Exploring interactions in high-dimensional tables: A bootstrap alternative to log-linear models

Annals of Statistics

Volumn 27, Issue 1, 1999, Pages 405-413

  Streitberg, Bernd ^b   Sawitzki, Günther ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

^b NONE

Author keywords

Additive interactions; Bootstrap; Contingency tables; Cumulants; Moebius function; Multiple comparisons

Indexed keywords

EID: 0033074841     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1018031118     Document Type: Article

References (25)

1. AIGNER, M. (1975). Kombinatorik I. Grundlagen und Zähltheorie. Berlin.
2. BAHADUR, R. R. (1961). A representation of the joint distribution of responses to n dichotomous items. In Studies in Item Analysis and Prediction (H. Solomon, ed.) 158-176. Stanford.
3. BARTLETT, M. S. (1935). Contingency table interactions. J. Roy. Statist. Soc. Suppl. 2 248-252.
4. BAUER, P., HOMMEL, G. and SONNEMANN, E., eds. (1987). Multiple Hypotheses Testing. Springer, Berlin.
5. CARNEY, E. J. (1968). Relationship of generalized polykays to unrestricted sums for balanced complete finite populations. Ann. Math. Statist. 39 643-656.
6. DARROCH, J. N. and SPEED, T. P. (1983). Additive and multiplicative models and interactions. Ann. Statist. 11 724-738.
7. EFRON, B. (1979). Bootstrap methods. Ann. Statist. 7 1-26.
8. EFRON, B. (1990). More efficient bootstrap computations. J. Amer. Statist. Assoc. 85 79-89.
9. GRAHAM, R. L., KNUTH, D. E. and PATASHNIK, O. (1989). Concrete Mathematics. A Foundation for Computer Science. Addison-Wesley, Reading, MA.
10. HOLM, S. (1979). A simple sequentially rejective multiple test procedure. Scand. J. Statist. 6 65-70.
11. IVERSON, K. E. (1962). A Programming Language. New York.
12. LANCASTER, H. O. (1969). The Chi-Squared Distribution. London.
13. LAZARSFELD, P. F. (1961). The algebra of dichotomous systems. In Studies in Item Analysis and Prediction (H. Solomon, ed.) 111-157. Stanford.
14. MACCULLAGH, P. (1988). Tensor Methods in Statistics. Chapman and Hall, London.
15. MOEBIUS, A. F. (1832). Über eine besondere Art der Umkehrung der Reihen. J. Reine Angew. Math. 9 105-132.
16. ROTA, G. C. (1964). On the foundations of combinatorial theory I. Theory of Moebius functions. Z. Wahrsch. Verw. Gebiete 2 340-368.
17. ROTA, G. C. (1986). Introduction. In Percy Alexander MacMahon: Collected Papers II: Number Theory, Invariants and Applications. Cambridge.
18. SONNEMANN, E. (1982). Allgemeine Lösungen multipler Testprobleme. EDV in Medizin und Biologie 13 120-128.
19. SPEED, T. P. (1983). Cumulants and partition lattices. Austral. J. Statist. 25 378-388.
20. SPEED, T. P. (1986a). Cumulants and partition lattices II: generalized k-statistics. J. Austral. Math. Soc. Ser A 40 34-53.
21. SPEED, T. P. (1986b). Cumulants and partition lattices III: multiply indexed arrays. J. Austral. Math. Soc. Ser. A 40 161-182.
22. STANLEY, P. (1989). Enumerative Combinatorics 1. Monterey, CA.
23. STREITBERG, B. (1990). Lancaster interactions revisited. Ann. Statist. 18 1878-1885.
24. TOEWE, J., BOCK, J. and KUNDT, G. (1985). Interactions in contingency table analysis. Biometrikal J. 27 1-7.
25. ZENTGRAF, R. (1975). A note on Lancaster's definition of higher order interactions. Biometrika 62 375-378.