Catanova Method for Determining of Zero Partial Association Structures in Multidimensional Contigency Tables
Öz
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.
Anahtar Kelimeler
multidimensional contingency tables; zero partial association; CATANOVA; model search
Kaynakça
- 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).
Yıl 2014,
Cilt: 27 Sayı: 3, 953 - 963, 20.08.2014
Öz
Kaynakça
- 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).
Toplam 13 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Statistics |
| Yazarlar | |
| Yayımlanma Tarihi | 20 Ağustos 2014 |
| Yayımlandığı Sayı | Yıl 2014 Cilt: 27 Sayı: 3 |