Censored Ordinal Outcome in blrm

Hi all,
I came across this wonderful post (https://hbiostat.org/r/examples/blrm/blrm#censored-data) by @f2harrell on how interval-censored data can be handled by the PO model.

However, I am still not quite sure if I understand the following scentence.
β€œIn full-likelihood models such as our extended PO model, censored data are easily handled. One just has to compute the contribution to the log-likelihood for each observation from the information it provides.”

I would like to ask if anyone can share your insight about how exactly Ocens (or blrm) handles the interval-centered data and how it contributes to the overall estimates

Many thanks,

As an analogy considered a right-censored event time variable Y. When Y is completely observed (not censored) and has a value of y, the likelihood component is the probability density function evaluated at y. When Y is right censored at c the likelihood component is the cumulative probability that Y >= c. Same idea for interval censoring. For the proportional odds model the probability of being in an interval is the difference in two cumulative probabilities. Ocens sets up so that the Stan code for the likelihood does all this.

Dear @f2harrell ,
Thank you so much for this explanation. It helps a lot

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