I wanted to know if it is possible to use predictors that came from an Bayesian estimation with their specific posterior distributions instead of their standard error.
The idea behind this question: I’m thinking about how to best using all my data I collected for a new measurement instrument - call it X. I used IRT to get item parameters. To model these parameters I had a bigger and more heterogene sample of size A.
Now I want to do a regression on the skill of a subsample B. The subsample are students of the corresponding topic. The sample A additionally holds data from people who are not studying this subject and those who are teaching this subject but only regarding instrument X. For the subsample I have addional data - call it Y and Z. Y can be assumed to be identical distributed over the whole population (say all adults, e. g. fluid intelligence). Z probably is differently distributed over subsets (e. g. chemistry knowledge).
So my first idea was to model the item parameters in the heterogeniouse group and use them in the latent regression of the subset (with se or distribution). The other idea was to use the whole sample and specify missiongs for the additional people not part of subset B. But there I’m worried about specifiying a group specific mean for chemistry knowledge for the people who are not studying it when I only have knowledge about the chemistry students. (For intelligence I could assume its the same mean.)
So to come back to my question stated at the beginning. Is it possible to use the whole distribution instead of the se for item parametrs?
And second: Is it a (more) valid way to use there parameters as predictors in the subsample instead of working with missiongs for the whole sample?
(Or is there a way to specify an estimation for mean chemistry skill level for non chemitsry students? My assumption would be the mean is lower so maybe I could work with something like ordinal strzucture?)