Suppose that we have fitted a multilevel model over data from multiple groups called A, B, C and D and that we’re trying to estimate the population means for these 4 groups. For example, this could look something like the figure below.
Now, suppose we also have information from the literature on a fifth group E, for which the sample mean mₑ, standard deviation sₑ and distribution are known. The distribution is a normal distribution. Could this information be added to the model in a way that E shows up in the posterior too?
I think that it would technically be possible by generating a bunch of samples with
Normal(mₑ, sₑ), but I wonder if this actually makes sense.