Japan Women’s University Journal: The Graduate School of Integrated Arts and Social Sciences, 2016, March, No. 22, 153-169.
Hierarchical modeling for Bayesian approach in
generalizability theory
Yasuharu Okamoto
Abstract
A natural correspondence between generalizability theory and Bayesian data analysis has been observed.
To conduct Bayesian data analyses, explicit stochastic models of generalizability theory were presented with hierarchical priors,
which represent random effects, and algorithms of Markov chain Monte Carlo (MCMC)
for Bayesian analysis were proposed. To obtain stable posterior distributions of variances,
inverse-gamma distributions of variances were employed.
The proposed algorithms treat one-facet and two-facet designs whose facets are assumed to be random effects.
Successful applications of the proposed Bayesian methods to hypothetical data sets indicate
the usefulness and importance of the proposed Bayesian approach in generalizability theory.
Key words: generalizability, reliability, Bayesian analysis, MCMC, hierarchical model
Full Text
(link to JWU's repository),
Full Text (link to the pdf file)
Programs developed to prepare the paper
Two programs have been developed. They have been compressed into zipped folders, NiVaried.zip and NiNoVaried.zip . If they are unzipped, they can be opened by Visual Studio 2015. The document ReadMe.pdf shows how to use them.
Program NiVaried was developed to analyze data of one-facet design. One facet-design uses the following structural model of ANOVA
Set
then we have
Equation (3) is derived mathematically, without using decomposition of Sum of Squares (SS).
To estimate generalizability coefficient, the program uses Equation (3).
Program NiNoVaried was developed to analyze data of two-facet design, which uses the following structural model of ANOVA
Set
then we have
Equation (8) is also derived mathematically, without using decomposition of SS.
To estimate generalizability coefficient, the program uses Equation (8).
For the details, see the paper.