Best way to model a binary, co-occurring event (binge episodes) affecting a continuous process?

[steffhart]

Hello!

First off, thanks for ctsem and the supporting papers/tutorials, which really helped me get into continuous-time thinking!

I'm currently working on a research question about the effects of binge-eating episodes on momentary negative affect, and a continuous-time model seems like the perfect fit. The ambulatory assessment data contain around 130 participants, 20–25 prompts per participant across 5 days, with a mean interval of ~3h. My outcome is negative affect (NA). The binge episodes (and their timing) were recorded on a continuous scale, but they were heavily zero-inflated, so I recoded them into a binary 0/1 indicator using prespecified clinical thresholds.
What I want to know is whether a binge changes the post-binge NA trajectory beyond the ordinary auto-effect, in other words, whether regulation is faster than usual in the window after a binge (previous discrete models implicate this but ignored regression-to-the-mean effects). I'm currently trying to figure out how best to model that.

My first instinct was a TDpred impulse for the binges: it's the sparsest option, captures their immediate impact, and fits the data really well. But since binges are associated with elevated NA, they aren't really external shocks, so I suspect the impulse effect would mostly just absorb the contemporaneous binge–NA association (or am I missing something?).

So I'm weighing a few options and would really appreciate some advice, because I'm not sure which is best:

1. Dissipative impulse. This still has the same binge-NA association problem, and I'm also worried it won't stabilize: with ~500 episodes and 3000 measurements, there's often little recovery time between them, so the process rarely returns to baseline.
2. Moderator on the NA auto-effect for the a post-binge window (e.g., 3h) by adding a "empty" measurement cell including information about the predictor, analogous to the time-dependent moderator in the couples tutorial but on the diagonal (auto_base + auto_mod*BingeWindow). This seems to target the rate of return directly, but I'm unsure whether moderating the auto-effect could cause estimation problems, since I'd be overwriting the default transformation of the auto effect.
3. Binge as part of a bivariate process (a second process driven by the binary indicator, coupled through the drift matrix) rather than an exogenous input. This is of course better in principle, since the binge is endogenous, but I don't know whether I have enough data for it. I haven't figured out whether there is a way of integrating the zero-inflated continous data.

I appreciate any tips and there's probably an even better approach I haven't thought of.

Thanks so much!
Steffen

Code:

#Impulse Model:
ct_model <- ctModel(type = 'ct',
manifestNames = "negAffect",
latentNames = "negAffect",
time = 'continuous_time',
id = 'id',
LAMBDA = matrix(1, nrow = 1, ncol = 1),
MANIFESTMEANS = 'B||TRUE',
MANIFESTVAR = 'residualSD',
T0MEANS = 'initialAffect||TRUE',
CINT = 0,
DRIFT = 'tendency_NA||TRUE',
DIFFUSION = 'systemNoise',
TDpredNames = 'Binge_Imp',
TDPREDEFFECT = 'bingeImpulse' )

#Disspiative:
ct_model <- ctModel(type = 'ct',
manifestNames = "negAffect",
latentNames = c("negAffect", "Binge),
time = 'continuous_time',
id = 'id',
LAMBDA = matrix(c(1,0), nrow = 1, ncol = 2),
MANIFESTMEANS = matrix(c('B||TRUE'),nrow=1, ncol=1),
MANIFESTVAR = matrix(c('residualSD'), nrow=1, ncol=1),
T0MEANS = matrix(c('initialAffect||TRUE',0), nrow=2, ncol=1),
T0VAR = matrix(c('T0sd_NA', 0,0,0), nrow = 2, ncol = 2),
CINT = 0,
DRIFT = matrix(c('tendency_NA||TRUE', 0,'bingeEffect', 'binge_Regulation'), nrow=2, ncol=2), DIFFUSION = matrix(c('systemNoise',0,0,0),nrow=2, ncol=2),
TDpredNames = 'Binge_Imp',
TDPREDEFFECT = matrix(c(0, 1), nrow=2, ncol=1))

#Moderator:
ct_model <- ctModel(type = 'ct',
manifestNames = "negAffect",
latentNames = "negAffect",
time = 'continuous_time',
id = 'id',
LAMBDA = matrix(1, nrow = 1, ncol = 1),
MANIFESTMEANS = 'B||TRUE',
MANIFESTVAR = 'residualSD',
T0MEANS = 'initialAffect||TRUE',
CINT = 0,
DRIFT = 'tendency_NA+tendency_post*postBinge’,
DIFFUSION = 'systemNoise',
TDpredNames = c('Binge_Imp','postBinge'),
TDPREDEFFECT = c('Binge_Impulse', 0),
PARS=c('tendency_NA','tendency_post') #extra params )

#Transform for Pars (?)
ct_model$pars$transform[ct_model$pars$param == "tendency_NA"] <- "-log(exp(-1.5 * param) + 1)"

[cdriveraus]

This gets a bit complicated I think honestly! To do it really properly you need to consider that the regulation of NA may anyway differ based on the level of NA itself, and then ask whether allowing this to be additionally moderated by binge is improving the model. I gave it a few iterations with some ai help, see if this makes sense to you:

binge_ctsem_zero_inflated.html

[cdriveraus]

btw don't treat everything in that as carefully vetted by me, but in general it looks roughly appropriate and a useful starting point.