Skip to main content

Generalised Linear Models and Some Extensions: Geometry and Algorithms

  • Conference paper
Statistical Modelling

Part of the book series: Lecture Notes in Statistics ((LNS,volume 57))

  • 419 Accesses

Abstract

The class of generalised linear models that are considered as standard excludes regression models needed for many important practical problems. Some extensions that have been proposed are discussed, together with implications for the GLIM system.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight 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

  • Aitkin, M. A. (1985) GLIM4 - directions for development. Lecture notes in Statistics, 32, 6–14, Springer, Berlin. GLIM 85: Proceedings of the International Conference on Generalized Linear Models, September 1985.

    Google Scholar 

  • Anderson, J. A. (1984) Regression and ordered categorical variables (with discussion). J. Roy. Statist. Soc., B, 46, 1–30.

    MATH  Google Scholar 

  • Baker, R. J., Nelder, J. A. (1978) The GLIM manual: Release 3. Numerical Algorithms Group, Oxford.

    Google Scholar 

  • Bates, D. M., Watts, D. G. (1980) Relative curvature measures of nonlinearity (with discussion). J. Roy. Statist. Soc. B, 42, 1–25.

    MathSciNet  MATH  Google Scholar 

  • Green, P. J., (1984) Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives (with discussion). J. Roy. Statist. Soc. B, 46, 149–192.

    MATH  Google Scholar 

  • Green, P. J., (1987) Penalized likelihood for general semi-parametric regression models. International Statistical Review, 55, 245–259 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  • Green, P. J., Yandell, B. S. (1985) Semi-parametric generalised linear models. Lecture notes in Statistics, 32, 44–55, Springer, Berlin. GLIM 85: Proceedings of the International Conference on Generalized Linear Models, September 1985.

    Google Scholar 

  • Hastie, T., Tibshirani, R. J. (1986) Generalized additive models (with discussion), Statist. Science, 1, 297–318.

    MathSciNet  Google Scholar 

  • Hinde, J. (1982) Compound Poisson regression models. Lecture notes in Statistics, 14, 109–121, Springer, Berlin. GLIM 82: Proceedings of the International Conference on Generalized Linear Models, September 1982.

    Google Scholar 

  • Jørgensen, B. (1983) Maximum likelihood estimation and large-sample inference for generalized linear and nonlinear regression models. Biometrika, 70, 19–28.

    MathSciNet  Google Scholar 

  • McCullagh, P. (1980) Regression models for ordinal data (with discussion). J. Roy. Statist. Soc., B, 42, 109–142.

    MathSciNet  MATH  Google Scholar 

  • McCullagh, P. (1983) Quasi-likelihood functions. Ann. Statist., 11, 59–67.

    Article  MathSciNet  MATH  Google Scholar 

  • Nelder, J. A. (1985) Quasi-likelihood and GLIM. Lecture notes in Statistics, 32, 120–127, Springer, Berlin. GLIM 85: Proceedings of the International Conference on Generalized Linear Models, September 1985.

    Google Scholar 

  • Nelder, J. A., Pregibon, D. (1987) An extended quasi-likelihood function. Biometrika, 74, 221–232.

    Article  MathSciNet  MATH  Google Scholar 

  • Nelder, J. A., Wedderburn, R.W.M. (1972) Generalized linear models. J. Roy. Statist. Soc., A., 135, 370–384.

    Article  Google Scholar 

  • O’Sullivan, F., Yandell, B. S., Raynor, W. J. (1986) Automatic smoothing of regression functions in generalised linear models, J. Amer. Stat. Assoc., 81, 96–103.

    Article  MathSciNet  Google Scholar 

  • del Pino, G. (1989) The unifying rôle of iterative generalized least squares in statistical algorithms. Statistical Science (to appear).

    Google Scholar 

  • Scallan, A., Gilchrist, R., Green, M. (1984) Fitting parametric link functions in generalised linear models. Comp. Statist, and Data Anal., 2, 37–49.

    Article  Google Scholar 

  • Stirling, W. D. (1985) General algorithms based on least squares calculations for maximum likelihood estimation in multiparameter models. Ph.D. thesis, Massey University.

    Google Scholar 

  • Thompson, R., Baker, R. J. (1981) Composite link functions in generalised linear models. Appl. Statist., 30, 125–131.

    Article  MathSciNet  MATH  Google Scholar 

  • Wedderburn, R. W. M. (1974) Quasi-likelihood functions, generalised linear models and the Gauss-Newton method. Biometrika, 61, 439–447.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Green, P.J. (1989). Generalised Linear Models and Some Extensions: Geometry and Algorithms. In: Decarli, A., Francis, B.J., Gilchrist, R., Seeber, G.U.H. (eds) Statistical Modelling. Lecture Notes in Statistics, vol 57. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3680-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3680-1_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97097-4

  • Online ISBN: 978-1-4612-3680-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics