Abstract
The issue concerning this chapter is that covariates need not enter a generalised linear model merely as linear terms. Quadratic and higher-order terms can sometimes be useful in explaining variation in the data. In this chapter nonlinearities are explored using several techniques; discretisation, polynomial regression, splines and generalised additive models. These methods are explored using a single example to highlight the advantages and disadvantages of each approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burns, J., Sivananthan, M. U., Ball, S. G., Mackintosh, A. F., Mary, D. A., & Greenwood, J. P. (2007). Relationship between central sympathetic drive and magnetic resonance imaging-determined left ventricular mass in essential hypertension. Circulation, 115, 1999–2005.
de Boor, C. (1978). A practical guide to splines. New York: Springer.
Eilers, P. H. C., & Marx, B. D. (1996). Flexible smoothing with B-splines and penalties. Statistical Science, 11, 89–121.
Graunt, J. (1662). Natural and political observations on the bills of mortality. London.
Hastie, T. J., & Tibshirani, R. J. (1986). Generalised additive models (with discussion). Statistical Science, 1, 295–318.
Hastie, T. J., & Tibshirani, R. J. (1990). Generalised additive models. Boca Raton: Chapman and Hall/CRC.
Kennedy, W. J., & Gentle, J. E. (1980). Statistical computing. New York.
Miller, A. J. (2002). Subset selection in regression (2nd ed.). Boca Raton: Chapman and Hall/CRC.
O’Sullivan, F., Yandell, B., & Raynor, W. (1986). Automatic smoothing of regression functions in generalised linear models. Journal of the American Statistical Association, 18, 96–103.
R Development Core Team. (2010). 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.
Runge, C. (1901). Uber empirische funktionen und die interpolation zwischen aquidistanten ordinaten. Zeitschrift fur Mathematik und Physik, 46, 224–243.
Venables, W. N., & Ripley, B. D. (2002). Modern applied statistics with S (4th ed.). NewYork: Springer Science and Business Media.
Wahba, G. (1990). Spline models for observational data. Philadelphia: SIAM.
Wilkinson, G., & Rogers, C. (1973). Symbolic description of factorial models for the analysis of variance. Applied Statistics, 22, 329–399.
Wood, S. N. (2006). Generalised additive models: An introduction with R. Boca Raton: Chapman and Hall/CRC.
Yee, T. W., & Wild, C. J. (1996). Vector generalised additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
West, R.M. (2012). Generalised Additive Models. In: Tu, YK., Greenwood, D. (eds) Modern Methods for Epidemiology. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3024-3_15
Download citation
DOI: https://doi.org/10.1007/978-94-007-3024-3_15
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-3023-6
Online ISBN: 978-94-007-3024-3
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)