Estimation of the Correlation Coefficient for Triangular Contingency Tables under the Bivariate Normal Distribution

Triangular contingency tables are a special class of incomplete contingency tables. Association and independence models are used to analyze such tables. Association models can be described in terms of the association parameters for the analysis of triangular contingency tables having ordered categories. The aim of this study is to show the relation between the association parameters of the uniform association model and the sample correlation coefficient under the structural zeros. For this purpose, a simulation study based on random contingencytables containing structural zeros is performed. Association parameters are estimated under the uniform association models. The samplecorrelation coefficients are computed using these parameter estimates and compared with the population correlation coefficients. It is shown that by using the association parameter estimates under the uniform association model, better estimates can be achieved for the population correlation coefficient in the case of structural zeros.

Keywords:

Triangular contingency tables, Uniform association model Bivariate normal distribution,

PDF

___

Altham, P. M. Quasi-independent triangular contingency tables, Biometrics 31, 233–238, 1975.
Bishop, Y. M. M. and Fienberg. S. E. Incomplete two-dimensional contingency tables, Bio- metrics 28, 177–202, 1969.
Bishop, Y. M, M., Fienberg, S. E. and Holland. P. W. Discrete Multivariate Analysis (Cam- bridge, MA: MIT Press, 1975).
Goodman, L. A. On quasi-independence in triangular contingency tables, Biometrics 35, 651–655, 1979.
Goodman, L. A. The analysis of cross-classified data: Independence, quasi-independence and interactions in contingency tables with or without missing entries, J. A. S. A. 63, 1091–1131, 1968.
Goodman, L. A. Association models and the bivariate normal distribution in the analysis of cross-classifications having ordered categories, Biometrika 68, 347–355, 1981.
Goodman, L. A. The Analysis of cross-classified data having ordered and/or unordered cat- egories: Association models, correlation models,and asymmetry models for contingency ta- bles with or without missing entries, The Annals of Statistics 13 (1), 10–69, 1985.
Goodman, L. A. On quasi-independence and quasi-dependence in contingency tables, with special reference to ordinal triangular contingency tables, J. A. S. A. 89, 1059–1063, 1994.
Mantel, N. Incomplete contingency tables, Biometrics 26, 291–304, 1970.
Sarkar, S. K. Quasi-independence in ordinal triangular contingency tables, J. A. S. A. 84, 592–597, 1989.