I have time-series sensor data from different participants in a repeated experiment. In each run of the experiment, there is either a specific time when the participant has done a certain decision or not (at all). I can read this directly from the data. Now, given that I take all of this data for training and test, I would like to build a time-series dependent model. The model shall give at any time (and with the sensor data at that time) a prediction between 0 and 1, where 0 would mean that the person would not do take decision and 1 that the person takes the decision. I also want to investigate if the model can be improved by including past measurement samples.
What would you recommend for tackling this modeling problem? My first try would be some sort of logistic regression which I train on every time-sample, either with response 1 (after the decision was made) or 0 (before the decision was made). The sensor readings at that time (and possibly in the past) would be the covariates of the linear predictor. I have so far mainly encountered usage of logistic regression in “static” rather than time-series problems. Furthermore, how could I do this in a Bayesian setting? Are there already functions for instance in brms?