Partitioning Pearson's chi-squared statistic for a completely ordered three-way contingency table

Australian and New Zealand Journal of Statistics

Volumn 40, Issue 4, 1998, Pages 465-477

  Beh, Eric J ^a   Davy, Pamela J ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

Dispersion and higher order components; Location; Ordinal log linear models; Orthogonal polynomials; Three way contingency table

Indexed keywords

EID: 0043064959     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-842X.00050     Document Type: Article

References (36)

1. AGRESTI, A. (1994). Analysis of Ordinal Categorical Data. New York: Wiley.
2. BEH, E.J. (1997). Simple correspondence analysis of ordinal cross-classifications using orthogonal polynomials. Biometrical J. 39, 1-25.
3. _ (1998). A comparative study of scores for correspondence analysis with ordered categories. Biometrical J. (to appear).
4. _ & DAVY, P.J. (1997). Multiple correspondence analysis of ordinal multi-way contingency tables using orthogonal polynomials. (In preparation.)
5. _ & _ (1999). Partitioning Pearson's chi-squared statistic for an ordered three-way contingency table: Part 2. Austral. & New Zealand J. Statist. (to appear).
6. BEST, E.J. & RAYNER, J.C.W. (1996). Nonparametric analysis for doubly ordered two-way contingency tables. Biometrics 52, 1153-1156.
7. CLOGG, C.C. (1982). Some models for the analysis of association in multiway cross-classifications having ordered categories. J. Amer. Statist. Assoc. 77, 803-815.
8. DANAHER, P.J. (1991). Canonical expansion model for multivariate media exposure distributions: a generalisation of the 'Duplication of Viewing Law'. J. Marketing Res. 28, 361-367.
9. DARROCH, J.N., LAURITZEN, S.L. & SPEED, T.P. (1980). Markov fields and log-linear interaction models for contingency tables. Ann. Statist. 8, 539-552.
10. DAVIS, J.A. (1977). Codebook for the 1977 General Social Survey. Chicago: National Opinion Research Centre.
11. EVERITT, B.S. (1992). The Analysis of Contingency Tables. London: Chapman & Hall.
12. RENBERG, S.E. (1977). The Analysis of Cross-Classified Categorical Data. Cambridge: MIT Press.
13. GILULA, Z. & HABERMAN, S.J. (1988). The analysis of multivariate contingency tables by restricted canonical and restricted association models. J. Amer. Statist. Assoc. 83, 760-771.
14. _, KRIEGER, A.M. & RITOV, Y. (1988). Ordinal association in contingency tables: some interpretive aspects. J. Amer. Statist. Assoc. 83, 540-545.
15. GOODMAN, L.A. (1970). The multivariate analysis of quantitative data: interactions among multiple classifications. J. Amer. Statist. Assoc. 65, 226-256.
16. _ (1979). Simple models for the analysis of association in cross-classifications having ordered categories. J. Amer. Statist. Assoc. 74, 537-552.
17. _ (1981). Association models and canonical correlation in the analysis of cross-classifications having ordered categories. J. Amer. Statist. Assoc. 76, 320-334.
18. _ (1985). The analysis of cross-classified data having ordered and/or unordered categories: association models, correlation models, and asymmetry models for contingency tables with or without missing entries. Ann. Statist. 13, 10-69.
19. _ (1986). Some useful extensions of the usual correspondence analysis approach and the usual log-linear models approach in the analysis of contingency tables. Internat. Statist. Rev. 54, 243-309.
20. _ (1996). A single general method for the analysis of cross-classified data: reconciliation and synthesis of some methods of Pearson, Yule and Fisher, and also some methods of correspondence analysis and association analysis. J. Amer. Statist. Assoc. 91, 408-428.
21. HABERMAN, S.J. (1974). Log-linear models for frequency tables with ordered classifications. Biometrics 30, 589-600.
22. HIROTSU, C. (1978). Ordered alternatives for interaction effects. Biometrika 65, 561-570.
23. _ (1982). Use of cumulative efficient scores for testing ordered alternatives in discrete models. Biometrika 69, 567-577.
24. _ (1983). Defining the pattern of association in two-way contingency tables. Biometrika 70, 579-589.
25. _ (1986). Cumulative chi-square statistic as a tool for testing goodness of fit. Biometrika 73, 165-173.
26. KENDALL, M.G. & STUART, A. (1979). The Advanced Theory of Statistics, Vol.2. London: Charles Griffin.
27. KROONENBERG, P.M. (1989). Singular value decomposition of interactions in three-way contingency tables. In Multiway Data Analysis, eds R. Coppi & S. Bolasco, 169-184. Amsterdam: North Holland.
28. 2. J. Roy. Statist. Soc. Ser. B 13, 242-249.
29. 2 considered from metrical and enumerative aspects. Sankhyā 13, 1-10.
30. _ (1980). Orthogonal models for contingency tables. In Development in Statistics, Vol.3, ed. P. R. Krishnaiah, 99-157. New York: Academic Press.
31. NAIR, V.N. (1986). Testing industrial experiments with ordered categorical data. Technometrics 28, 283-311.
32. RAYNER, J.C.W. & BEST, D.J. (1996). Smooth extensions of Pearson's product moment correlation and Spearman's rho. Statist. Probab. Lett. 30, 171-177.
33. ROM, D. & SARKAR, S.K. (1992). A generalised model for the analysis of association in ordinal contingency tables. J. Statist. Plann. Inference 33, 205-212.
34. van der HEIJDEN, P.G.M. & de LEEUW, J. (1985). Correspondence analysis used complimentary to log-linear analysis. Psychometrika 50, 429-447.
35. _ & WORSLEY, K.J. (1988). Comment on 'Correspondence analysis used complimentary to log-linear analysis'. Psychometrika 53, 287-291.
36. _, de FALGUEROLLES, A. & de LEEUW, J. (1989). A combined approach to contingency table analysis using correspondence analysis and log-linear analysis. Appl. Statist. 38, 249-292.