Statistical modeling

# Modeling Brainstorming

## Hypotheses

* Broadly, checkin engagement can be modeled as a point process
* Periods of high engagement vs. periods of low/no engagement can be modeled as a regime-switching process
* Regime will likely be correlated with ADL consistency, emotional state, target behaviors, etc.
* I.e. latent "regime" should capture something along the lines of "depressedness"
* Data missing very much not at random (MNAR)
* Time series exhibits auto-correlation both along individual features and engagement (checking in) generally
* Given a regime, checkins can be modeled as a hawkes process (self-exciting point-process).
* Features (eventtypes) that share a parent eventtype will exhibit correlation amongst each other.

## Desired outputs

* overall "how am I doing" measure (regime?)
* imputation (prediction) of unreported values for target behaviors/emotions

## Modeling procedure

* Model a regime-switching process to capture whether or not data is being generated at all
* Within a data generating regime, model a second (i.e. conditional) regime switching process to predict covariates.
* latent regime should be able to predict basically any variable given the others? Or maybe one parent vs. others?