Model determination for the variance component model using reference priors |
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| Affiliation: | 1. School of Economics, Business Administration and Accounting, University of São Paulo, Brazil;2. Production Engineering Department, Polytechnic School, University of São Paulo, Brazil;3. Universidade Federal de Alfenas, Instituto de Ciência e Tecnologia, Brazil;4. Production Engineering Department, Campus Itapeva, São Paulo State University (UNESP), Brazil;1. Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94550, United States;2. Nevada Water Science Center, U.S. Geological Survey, Boulder City, NV 89005, United States;3. Department of Natural Sciences, Northwest Missouri State University, Maryville, MO 64468, United States;4. Division of Earth and Ecosystems Sciences, Desert Research Institute, Las Vegas, NV 89119, United States;5. Division of Hydrologic Sciences, Desert Research Institute, Las Vegas, NV 89119, United States;6. School of Life Sciences, University of Nevada, Las Vegas, NV 89154, United States;7. Biology Department, Indiana University Northwest, Gary, IN 46408, United States;8. Department of Microbiology, Southern Illinois University Carbondale, Carbondale, IL 62901, United States |
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| Abstract: | For the balanced variance component model when the inference concerning intraclass correlation coefficient is of interest, Bayesian analysis is often appropriate. However, the question remains is to choose the appropriate prior. In this paper, we consider testing of the intraclass correlation coefficient under a default prior specification. Berger and Bernardo's (1992) On the development of the reference prior method. In: Bernardo, J.M., Berger, J.O., Dawid, A.P., Smith, A.F.M. (Eds.), Bayesian Statist. Vol. 4. Oxford University Press, London, pp. 35–60 reference priors are developed and are used to obtain the intrinsic Bayes factor (Berger and Pericchi, 1996) The intrinsic Bayes factor for model selection and prediction. J. Amer. statist. Assoc. 91, 109–122 for the nested models. Influence diagnostics using intrinsic Bayes factors are also developed. Finally, one simulated data is provided which illustrates the proposed methodology with appropriate simulation based on computational formulas. Then in order to overcome the difficulty in Bayesian computation, MCMC method, such as Gibbs sampler and Metropolis–Hastings algorithm, is employed. |
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