Abstract
In this chapter we shall discuss a class of statistical models that generalize the well-understood normal linear model. A normal or Gaussian model assumes that the response Y is equal to the sum of a linear combination X T β of the d-dimensional predictor X and a Gaussian distributed error term. It is well known that the least-squares estimator \(\hat \beta \) of β performs well under these assumptions. Moreover, extensive diagnostic tools have been developed for models of this type.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aitkin, M., Anderson, D., Francis, B. and Hinde,.J. (1989). Statistical Modelling in GLIM. Vol. 4 of Oxford Statistical Science Series, Oxford University Press. Oxford.
Anscombe, F.J. (1953). Contribution to the discussion of H. Hotelling’s paper, Journal of the Royal Statistical Society, Series B 15 (2): 229–230.
Baxter. L.A., Coutts, S.M. and Ross, G.A.F. (1980). Applications of linear models in motor insurance, Proceedings of the 21st International Congress of Actuaries. Zürich, pp. 11–29.
Cox, D.R. and Snell, E.J. (1908). A general definition of residuals (with discussion). Journal of the Royal Statistical Society, Series B 30 (2): 248–275.
Dobson, A.J. (1990). An Introduction to Generalized Linear Models. Chapman and Hall, London.
Hilbe, J.M. (1994a). Generalized linear models. The American Statistician. To appear.
Hilbe, J.M. (1994b). Log negative binomial regression as a generalized linear model, Technical Report 26, Graduate College Commitee on Statistics, Arizona State University, Tempe.
Lee, Y. and Nelder, J.A. (1994). Double generalized linear models. Manuscript.
Liang, K.Y. and Zeger, S.L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73 (1): 13–22.
McCullagh, P. and Ncldcr, J.A. (1989). Generalized Linear Models, Vol. 37 of Monographs on Statistics and Applied Probability, 2nd edn. Chapman and Hall, London.
Nelder, J.A. and Wedderbum, R.W.M. (1972). Generalized linear models. Journal of the Royal Statistical Society. Series A 135 (3): 370–384.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Hilbe, J., Turlach, B.A. (1995). Generalized Linear Models. In: XploRe: An Interactive Statistical Computing Environment. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4214-7_10
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4214-7_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8699-8
Online ISBN: 978-1-4612-4214-7
eBook Packages: Springer Book Archive