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Modelling two way contingency tables with recursive logits and odds ratios

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Abstract

In this work a new type of logits and odds ratios, which includes as special cases the continuation and the reverse-continuation logits and odds ratios, are defined. We prove that these logits and odds ratios define a parameterization of the joint probabilities of a two way contingency table. The problem of testing equality and inequality constraints on these logits and odds ratios is examined with particular regard to two new hypotheses of monotone dependence.

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References

  • Barndoff-Nielsen O (1978) Information and exponential families in statistical theory. Wiley, Chichester

    Google Scholar 

  • Barnhart HX, Sampson AR (1994) Overview of multinomial models for ordinal data. Commun Stat Theory Methods 23:3395–3416

    Article  MATH  MathSciNet  Google Scholar 

  • Bartolucci F, Colombi R, Forcina A (2007) An extended class of marginal link functions for modelling contingency tables by equality and inequality constraints. Stat Sin 17:691–711

    MATH  MathSciNet  Google Scholar 

  • Cazzaro M, Colombi R (2006) Maximum likelihood inference for log-linear models subject to constraints of double monotone dependence. Stat Methods Appl 15:177–190

    Article  MathSciNet  Google Scholar 

  • Colombi R, Forcina A (2001) Marginal regression models for the analysis of positive association of ordinal response variables. Biometrika 88:1007–1019

    Article  MATH  MathSciNet  Google Scholar 

  • Dardanoni V, Forcina A (1998) A unified approach to likelihood inference on stochastic orderings in a nonparametric context. J Am Stat Assoc 93:1112–1123

    Article  MATH  MathSciNet  Google Scholar 

  • Lang JB (2004) Multinomial Poisson Homogeneous models for contingency tables. Ann Stat 32:340–383

    Article  MATH  Google Scholar 

  • Lang JB (2005) Homogeneous Linear Predictor models for contingency tables. J Am Stat Assoc 100:121–134

    Article  MATH  Google Scholar 

  • Müller A, Stoyan D (2002) Comparison methods for stochastic models and risks. Wiley, New York

    MATH  Google Scholar 

  • R Development Core Team (2006) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org

  • Silvapulle MJ, Sen PK (2005) Constrained statistical inference. Wiley, New Jersey

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dip. Met. Quant. per le Sc. Ec. Az., Università di Milano Bicocca, Piazza dell’Ateneo Nuovo, 1, 20126, Milan, Italy

    Manuela Cazzaro

  2. Dip. Ing. dell’Informazione e Met. Matematici, Università di Bergamo, Viale Marconi, 5, 24044, Dalmine, Italy

    Roberto Colombi

Authors
  1. Manuela Cazzaro
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  2. Roberto Colombi
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Corresponding author

Correspondence to Manuela Cazzaro.

Additional information

Work partially supported by a MIUR2004 grant. Preliminary findings have been presented at SIS (Società Italiana di Statistica) Annual Meeting, Torino, 2006.

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Cazzaro, M., Colombi, R. Modelling two way contingency tables with recursive logits and odds ratios. Stat Meth Appl 17, 435–453 (2008). https://doi.org/10.1007/s10260-007-0068-2

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  • DOI: https://doi.org/10.1007/s10260-007-0068-2

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