Open Science Research Excellence
%0 Journal Article
%A Satoshi Usami
%D 2009 
%J  International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
%B World Academy of Science, Engineering and Technology
%I International Science Index 30, 2009
%T Applying Gibbs Sampler for Multivariate Hierarchical Linear Model
%V 30
%X Among various HLM techniques, the Multivariate Hierarchical Linear Model (MHLM) is desirable to use, particularly when multivariate criterion variables are collected and the covariance structure has information valuable for data analysis. In order to reflect prior information or to obtain stable results when the sample size and the number of groups are not sufficiently large, the Bayes method has often been employed in hierarchical data analysis. In these cases, although the Markov Chain Monte Carlo (MCMC) method is a rather powerful tool for parameter estimation, Procedures regarding MCMC have not been formulated for MHLM. For this reason, this research presents concrete procedures for parameter estimation through the use of the Gibbs samplers. Lastly, several future topics for the use of MCMC approach for HLM is discussed.

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