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Generalized Additive Models; Some Applications

  • Conference paper
Generalized Linear Models

Part of the book series: Lecture Notes in Statistics ((LNS,volume 32))

Summary

Generalized additive models have the the form η(x)=α+Σfj(Xj), where η might be the regression function in a multiple regression, or the logistic transformation of the posterior probability p(y=l/ x) in logistic regression. In fact, these models generalize the whole family of GLIM models η(x)=β’x where η(x)=g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions, which uses a scatterplot smoother as a building block. The models are demonstrated in a non-parametric logistic regression. A variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions. The procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis.

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Author information

Authors and Affiliations

  1. Institute for Biostatistics, South African Medical Research Council, South African

    Trevor Hastie

  2. Department of Preventive Medicine and Biostatistics, University of Toronto, Canada

    Robert Tibshirani

Authors
  1. Trevor Hastie
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  2. Robert Tibshirani
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Statistics and Computing, The Polytechnic of North London, Holloway Road, London, N7 8DB, UK

    Robert Gilchrist , Brian Francis  & Joe Whittaker ,  & 

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© 1985 Springer-Verlag Berlin Heidelberg

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Hastie, T., Tibshirani, R. (1985). Generalized Additive Models; Some Applications. In: Gilchrist, R., Francis, B., Whittaker, J. (eds) Generalized Linear Models. Lecture Notes in Statistics, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4615-7070-7_8

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  • DOI: https://doi.org/10.1007/978-1-4615-7070-7_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96224-5

  • Online ISBN: 978-1-4615-7070-7

  • eBook Packages: Springer Book Archive

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