I have a hierarchical linear model I've applied to a dataset in which the effect of a factor on my outcome measure can vary for different people.
Say I have a new individual for whom I have some data. I want to obtain properly shrunk estimates of the effect of this factor for this individual given my hierarchical model, but without refitting the model including the new data.
A hypothetical example:
Say I'm trying to estimate the batting average for different baseball players, and I think that some of them are more or less affected by the cloud cover on a given day.
I've fit my model, and now I have some data for a new batter. I want to be able to quickly estimate the effects of cloud level for this individual, using the hierarchical model but without without having to refit the model with the new batter's data.
What approaches are there for doing this? I know it won't be strictly correct given that the new data should theoretically affect my hierarchical model estimates, but I'm wondering if there are relatively simple ways to assume my hierarchical model parameters as fixed and combine them with the new data to obtain somewhat "properly" shrunk estimates.
