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Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables

Year 2014, Volume: 27 Issue: 3, 953 - 963, 20.08.2014

Abstract

Zero partial association models correspond to the conditional independence relation of a variable pair, given the rest of variables in the model. For determining the model that best fits the data from the contingency tables measured at a nominal level, this study has used the C (CATANOVA) test statistic (with response as one of its variables, and factor as another one of its variables) instead of the chi-square statistic, which is used as the test statistic in Wermuth’s backward elimination method with zero partial associations. Numerical analyses were performed on two samples, and the associations between these statistics were evaluated. Interpretations were provided for the obtained results.

References

  • Anderson, R.J. and Landis, J.R.,“Catanova for multidimensional contingency tables: Nominal-scale response”, Communications in Statistics-Theory and Methods, 9(11), 1191-1206(1980),
  • Camminatiello, I. and D’ambra, L., “Visualization of the significant explicative categories using CATANOVA method and non-symmetrical correspondence analysis for evaluation of passenger satisfaction”, Journal of Applied Quantitative Methods, 5(1):64-72, (2010).
  • Christensen, R., Log-linear models and logistic regression. Second edition, Springer-Verlag New York (1990).
  • Darroch, J.N., Lauritzen,S.L. and Speed,T.P., “Markov fields and log-linear interactions models for contingency tables”, Annals Statistics, 8:522-539, (1980).
  • D'ambra, L.,Beh, E. J. and Amenta, P., “CATANOVA for two-way contingency tables with ordinal variables using orthogonal polynomials”, Communications in Statistics, Theory and Methods, 34:1755-1769(2005).
  • Edwards,D., and Kreiner, S., “The analysis of contingency tables by graphical models”, Biometrika, 70: 553-562(1983).
  • Erbaş,E.O. and Bayrak,H., Graphical Models. Bizim Publications Office, ISBN: 975-97011-0-3, Ankara / Turkey (1999). Light, R. and Margolin,B., “An analysis of variance for categorical data”, Journal of the American Statistical Association, 66 :534-544 (1971).
  • Margolin, B.H. and Light,R.J., “An analysis of variance for categorical data II. Small samples comparisons with Chi-square and other competitors”, Journal American Statistics Association, 69 : 755-761(1974).
  • Lombardo, R. and Camminatiello, I., “CATANOVA for two-way cross classified categorical data”, Statistics. 44(1): 57-71 (2010).
  • Singh,B.,“On the analysis of variance method for nominal data”, Sankhya: The Indian Journal of Statistics, 55 (B):40-47, (1993).
  • Singh, B., “On CATANOVA method for analysis of twoway classified nominal data”, Sankhyā: The Indian Journal of Statistics, 58(3): 379-388, (1996).
  • Wermuth, N., “Analogies between multiplicative models in contingency tables and covariance selection”, Biometrics, 32: 95-108, (1976a).
  • Wermuth, N., “Model search among multiplicative models”, Biometrics, 32:256-263,(1976b).
Year 2014, Volume: 27 Issue: 3, 953 - 963, 20.08.2014

Abstract

References

  • Anderson, R.J. and Landis, J.R.,“Catanova for multidimensional contingency tables: Nominal-scale response”, Communications in Statistics-Theory and Methods, 9(11), 1191-1206(1980),
  • Camminatiello, I. and D’ambra, L., “Visualization of the significant explicative categories using CATANOVA method and non-symmetrical correspondence analysis for evaluation of passenger satisfaction”, Journal of Applied Quantitative Methods, 5(1):64-72, (2010).
  • Christensen, R., Log-linear models and logistic regression. Second edition, Springer-Verlag New York (1990).
  • Darroch, J.N., Lauritzen,S.L. and Speed,T.P., “Markov fields and log-linear interactions models for contingency tables”, Annals Statistics, 8:522-539, (1980).
  • D'ambra, L.,Beh, E. J. and Amenta, P., “CATANOVA for two-way contingency tables with ordinal variables using orthogonal polynomials”, Communications in Statistics, Theory and Methods, 34:1755-1769(2005).
  • Edwards,D., and Kreiner, S., “The analysis of contingency tables by graphical models”, Biometrika, 70: 553-562(1983).
  • Erbaş,E.O. and Bayrak,H., Graphical Models. Bizim Publications Office, ISBN: 975-97011-0-3, Ankara / Turkey (1999). Light, R. and Margolin,B., “An analysis of variance for categorical data”, Journal of the American Statistical Association, 66 :534-544 (1971).
  • Margolin, B.H. and Light,R.J., “An analysis of variance for categorical data II. Small samples comparisons with Chi-square and other competitors”, Journal American Statistics Association, 69 : 755-761(1974).
  • Lombardo, R. and Camminatiello, I., “CATANOVA for two-way cross classified categorical data”, Statistics. 44(1): 57-71 (2010).
  • Singh,B.,“On the analysis of variance method for nominal data”, Sankhya: The Indian Journal of Statistics, 55 (B):40-47, (1993).
  • Singh, B., “On CATANOVA method for analysis of twoway classified nominal data”, Sankhyā: The Indian Journal of Statistics, 58(3): 379-388, (1996).
  • Wermuth, N., “Analogies between multiplicative models in contingency tables and covariance selection”, Biometrics, 32: 95-108, (1976a).
  • Wermuth, N., “Model search among multiplicative models”, Biometrics, 32:256-263,(1976b).
There are 13 citations in total.

Details

Primary Language English
Journal Section Statistics
Authors

Hülya Olmuş

Semra Erbaş

Publication Date August 20, 2014
Published in Issue Year 2014 Volume: 27 Issue: 3

Cite

APA Olmuş, H., & Erbaş, S. (2014). Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables. Gazi University Journal of Science, 27(3), 953-963.
AMA Olmuş H, Erbaş S. Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables. Gazi University Journal of Science. August 2014;27(3):953-963.
Chicago Olmuş, Hülya, and Semra Erbaş. “Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables”. Gazi University Journal of Science 27, no. 3 (August 2014): 953-63.
EndNote Olmuş H, Erbaş S (August 1, 2014) Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables. Gazi University Journal of Science 27 3 953–963.
IEEE H. Olmuş and S. Erbaş, “Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables”, Gazi University Journal of Science, vol. 27, no. 3, pp. 953–963, 2014.
ISNAD Olmuş, Hülya - Erbaş, Semra. “Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables”. Gazi University Journal of Science 27/3 (August 2014), 953-963.
JAMA Olmuş H, Erbaş S. Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables. Gazi University Journal of Science. 2014;27:953–963.
MLA Olmuş, Hülya and Semra Erbaş. “Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables”. Gazi University Journal of Science, vol. 27, no. 3, 2014, pp. 953-6.
Vancouver Olmuş H, Erbaş S. Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables. Gazi University Journal of Science. 2014;27(3):953-6.