Skip to main content
SpringerLink
Log in

Generalized Linear Models

  • Chapter
Breakthroughs in Statistics

Part of the book series: Springer Series in Statistics ((PSS))

Summary

The technique of iterative weighted linear regression can be used to obtain maximum likelihood estimates of the parameters with observations distributed according to some exponential family and systematic effects that can be made linear by a suitable transformation. A generalization of the analysis of variance is given for these models using log- likelihoods. These generalized linear models are illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables) and gamma (variance components).

The implications of the approach in designing statistics courses are discussed.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

  • Birch. M.W.(1963). Maximum likelihood in three-way contingency tables. JR. Statist. Soc. B. 25. 220–233.

    MathSciNet  MATH  Google Scholar 

  • Bishop. Y.M.M. (1969). Full contingency tables, logits. and split contingency tables. Biometrics. 25, 383–399.

    Article  Google Scholar 

  • Cox, D.R. (1968). Notes on some aspects of regression analysis. J. R. Statist. Soc. A, 131. 265–279.

    Google Scholar 

  • Cox, D.R. (1970). Analysis of Binary Data. London: Methuen.

    MATH  Google Scholar 

  • Dempster. A.P. (1971). An overview of multivariate data analysis. J. Multiuar. Anal., 1. 316–346.

    Article  MathSciNet  MATH  Google Scholar 

  • Dyke, G.V. and Patterson. H.D. (1952). Analysis of factorial arrangements when the data are proportions. Biometrics, 8, 1–12.

    Article  Google Scholar 

  • Finney, DJ. (1952). Probit Analysis. 2nd ed. Cambridge: University Press.

    MATH  Google Scholar 

  • Fisher. R.A. (1949). A biological assay of tuberculosis. Biometrics, 5. 300–316.

    Article  Google Scholar 

  • Good, I. J. (1967). Analysis of log-likelihood ratios. “ANO∧”. (A contribution to the discussion of a paper on least squares by F.J. Anscombe.) J R. Statisi. Soc. B. 29. 39–42.

    MathSciNet  Google Scholar 

  • Ireland, C.T. and Kullback. S. (1968). Contingency tables with given marginals. Biometrika. 55. 179–188.

    Article  MathSciNet  MATH  Google Scholar 

  • Irwin, J.O. (1949). A note on the subdivision of X 1 into components. Biometrika. 36. 130–134.

    MathSciNet  MATH  Google Scholar 

  • Kendall. M.G. and Stuart, A. (1967). The Advanced Theory of Statistics, 2nd ed. Vol. I I. London: Griffin.

    Google Scholar 

  • Kimball, AAV. (1954). Short-cut formulas for the exact partition of X1 in contingency tables Biometrics. 10, 452–458.

    Article  MathSciNet  MATH  Google Scholar 

  • Ku. H.H. Varner, R.N. and Kullback. S. (1971). On the analysis of multidimensional contingency tables. J. Amer. Statist. Ass., 66, 55–64

    Article  MathSciNet  MATH  Google Scholar 

  • Kullback. S. (1968). Information Theory and Statistics. 2nd ed. New York: Dover.

    Google Scholar 

  • Lancaster. H.O. (1949). The derivation and partition of X 2 in certain discrete distributions. Biometrika. 36. 117–128.

    MathSciNet  MATH  Google Scholar 

  • Lancaster, H.O. (1950). The exact partition of X2 and its application to the problem of the pooling of small expectations. Biometrika. 37. 267–270.

    MathSciNet  MATH  Google Scholar 

  • Lehmann, E.L. (1959). Testing Statistical Hypotheses. London: Wiley.

    MATH  Google Scholar 

  • Maxwell. A.E. (1961). Analysing Qualitative Data. London: Methuen.

    MATH  Google Scholar 

  • Nelder, J.A. (1966). Inverse polynomials, a useful group of multi-factor response functions. Biometrics. 22, 128–141.

    Article  Google Scholar 

  • Nelder, J.A. (1968). Weighted regression, quanta! response data and inverse polynomials. Biometrics, 24, 979–985.

    Article  Google Scholar 

  • Patil, G.P. and Shorrock, R. (1965). On certain properties of the exponential-type families. J. R. Statist. Soc. B. 27, 94–99.

    MathSciNet  MATH  Google Scholar 

  • Simpson. C.H. (1951). The interpretation of interaction in contingency tables. J.R. Statist. Soc. B, 13, 238–241.

    MathSciNet  MATH  Google Scholar 

  • Yates. F. (1940). The recovery of inter-block information in balanced incomplete block designs. Ann. Eugen., 10, 317–325.

    Article  Google Scholar 

  • Yates, F. (1948). The analysis of contingency tables with groupings based on quantitative characters. Biometrika, 35. 176–181.

    MATH  Google Scholar 

  • Yates, F. (1970). Experimental Design: Selected Papers. London: Griffin.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rothamsted Experimental Station, UK

    J. A. Nelder & R. W. M. Wedderburn

Authors
  1. J. A. Nelder
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. W. M. Wedderburn
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Business and Management, University of Maryland at College Park, 20742, College Park, MD, USA

    Samuel Kotz

  2. Department of Statistics Phillips Hall, The University of North Carolina at Chapel Hill, 27599, Chapel Hill, NC, USA

    Norman L. Johnson

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Nelder, J.A., Wedderburn, R.W.M. (1992). Generalized Linear Models. In: Kotz, S., Johnson, N.L. (eds) Breakthroughs in Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4380-9_39

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4380-9_39

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94039-7

  • Online ISBN: 978-1-4612-4380-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation