Abstract:
Multilevel modeling is a modern approach to deal with hierarchical or a
nested data structure which can assess the variability between clusters.
Bayesian Markov Chain Monte Carlo (MCMC) methods of estimations are
advanced methods applicable for estimating multilevel models. However,
these estimation methods are not as yet tested to identify its’ performances
as well as the properties associated with these estimation methods.
This study targets to conduct a comparison of Bayesian MCMC methods
which are developed for multilevel models where the response is normally
distributed. The comparison is based upon extensive simulations and an
application to a real-life dataset. The performance of Gibbs sampling (GS)
and Metropolis Hastings (MH) methods are compared using a simulation
study and additionally the factors which can affect the performance of
both MCMC methods are identified. Practicality of these methods in real
world scenario is confirmed through the application of MCMC method to a
dataset. In the simulations though the Metropolis Hastings (MH) shows
slightly better performance than Gibbs, there is no evidence to indicate
that significant differences exist between these methods except for small
samples where MH is superior. The results from the example are not as
clear as from the simulations.
