Bayesian Hierarchical Modeling of Asymmetric Effect of Autocorrelated Error

Abstract

This study investigates the asymmetric effect of autocorrelated error of hierarchical model via Bayesian paradigm. The study employed full Bayesian experiment by considering the marginal conditional posteriors density of the model parameters estimate. The extreme cases of autocorrelated error were considered by selecting -0.99 and 0.99 for rho.  The seed was set to 12345;   were set at 2.5, 1.5, 0.5; Xs variables were generated using uniform distribution. The number of replications of our experiment was set at 11,000 with burn-in of 1000 which specified the draws that were discarded to remove the effect of the initial values. The thinning was set at 5 to ensure removal of the effect of autocorrelation in Markov Chain Monte Carlo simulation. The study revealed that positive correlation had higher impact than negative correlation when the magnitude is 0.9; whereas at lower correlation, negative correlation had higher impact. The study affirmed improvement in consistency and efficiency on the model parameters estimates.