, any simple model comparison is comparing models for different data. It would be possible to compare based on something like predictive performance for each process, but would take some figuring out.

The choice to make here is less about model performance and more how you conceptualize situation - are they fleeting things that happen which you want to track the impact of, or is it a constant source of influence which you happen to measure sometimes?

[derekasimon]

Thanks for the response! Right now, I am just looking at the accuracy of predicted personality states for the two models compared to the raw data. I have stayed away from LOO-CV comparisons between the univariate and bivariate models for that exact reason. To clarify, my question is simply examining how best to conceptualize the situation's influence on personality state dynamics, as an impulse or as an additional latent process with constant influence on personality state dynamics, and I thought a model comparison approach (using whatever metric feasible) between models with differing situation parameterization would reveal some important insights. With that, however, I am under the impression that in the bivariate models, I cannot capture both the instantaneous influence of the situation on personality state change (TD pred effect) and its cross-effects. I was motivated by previous DSEM models incorporating both the cross-lagged effects of the situation on the next personality state measurement and the contemporaneous effect of the current situation on current personality state levels. Granted, DSEM is not estimating rate of change, hence why I was wondering if such an implementation of including the situation as an impulse as well as a latent process is doable.

[derekasimon]

Also, the Bayesian models are indeed very slow (~2 weeks to estimate!); however, I am in a fully-Bayesian lab.

[cdriveraus]

Ok, don't understand this business about capturing both instantaneous and cross effects in bivariate, ctsem is very flexible these days, maybe zoom out a little and just describe in more general terms what you would like to achieve?

[derekasimon]

In general, I want to see if we make better personality state predictions if the situation is positioned as a time dependent predictor or if we model its influence through cross-effects as an additional latent process. In saying this, however, I no longer see the need to combine both within one bivariate model, as I would want to separate these to compare them.

My initial desire to do so was from me conflating the cross effects in ctsem with the cross-lagged paths in DSEM models, but in continuous time, the cross effect operates continuously, so I was wrong to think that the "drift_eta1_eta2" path in your 2017 paper was describing an effect between situation at occasion t and personality state at occasion t+1.

[cdriveraus]

Sorry I lost track of this over the Christmas period. To be honest, I don't really understand it as an interesting empirical question, the way you've framed it -- stepping back and thinking in terms of what you'd really like to know about the process (in general terms, not modelling components) would make it easier for me, and I think any readers, to understand :) the discrete time cross effects are analogous to the continuous time ones, but not exactly the same yes.