I am having trouble understanding when it is advantageous or when it is rational to use a hierarchical model set up in Bayesian Analysis. Basically what kinda of data do I have or what kind of analysis do I want to perform that warrants using a hierarchical model set up.
This is my understanding of the set up of his model. There are s prior distributions for θ, each having the same given K value. The ω for each distribution of θ may not be the same, but come from the same distribution for ω. If we are interested in the overall success rate of the drug, we want to look at expected value of ω, which is the mode of all the distributions of θ. (Thus if K is the same for all distributions of θ and ω comes from the same distribution, then all the prior distributions of θ are the same as well).
My question is, why do we need such a complicated model? Can we not just have only one distribution for θ, where instead of θ following a beta distribution, we have it follow a normal distribution. Depending on what we end up for parameters mu and SD, we get almost the same information as before for the overall effect of the drug? Wouldn't (mu, SD) provide almost the same information as (ω, K) for the effectiveness and variability among patients for the drug? Except our model is simpler.