DEPARTURE FROM QUASI-UNIFORM ASSOCIATION MODEL IN ORDERED SQUARE CONTINGENCY TABLES

Yıl 2021, Cilt: 7 Sayı: 2, 79 - 83, 31.12.2021

Serpil Aktaş , Ayfer Ezgi Yılmaz

https://doi.org/10.22531/muglajsci.960976

Öz

The Uniform Association (UA) and Quasi-Uniform Association (QUA) models are used for analysis of two-way square contingency tables with ordered categories. When the QUA model does not fit the data, one wants to measure the degree of departure from the quasi-uniform association model. The degree of the departure from the model is calculated by using
the power divergence statistics. In this study, as an alternative to measures in the literature, a measure to estimate the degree of departure from the QUA model is suggested. This suggested measure allows us to compare the several R×R tables in terms of the departure from the model. The measures are compared by the simulation study and discussed by three unaided distance vision data. 

Anahtar Kelimeler

Square contingency tables, Ordinal categories, Uniform association model, Quasi-uniform association model, Kullback-Leiber divergence

Kaynakça

• Altun, G., "Quasi Local Odds Symmetry Model for Square Contingency Table with Ordinal Categories", Journal of Statistical Computation and Simulation, 89(15), 2899-2913, 2019.
• Altun, G. and Aktaş, S., “Measures of departure from marginal homogeneity model in square contingency tables”, İstatistikçiler Dergisi: İstatistik ve Aktüerya, 11(2), 93-108, 2018.
• Goodman, L.A., "Simple Models for the Analysis of Association in Cross-Classifications having Ordered Categories", Journal of the American Statistical Association, 74, 537-552, 1979.
• Tomizawa, S., "The Decomposition of a Quasi-uniform Association Model and Its Application to the Analysis of British Occupational Mobility Table Data", Behaviormetrika, 17(27), 115-121, 1990.
• Kullback, S., Information Theory and Statistics, Dover Publications, New York, 1996.
• Tomizawa, S., "Two Kinds of Measures of Departure from Symmetry in Square Contingency Tables having Nominal Categories", Statistica Sinica, 4, 325-334, 1994.
• Tomizawa, S., Seo, T. and Yamamoto, H., "Power-divergence-type Measure of Departure from Symmetry for Square Contingency Tables that have Nominal Categories", Journal of Applied Statistics, 25(3), 387-398, 1998.
• Miyamoto, N., Kato, T. and Tomizawa, S., "A Measure of Departure from Diagonals-parameter Symmetry based on Association Measure for Square Contingency Tables", Journal of Statistics: Advances in Theory and Application, 3(1), 1-15, 2010.
• Cressie, N.A.C. and Read, T.R.C., "Multinomial Goodness-of-fit Tests", Journal of the Royal Statistical Society Series, B46, 440–464, 1984.
• Patil, G.P. and Taillie, C., "Diversity as a Concept and its Measurement", Journal of the American Statistical Association, 77, 548-561, 1982.
• Read, T.R.C. and Cressie, N., Goodness-of-fit Statistics for Discrete Multivariate Data, Springer, New York, 1988.
• Sgarro, A., "Informational Divergence and the Dissimilarity of Probability Distributions", Calcolo, 18(3), 293–302, 1981.
• Matusita, K., "On the Estimation by the Minimum Distance Method", Annals of the Institute of Statistical Mathematics, 5, 59-65, 1954.
• Matusita, K., "Decision Rules, based on the Distance, for Problems of Fit, Two Samples, and Estimation", The Annals of Mathematical Statistics, 26(4), 631-640, 1955.
• Yamamoto, K., Miyamoto, N., Tsuboi, H. and Tomizawa, S., "Distance Measure of Departure from Symmetry for Square Contingency Tables with Nominal Categories", International Journal of Pure and Applied Mathematics, 48:4, 483-489, 2008.
• Beh, E.J., "Simple Correspondence Analysis: A Bibliographic Review", International Statistical Review, 72(2), 257-284, 2004.
• Stuart, A., "A Test for Homogeneity of the Marginal Distributions in a Two-way Classification", Biometrika, 42, 412-416, 1955.
• Stuart, A., "The Estimation and Comparison of Strengths of Association in Contingency Tables", Biometrika, 40, 105-110, 1953.
• Tomizawa, S., "Three Kinds of Decompositions for the Conditional Symmetry Model in a Square Contingency Table", Journal of the Japan Statistical Society, 14(1), 35-42, 1984.