Analysis of the random effects estimator of a hierarchical model with heavy tailed priori distributions
Abstract
Hierarchical Bayesian models are used in data modeling in different areas in which hierarchical structures are reflected through random effects.Usually the Normal distribution is used to model the random
effects. The Inverse-gamma(ε , ε ) distribution is used as prior distribution for scale parameters with very small ε values, this selection has been criticized, some authors comment that unstable posterior distributions can be obtained, which causes not robust inference. Distributions such as half -Cauchy, Scaled Beta2 (SBeta2) and Uniform are considered as alternatives by many authors to model the scale parameter. In the present research work, the behavior of the random effects estimators in a hierarchical model with a Baye- sian approach was examined. It was assumed random effects distribution t-Student and scale parameter distributions half -Cauchy, SBeta2 and Uniform. A simulation study was carry on to evaluate the behavior of the random effects estimators. Based on the obtained results, and under differen scenarios, it was possible to examine the shrinkage of the posterior parameters of the model. We concluded that in presence of atypical values, the shrinkage is lower when the effects are modeled with a t-Student distribution compared with those obtained when a Normal distribution is associated to the random effects, under the same prior distribution for the scale parameter.
Keywords
Bayesian Inference, Hierarchical model, Scale parameter, t-Student distribution
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