On partitioning conditional independence model for three-way contingency tables

Article type: Research Article

Authors: Iki, Kiyotaka | Tahata, Kouji^{; *} | Tomizawa, Sadao

Affiliations: Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, Japan

Correspondence: [*] Corresponding author. E-mail: [email protected]

Abstract: For three-way contingency tables with two ordinal and one nominal variables, this paper shows that (i) the conditional independence model holds if and only if conditional covariance between ordinal variables at each level of the nominal variable equals zero and the heterogeneous linear-by-linear association model holds, (ii) the conditional independence model holds if and only if an average conditional covariance between ordinal variables across levels of the nominal variable equals zero and the homogeneous linear-by-linear association model holds, and (iii) the likelihood ratio test statistic for the conditional independence model is asymptotically equivalent to the sum of the likelihood ratio test statistic for the decomposed models.

Keywords: Conditional independence, correlation, covariance, decomposition, likelihood ratio statistic, linear-by-linear association, separability

DOI: 10.3233/MAS-2011-0194

Journal: Model Assisted Statistics and Applications, vol. 6, no. 4, pp. 349-355, 2011