Simple correspondence analysis of ordinal cross-classifications using orthogonal polynomials

Biometrical Journal

Volumn 39, Issue 5, 1997, Pages 589-613

  Beh, Eric J ^a  

^a UNIVERSITY OF WOLLONGONG   (Australia)

Author keywords

Chi squared partitioning; Dispersion and higher order components; Location; Orthogonal polynomials

Indexed keywords

DISPERSIONS; ORTHOGONAL FUNCTIONS;

CHI-SQUARED; CHI-SQUARED PARTITIONING; CORRESPONDENCE ANALYSIS; DISPERSION AND HIGH ORDER COMPONENT; HIGH-ORDER; HIGHER-ORDER; ORDER COMPONENT; ORTHOGONAL POLYNOMIAL; SIMPLE++; TWO WAYS;

POLYNOMIALS;

EID: 0031527466     PISSN: 03233847     EISSN: None     Source Type: Journal    
DOI: 10.1002/bimj.4710390507     Document Type: Article

References (31)

1. BEST, D. J. and RAYNER, J. C. W., 1994: Analysis of ordered contingency tables via orthogonal polynomials. Department of Applied Statistics, University of Wollongong, Australia.
2. BEST, D. J. and RAYNER, J. C. W., 1996: Nonparametric analysis for doubly ordered two-way contingency tables. Biometrics, 52, 1153-1156.
3. BROYDEN, C. G., 1975: Basic Matrices. McMillian Press, London.
4. EMERSON, P. L., 1968: Numerical construction of orthogonal polynomials from a general recurrence formula Biometrics 24, 695-701.
5. EVERITT, B. S., 1994: A handbook of Statistical Analyses using S-plus. Chapman and Hall, London.
6. GIFI, A., 1981: Nonlinear Multivariate Analysis. Department of Data Theory, University of Leiden, The Netherlands.
7. GRAUBARD, B. I. and KORN, E. L., 1987: Choice of column scores for testing independence in ordered 2 x K contingency tables Biometrics 43, 471-476.
8. GREENACRE, M., 1984: Theory and Applications of Correspondence Analysis. Academic Press, London, U.K.
9. GREENACRE, M. J., 1986: SIMCA - a program to perform simple correspondence analysis. Psychometrika 51, 172-173.
10. HEISER, W. J., 1981: Unfolding Analysis of Proximity Data. Doctor of Social Sciences thesis. Department of Data Theory, University of Leiden, The Netherlands.
11. HIROTSU, C., 1978: Ordered alternatives for interaction effects Biometrika 65, 561-570.
12. HIROTSU, C., 1982: Use of cumulative efficient scores for testing ordered alternatives in discrete models. Biometrika 69, 567-577.
13. HIROTSU, C., 1983: Defining the pattern of association in two-way contingency tables. Biometrika 70, 579-589.
14. HIROTSU, C., 1986: Cumulative chi-squared statistic as a tool for testing goodness of fit. Biometrika 73, 165-173.
15. HOFFMAN, D. L. and FRANKE, G. R., Correspondence analysis: graphical representation of categorical data in marketing research. Journal of Marketing Research 23, 213-227.
16. 2 considered from metrical and enumerative aspects. Sankyā 13, 1-10.
17. LANCASTER, H. O., 1980: Orthogonal models for contingency tables. In: P. R. Krishnaiah (ed.): Developments in Statistics. Vol. 3. Academic Press, New York 99-157.
18. LEBART, L., MORINEAU, A., and WARWICK, K. M., 1984: Multivariate Descriptive Statistical Analysis: Correspondence Analysis and Related Techniques for Large Matrices. John Wiley & Sons, New York.
19. NAIR, V. N., 1986: Testing in industrial experiments with ordered categorical data. Technometrics 28, 283-291.
20. NISHISATO, S., 1980: Analysis of Categorical Data: Dual Scaling and its Applications. University of Toronto Press, Toronto.
21. NISHISATO, S. and ARRI, P. S., 1975: Nonlinear programming approach to optimal scaling of partially ordered categories. Psychometrika 40, 525-548.
22. PARSA, A. R. and SMITH, B. S., 1993: Scoring under ordered constraints in contingency tables. Communications in Statistics (Theory & Methods) 22, 3537-3551.
23. RAYNER, J. C. W. and BEST, D. J., 1996: Smooth extensions of Pearson's product moment correlation and Spearman's rho. Statistics and Probability Letters 30, 171-177.
24. RAYNER, J. C. W., BEST, D. J. and STEPHENS, L. G., 1997: A smooth analysis of singly ordered two-way contingency tables. Submitted to Journal of Applied Mathematics & Decision Sciences.
25. RITOV, Y. & GILULA, Z., 1993: Analysis of contingency tables by correspondence models subject to ordered constraints. Journal of the American Statistical Association 88, 1380-1387.
26. SCHRIEVER, B. F., 1983: Scaling of order dependent categorical variables with correspondence analysis. International Statistical Review 51, 225-238.
27. SNELL, E. J., 1964: A scaling procedure for ordered categorical data. Biometrics 20, 592-607.
28. SROLE, L., LANGNER, T. S., MICHAEL, S. T., OPLER, M. K., and RENNIE, T. A. C., 1962: Mental Health in the Metropolis: The Midtown Manhattan Study. Mc-Graw-Hill, New York.
29. THOMPSON, P. A., 1995: Correspondence analysis in statistical package programs. The American Statistican 49, 310-316.
30. TIAN, D., SOROOSHIAN, S., and MYERS, D. E., 1993: Correspondence analysis with Matlab. Computers and Geosciences 19, 1007-1022.
31. WELLER, S. C. and ROMNEY, A. K., 1990: Metric Scaling: Correspondence Analysis. Sage University Paper Series of Quantification Applications in Social Sciences, 07-075, Newbury Park, Ca.