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Abstract:
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MCMC has made Bayesian analysis feasible for complex hierarchical models, but the literature about variance parameters is somewhat sparse. This paper uses simulation experiments to compare three point estimators, the posterior mode, median, and mean, for variance-structure parameters in hierarchical models. The comparisons are made for three parameterizations of the variance structure, in terms of precisions, standard deviations, and variances. We first compare linear regression, where fairly explicit expressions are possible, then three more complex models: the crossed random effects model, the conditional autoregressive model (CAR) with two neighbor relations, and smoothed ANOVA. We illustrate the results using periodontal data. The surprising finding is that the posterior mode is, on the whole, the best point estimator regardless of the variance structure's parameterization.
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