session time and land-use composition

[JMLBDHR]

Hi all,

I am using ctsem to investigate how environmental variables (e.g., air quality, noise, tree cover density, and surrounding land-use composition) predict arousal, measured via electrodermal activity (EDA).

The data have a nested structure: each participant completed 25 sessions, each lasting 24 hours. The time intervals between sessions vary (sometimes short, sometimes long). Additionally, variables were measured at different temporal resolutions (e.g., some every minute, others every 30 minutes).

I have three questions:

1. Time specification across sessions: Should the time variable reset to 0 at the beginning of each session, or should time increase continuously across sessions? If resetting time is recommended, would it be appropriate to modify the subject identifier to include session information (e.g., id = 1_1 for subject 1, session 1)?
2. Including land-use composition variables: What is the correct way to include these land-use proportion variables in a ctsem model? Currently, I omit one category to avoid multicollinearity and include the remaining categories as time-dependent predictors. Is this an appropriate approach, or would a compositional data treatment (e.g., log-ratio transformations) be more suitable in this context?
3. Specification of the outcome variable: Is it appropriate to specify electrodermal activity as both a latent and a manifest variable, with the factor loading fixed to 1?

Any advice or references would be greatly appreciated.

Thank you!

[cdriveraus]

1. Yes properly accounting for the nesting structure with more than 1 level of nesting is tricky -- would be possible by allowing time varying parameters but this would really complicate things. Best approach, so long as you have adequate data per session, will probably be to treat each session as independent, and if significance of moderation effects is a core issue, consider putting estimates into an lmer model or something in a 2 step procedure.

2. Re the covariates, they sound more like time independent predictors to me -- they are just static across time yes? How much data do you have per session though? If you have something like 24h of monitoring data, then it would be simpler and better to estimate the system separately for each session, compile the estimated parameters and sessionid into a data.frame, and use lmer or similar for estimating covariate relationships. If you don't have adequate data per session, then use them as time independent predictors that moderate any / all aspects of the system you are interested in.

3. yes!

[JMLBDHR]

Hi Charles,

thanks a lot for your help!

1. If I reset time to 0 for each session, the model fails to converge (1st pass optimization / carefulfit: Progress est. = 5.88%, LPchange = 3100, Iter = 640, LP = -282379.346…, worseCount = 20, Converged — count of non-improving iterations exceeded.) Each session has >200 observations. If I do not reset time to 0 for each session, I don't get the error message and the model converges properly. Would it therefore also make sense to let the model “figure out” that sessions are independent by itself—i.e., keep a continuous time variable where within-session steps are ~1 minute, but between sessions there are larger gaps (e.g., a jump of ~400 minutes)? I also z-standardized all variables, except for the Land-use proportions.
2. No they are not static across time, that's the interesting point. During each 24-hour session, all variables are continuously measured, resulting in time-dependent predictors. After merging the outcome and predictors into one table, I have roughly 200 time points per session, with each variable changing over time.

[cdriveraus]

1. you need 1 measurement (row of data) per time value per subject (whether that is individual / session or whatever you want). the starting time is not particularly relevant, though one way you could approach the multiple sessions thing would be to assume the parameters are constant for the individual, then have a long time interval between sessions, which would serve to 'reset' the process.
2. I see -- but then perhaps they are better conceptualised as ongoing processes and included in the model more explicitly -- not just as an impulse on the system at the moment they occur, but as continual forces that exert influence whether or not they are measured. for this you need to model each of them as an additional latent process.