[elsherbini]

As an example, maybe you want to know if freshmen from different dorms had more or less satisfaction that average, but wanted to deal with the fact that different dorms had different response rates or could even have different reasons for not responding. The fear is that the data are not "Missing Completely at Random," (MCAR) meaning the missingness of the data is correlated with some of your predictors, e.g. freshmen who are too busy having a great time at one dorm, or students who are ultra-depressed at another dorm didn't check their email.

One solution would be to impute your missing data taking into account what data you do have about the missing participants (e.g. maybe dorm, major, gender). In a bayesian context you can include this imputation as part of the model fitting, which means uncertainty gets appropriately added to the results.

This is a good primer on how to handle this using the `brms` package in R:

https://cran.r-project.org/web/packages/brms/vignettes/brms_...