TY - JOUR
T1 - Bayesian test on equality of score parameters in the order restricted RC association model
AU - Oh, Man Suk
N1 - Funding Information:
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( 2010-0010285 ).
PY - 2014/4
Y1 - 2014/4
N2 - In the RC association model for a two-way contingency table, it is often natural to impose order constraints on the score parameters of the row and column variables. In this article, a simple and efficient Bayesian model selection procedure is proposed that simultaneously compares all possible combinations of (in)equalities of successive score parameters in the order restricted RC association model. The method introduces normal latent variables into the model and uses a simple and accurate approximation to the likelihood function so that the full conditional posterior distributions of elements of the parameter are given as truncated normal distributions. The Gibbs sampling algorithm of Gelfand and Smith (1990) is employed to generate samples from the full model in which all the scores are strictly ordered, and posterior probabilities of all possible models are estimated by using the Gibbs output from the full model. A simulation study shows that the proposed method performs well in detecting the true model. Two real data sets are analyzed using the proposed method.
AB - In the RC association model for a two-way contingency table, it is often natural to impose order constraints on the score parameters of the row and column variables. In this article, a simple and efficient Bayesian model selection procedure is proposed that simultaneously compares all possible combinations of (in)equalities of successive score parameters in the order restricted RC association model. The method introduces normal latent variables into the model and uses a simple and accurate approximation to the likelihood function so that the full conditional posterior distributions of elements of the parameter are given as truncated normal distributions. The Gibbs sampling algorithm of Gelfand and Smith (1990) is employed to generate samples from the full model in which all the scores are strictly ordered, and posterior probabilities of all possible models are estimated by using the Gibbs output from the full model. A simulation study shows that the proposed method performs well in detecting the true model. Two real data sets are analyzed using the proposed method.
KW - Contingency tables
KW - Inequality constraints
KW - Markov chain Monte Carlo
KW - Model selection
KW - Ordinal categorical variables
UR - http://www.scopus.com/inward/record.url?scp=84889238840&partnerID=8YFLogxK
U2 - 10.1016/j.csda.2013.11.009
DO - 10.1016/j.csda.2013.11.009
M3 - Article
AN - SCOPUS:84889238840
VL - 72
SP - 147
EP - 157
JO - Computational Statistics and Data Analysis
JF - Computational Statistics and Data Analysis
SN - 0167-9473
ER -