A model is hierarchical (random coefficient) if the paramters in a GLM (General Linear Model) are themselves structured to be having a prior distribution involving parameters of its own (hyper parameters).
In a practical situation, this means that the posterior probability (or posterior odds) are a function of (prior odds) x (marginal distribution of hyper parameter1 – parameter describing centrality of the distribtion ) x (marginal distribution of hyper parameter2 – parameter describing the variability of the distribution).
There are no closed form solution for the calculation of posterior odds.
So the estimation procedures involve simulation based calculations:
– in the first step, we use estimation of a the basic GLM model parameters using existing data in the usual sense of the estimation
– in the second step, we use estimation of the hyper parameters based on outputs of first step which provides