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On the Application of Conditional Independence to Ordinal Data

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  • Nanny Wermuth
  • D.R. Cox

Abstract

A special log linear parameterization is described for contingency tables which exploits prior knowledge that an ordinal scale of the variables is involved. It is helpful, in particular, in guiding the possible merging of adjacent levels of variables and may simplify interpretation if higher‐order interactions are present. Several sets of data are discussed to illustrate the types of interpretation that can be achieved. The simple structure of the maximum likelihood estimates is derived by use of Lagrange multipliers. On décrit une paramétristaion adaptée particulièrement aux des variables ordinales. En particulier celle‐ci pemettra de guider l'operation commetn combiner les niveaux combiner les niveaux adjacents pour simplifier l'interprétation. une illustration des possibilités d'interpréinterprétation de la méthode à plusiurs enseieurs ensembles de données est presentée. La méthode de Largrange expose la structure des estimateurs de maximum vraisemblage.

Suggested Citation

  • Nanny Wermuth & D.R. Cox, 1998. "On the Application of Conditional Independence to Ordinal Data," International Statistical Review, International Statistical Institute, vol. 66(2), pages 181-199, August.
    • Handle: RePEc:bla:istatr:v:66:y:1998:i:2:p:181-199
    DOI: 10.1111/j.1751-5823.1998.tb00413.x
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    Cited by:

    1. Evžen Kocenda & Martin Vojtek, 2011. "Default Predictors in Retail Credit Scoring: Evidence from Czech Banking Data," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 47(6), pages 80-98, November.
    2. Guo, Jianhua & Geng, Zhi & Fung, Wing-Kam, 2001. "Consecutive Collapsibility of Odds Ratios over an Ordinal Background Variable," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 89-98, October.
    3. Elena Stanghellini, 2003. "Monitoring the Behaviour of Credit Card Holders with Graphical Chain Models," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(9‐10), pages 1423-1435, December.
    4. O. J. W. F. Kardaun & D. Salomè & W. Schaafsma & A. G. M. Steerneman & J. C. Willems & D.R. Cox, 2003. "Reflections on Fourteen Cryptic Issues Concerning the Nature of Statistical Inference," International Statistical Review, International Statistical Institute, vol. 71(2), pages 277-303, August.
    5. Ip, Edward H. & Wang, Yuchung J., 2008. "A note on cuts for contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2356-2363, November.
    6. Andrew Roddam, 2001. "An approximate maximum likelihood procedure for parameter estimation in multivariate discrete data regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(2), pages 273-279.
    7. Webb, Emily L. & Forster, Jonathan J., 2008. "Bayesian model determination for multivariate ordinal and binary data," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2632-2649, January.
    8. Claudio Castro-López & Purificación Vicente-Galindo & Purificación Galindo-Villardón & Oscar Borrego-Hernández, 2022. "TAID-LCA: Segmentation Algorithm Based on Ternary Trees," Mathematics, MDPI, vol. 10(4), pages 1-16, February.

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