Skip to main content

Analysis of Multiple Discrete Responses

  • Chapter
  • First Online:
Recursive Partitioning and Applications

Part of the book series: Springer Series in Statistics ((SSS,volume 0))

  • 2214 Accesses

Abstract

In Chapter 11 we introduced some contemporary approaches to analyzing longitudinal data for which the responses are continuous measurements. In fact, most people imply continuous responses when they refer to longitudinal data. The analysis of discrete longitudinal data is a relatively new, though active, subject. Readers who are interested in methodological developments may find many unanswered questions in this chapter. The purpose of this chapter is to shed some light on this growing subject. In the statistical literature, the topic may be tagged with clustered or correlated discrete/binary outcomes. So far, most progress has been made toward the binary outcomes; hence, therein lies the focus of this chapter.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Babiker and J. Cuzick. A simple frailty model for family studies with covariates. Statistics in Medicine, 13:1679–1692, 1994.

    Article  Google Scholar 

  2. G.E. Bonney. Regression logistic models for familial disease and other binary traits. Biometrics, 42:611–625, 1986.

    Article  Google Scholar 

  3. C. Cannings, E.A. Thompson, and M.H. Skolnick. Probability functions on complex pedigrees. Advances in Applied Probability, 10:26– 61, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  4. A.P. Dempster, N.M. Laird, and D.B. Rubin. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society-B, 39:1–22, 1977.

    MATH  MathSciNet  Google Scholar 

  5. P.J. Diggle, K.Y. Liang, and S.L. Zeger. Analysis of Longitudinal Data. Oxford Science Publications, Oxford, 1991.

    Google Scholar 

  6. B.G. Ferris, F.E. Speizer, J.D. Spengler, D.W. Dockery, Y.M.M. Bishop, M. Wolfson, and C. Humble. Effects of sulfur oxides and respirable particles on human health. American Review of Respiratory Disease, 120:767–779, 1979.

    Google Scholar 

  7. G.M. Fitzmaurice and N.M. Laird. A likelihood-based method for analysing longitudinal binary responses. Biometrika, 80:141–151, 1993.

    Article  MATH  Google Scholar 

  8. G.M. Fitzmaurice, N.M. Laird, and A.G. Rotnitzky. Regression models for discrete longitudinal responses. Statistical Science, 8:284–299, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  9. V.P. Godambe. An optimum property of regular maximum likelihood estimation. Annals of Mathematical Statistics, 31:1209–1211, 1960.

    Article  MathSciNet  Google Scholar 

  10. D.G. Kleinbaum, L.L. Kupper, and K.E. Muller. Applied Regression Analysis and Other Multivariable Methods. Duxbury Press, Belmont, California, 1988.

    Google Scholar 

  11. K.Y. Liang and S.L. Zeger. Longitudinal data analysis using generalized linear models. Biometrika, 73:13–22, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  12. K.Y. Liang, S.L. Zeger, and B. Qaqish. Multivariate regression analyses for categorical data. Journal of the Royal Statistical Society-B, 54:3–24, 1992.

    MATH  MathSciNet  Google Scholar 

  13. P. McCullagh and J.A. Nelder. Generalized Linear Models. Chapman and Hall, London, 1989.

    MATH  Google Scholar 

  14. R.M. Royall. Model robust inference using maximum likelihood estimators. International Statistical Review, 54:221–226, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  15. J. Scourfield, D.E. Stevens, and K.R. Merikangas. Substance abuse, comorbidity, and sensation seeking: gender difference. Comprehensive Psychiatry, 37:384–392, 1996.

    Article  Google Scholar 

  16. A. Sommer, J. Katz, and I. Tarwotjo. Increased risk of respiratory disease and diarrhea in children with preexisting mild vitamin A deficiency. American Journal of Clinical Nutrition, 40:1090–1095, 1984.

    Google Scholar 

  17. A. Sommer, I. Tarwotjo, G. Hussaini, and D. Susanto. Increased mortality in children with mild vitamin A deficiency. Lancet, 2:585– 588, 1983.

    Article  Google Scholar 

  18. A. Sommer, J.M. Tielsch, J. Katz, H.A. Quigley, J.D. Gottsch, J.C. Javitt, J.F. Martone, R.M. Royall, K.A. Witt, and S. Ezrine. Racial differences in the cause-specific prevalence of blindness in east Baltimore. New England Journal of Medicine, 325:1412–1417, 1991.

    Google Scholar 

  19. J.H. Ware, D.W. Dockery, A. Spiro, F.E. Speizer, and B.G. Ferris. Passive smoking, gas cooking, and respiratory health of children living in six cities. American Review of Respiratory Disease, 129:366–374, 1984.

    Google Scholar 

  20. S.L. Zeger, K.Y. Liang, and P.S. Albert. Models for longitudinal data: A generalized estimating equation approach. Biometrics, 44:1049– 1060, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  21. H.P. Zhang. Classification trees for multiple binary responses. Journal of the American Statistical Association, 93:180–193, 1998a.

    Article  MATH  Google Scholar 

  22. H.P. Zhang and Y. Ye. A tree-based method for modeling a mul-tivariate ordinal response. Statistics and Its Interface, 1:169–178, 2008.

    MathSciNet  Google Scholar 

  23. L.P. Zhao and R.L. Prentice. Correlated binary regression using a quadratic exponential model. Biometrika, 77:642–648, 1990.

    Article  MathSciNet  Google Scholar 

  24. K.Y. Liang and S.L. Zeger. Longitudinal data analysis using generalized linear models. Biometrika, 73:13–22, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  25. P. McCullagh and J.A. Nelder. Generalized Linear Models. Chapman and Hall, London, 1989.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Heping Zhang .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Zhang, H., Singer, B.H. (2010). Analysis of Multiple Discrete Responses. In: Recursive Partitioning and Applications. Springer Series in Statistics, vol 0. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6824-1_12

Download citation

Publish with us

Policies and ethics