Theory of Probability and Mathematical Statistics
On modeling the correlation as an additional parameter in random effects model
R. N. Muhumuza, O. Bodnar
Link
Abstract: In this paper, we develop objective Bayesian inference, i.\,e., Bayesian procedures based on non-informative priors, for the parameters in a generalized marginal random effects model where the correlation between random effects is introduced as an additional model parameter. This approach provides a generalization of the classical random effects model based on the assumption of normality and on the assumption that the random effects are independent. Assuming a generalized marginal random effects model, we derive the closed-form expression of the Fisher information matrix and the analytical expressions of both the Jeffreys prior and the Berger \& Bernardo reference prior. Furthermore, the posterior distributions are obtained and it is shown that the conditional posteriors for the location parameter of the model under the Jeffreys prior and under the Berger \& Bernardo reference prior are elliptically contoured distributed.
Keywords: Non-informative prior, generalized random effects model, meta-analysis, correlation coefficient, elliptically contoured distribution
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