I have a dataset in which each participant has to repeatedly solve a task (2 alternative forced choice, participants have to infer a rule to discriminate between them).

In order to finish a given “stage”, they have to have 6 consecutive successes .

If they manage, they enter a new stage (different rule determining which choice is right).

If they don’t manage to get 6 consecutive within 50 trials the experiment stops.

This is tricky to model (for me) because:

- the k “consecutive” successes: not a geometric (k successes), nor a negative binomial (“successive”). And ideed the fit is terrible. I’d need something more like this: https://www.ism.ac.jp/editsec/aism/pdf/046_1_0193.pdf
- the data is censored within “stage” (right censoring when the participants reach 50 trials)
- the data is censored between “stages” (some participants don’t reach the higher stages).

Are there similar worked out examples?