When fitting a beta likelihood model with individual random effect for matched pairs before-after measurement, the individuals’ effect estimated skewed in the same way as the outcome.
In particular, the model is of the form
logit(y) = intercept + treatment x time + respondent_id
where respondent_id ~ N(0, 1).
However, y skewed toward 1, and the posterior estimated of repsondent_id is also skewed in the same way as below.
So, there are few issues:
- when interpreting the treatment effect,
respondent_id = 0is not an average individual. - effect size could vary depending the individual starting point
- non-normal random-effect could be a problem with the estimation?
I was thinking to
- consider
respondent_idas fixed-effect (like econometrics’ approach), and report the estimated effect size for the allrespondent_id(~8000 in my data) - or transforming the random effect somehow
Could you recommend how would you aprroach this case?