Sains Malaysiana 45(10)(2016): 1573–1578

 

Power Divergence Statistics under Quasi Independence Model for Square

Contingency Tables

(Statistik Pencapahan Kuasa Model Kuasi Ketakbersandaraan untuk Jadual Kontingensi

Segi Empat Sama)

 

SERPIL AKTAŞ*

 

Department of Statistics, Hacettepe University, 06800 Beytepe, Ankara,Turkey

 

Received: 10 May 2015/Accepted: 7 March 2016

 

ABSTRACT

In incomplete contingency tables, some cells may contain structural zeros. The quasi-independence model, which is a generalization of the independence model, is most commonly model used to analyze incomplete contingency tables. Goodness of fit tests of the quasi-independence model are usually based on Pearson chi square test statistic and likelihood ratio test statistic. In power divergence statistics family, the selection of power divergence parameter is of interest in multivariate discrete data. In this study, a simulation study is conducted to evaluate the performance of the power divergence statistics under quasi independence model for particular power divergence parameters in terms of power values.

 

Keywords: Power divergence family; square contingency tables; structural zeros

 

ABSTRAK

Dalam jadual kontingensi tidak lengkap, sesetengah sel boleh mengandungi struktur sifar. Model kuasi ketakbersandaran yang merupakan suatu generalisasi daripada model ketakbersandaran adalah model yang paling biasa digunakan untuk menganalisis jadual kontingensi yang tidak lengkap. Ujian kebagusan penyuaian model kuasi ketakbersandaran biasanya berdasarkan statistik ujian khi kuasa dua Pearson dan ujian statistik nisbah kebolehjadian. Dalam keluarga statistik pencapahan kuasa, pemilihan parameter pencapahan kuasa adalah penting dalam data diskret multivariat. Dalam penyelidikan ini, suatu kajian simulasi dijalankan untuk menilai prestasi statistik pencapahan kuasa di bawah parameter model kuasi ketakbersandaran untuk parameter pencapahan kuasa daripada segi nilai kuasa tertentu.

 

Kata kunci: Jadual kontinjensi segi empat sama; kuasa keluarga pencapahan; struktur sifar

REFERENCES

Agresti, A. 2002. Categorical Data Analysis. New York: John Wiley & Sons.

Basu, A. & Basu, S. 1998. Penalized minimum disparity methods for multinomial models. Stat. Sin. 8. 841-860.

Bishop, Y.M.M., Fienberg, S.E. & Holland, P.W. 1975. Discrete Multivariate Analysis: Theory and Practice. Cambridge: MIT Press.

Cressie, N. & Read, T.R.C. 1984. Multinomial goodness-of-fit tests. Journal of the Royal Statistic Society, Series B 46: 440-464.

Fienberg, S.E. 1980. The Analysis of Cross-Classified Categorical Data. Cambridge, Massachusetts: The MIT Press.

García-Pérez, M.A. & Núñez-Antón, V. 2009. Accuracy of power-divergence statistics for testing independence and homogeneity in two-way contingency tables. Communications in Statistics - Simulation and Computation 38(3): 503-512.

Goodman, L. 1979. A multiplicative models for square contingency tables with ordered categories. Biometrika 61: 207-214.

Goodman, L.A. 1968. The analysis of cross-classied data: Independence, quasi- Independence, and interactions in contingency tables with or without missing entries. J. Amer. Statist. Assoc. 63: 1091-1131.

Haberman, S.J. 1979. Analysis of Qualitative Data. Volume 2 New Developments. New York: Academic Press.

Ireland, C.T., Ku, H. & Kullback S. 1965. Symmetry and marginal homogenity of a R*R contingency table. JASA 64: 1323-1341.

Lawal, H.B. 2003. Categorical Data Analysis with SAS and SPSS Applications. New Jersey: Lawrence Erlbaum Associates Inc.

Lawal, H.B. 1993. Association symmetry and diagonal models for occupational mobility and other similar square contingency tables having ordered categorical variables. Biometrical J. 35: 193-206.

McCullagh, P. 1978. A class of parametric models for the analysis of square contingency tables with ordered categories. Biometrika 65: 413-418.

Read, T.R.C. & Cressie, N. 1988. Goodness-of-Fit Statistics for Discrete Multivariate Data. New York: Springer-Verlag.

Tomizawa, S. 1985. Analysis of data in square contingency tables with ordered categories using the conditional symmetry model and its decomposed models. Environmental Health Perspectives 63: 235-239.

Zelterman, D. 1987. Goodness-of-fit tests for large sparse multinomial distributions. J. Amer. Statist. Assoc. 82(398): 624-629.

 

 

*Corresponding author; email: serpilaltunay@gmail.com

 

 

 

 

 

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