TY - JOUR
T1 - Objective Bayesian hypothesis testing and estimation for the intraclass model
AU - Zhang, Duo
AU - He, Daojiang
AU - Sun, Xiaoqian
AU - Lu, Tao
AU - Wang, Min
N1 - Funding Information:
The authors thank the editor, an associate editor and one referee for their detailed and constructive comments, which have led to a significant improvement of the manuscript. This work was based on the first author's dissertation research which was supervised by the corresponding author. MW and DZ initiated and carried out the study. MW and DZ drafted the manuscript. DH, TL, and XS participated in the discussion and proofread the manuscript. All authors read and approved the final manuscript.
Publisher Copyright:
© 2018, © East China Normal University 2018.
PY - 2018/1/2
Y1 - 2018/1/2
N2 - The intraclass correlation coefficient (ICC) plays an important role in various fields of study as a coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICC in the context of normal linear regression model. We first derive two objective priors for the unknown parameters and show that both result in proper posterior distributions. Within a Bayesian decision-theoretic framework, we then propose an objective Bayesian solution to the problems of hypothesis testing and point estimation of the ICC based on a combined use of the intrinsic discrepancy loss function and objective priors. The proposed solution has an appealing invariance property under one-to-one reparametrisation of the quantity of interest. Simulation studies are conducted to investigate the performance the proposed solution. Finally, a real data application is provided for illustrative purposes.
AB - The intraclass correlation coefficient (ICC) plays an important role in various fields of study as a coefficient of reliability. In this paper, we consider objective Bayesian analysis for the ICC in the context of normal linear regression model. We first derive two objective priors for the unknown parameters and show that both result in proper posterior distributions. Within a Bayesian decision-theoretic framework, we then propose an objective Bayesian solution to the problems of hypothesis testing and point estimation of the ICC based on a combined use of the intrinsic discrepancy loss function and objective priors. The proposed solution has an appealing invariance property under one-to-one reparametrisation of the quantity of interest. Simulation studies are conducted to investigate the performance the proposed solution. Finally, a real data application is provided for illustrative purposes.
KW - Bayesian reference criterion
KW - Intraclass correlation coefficient
KW - hypothesis testing
KW - intrinsic discrepancy
KW - intrinsic estimator
KW - reference priors
UR - http://www.scopus.com/inward/record.url?scp=85070442452&partnerID=8YFLogxK
U2 - 10.1080/24754269.2018.1481586
DO - 10.1080/24754269.2018.1481586
M3 - Article
AN - SCOPUS:85070442452
VL - 2
SP - 37
EP - 47
JO - Statistical Theory and Related Fields
JF - Statistical Theory and Related Fields
SN - 2475-4269
IS - 1
ER -