Ioannis Ntzoufras

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Bayesian Estimation of Unrestricted and Order-Restricted

 Association Models for a Two-Way Contingency Table

 

G. Iliopoulos, M. Kateri  

&

  I. Ntzoufras

Department of Statistics and Insurance Science,

University of Piraeus,

Piraeus, GREECE;

e-mails: geh@unipi.gr, mkateri@unipi.gr

 

Department of Statistics,

Athens University of Economics and Business,

Athens, GREECE;

e-mail: ntzoufras@aueb.gr.

 

First Draft 29/3/2006; Latest version 4/7/2007

Computational Statistics and Data Analysis, 51, 4643-4655, 2007.

 

ABSTRACT

In two-way contingency tables analysis, a popular class of models for describing the structure of the association between the two categorical variables are the so called ``association'' models. Such models assign scores to the classification variables which can be either fixed and prespecified or unknown parameters to be estimated. Under the row-column (RC) association model, both row and column scores are unknown parameters without any restriction concerning their ordinality.  It is natural to impose order restrictions on the scores when the classification variables are ordinal.  The Bayesian approach for the RC (unrestricted and restricted) model is adopted. MCMC methods are facilitated in order the parameters to be estimated. Furthermore, an alternative parametrization of the association models is proposed. This new parametrization simplifies computation in the MCMC procedure and leads to a natural parameter space for the order constrained model. The proposed methodology is illustrated via a popular dataset. 

Keywords:  Association models, ordinal classification variables, MCMC methods.

 Download:

  • Paper from journal's site.
  • R functions for RC unrestricted and order restricted models .
  • Short Manual for R functions.


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Last revised: 23/11/2011