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Abstract:
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We aim to evaluate scale parameter priors in linear mixed effects models for Bayesian prediction. As uncertainties in posterior prediction arise from prior selection and can be exacerbated if based on small samples, we propose mixtures of empirical and vague priors including half student t, inverse gamma, half Cauchy and half normal for scale parameters, and define the empirical prior hyperparameters and mixture weights by control rules of the prior distribution characteristics. The use of mixture priors allows to flexibly tune the influence of both empirical and vague priors given different sample sizes. In addition, the mixture priors and the four single priors are compared in terms of inference on the prior and posterior percentiles to provide general prior recommendation for the scale parameters.
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