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.
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. 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.
Anderson, J. A. (1984) Regression and ordered categorical variables (with discussion). J. Roy. Statist. Soc., B, 46, 1–30.
Baker, R. J., Nelder, J. A. (1978) The GLIM manual: Release 3. Numerical Algorithms Group, Oxford.
Bates, D. M., Watts, D. G. (1980) Relative curvature measures of nonlinearity (with discussion). J. Roy. Statist. Soc. B, 42, 1–25.
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.
Green, P. J., (1987) Penalized likelihood for general semi-parametric regression models. International Statistical Review, 55, 245–259 (1987).
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.
Hastie, T., Tibshirani, R. J. (1986) Generalized additive models (with discussion), Statist. Science, 1, 297–318.
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.
Jørgensen, B. (1983) Maximum likelihood estimation and large-sample inference for generalized linear and nonlinear regression models. Biometrika, 70, 19–28.
McCullagh, P. (1980) Regression models for ordinal data (with discussion). J. Roy. Statist. Soc., B, 42, 109–142.
McCullagh, P. (1983) Quasi-likelihood functions. Ann. Statist., 11, 59–67.
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.
Nelder, J. A., Pregibon, D. (1987) An extended quasi-likelihood function. Biometrika, 74, 221–232.
Nelder, J. A., Wedderburn, R.W.M. (1972) Generalized linear models. J. Roy. Statist. Soc., A., 135, 370–384.
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.
del Pino, G. (1989) The unifying rôle of iterative generalized least squares in statistical algorithms. Statistical Science (to appear).
Scallan, A., Gilchrist, R., Green, M. (1984) Fitting parametric link functions in generalised linear models. Comp. Statist, and Data Anal., 2, 37–49.
Stirling, W. D. (1985) General algorithms based on least squares calculations for maximum likelihood estimation in multiparameter models. Ph.D. thesis, Massey University.
Thompson, R., Baker, R. J. (1981) Composite link functions in generalised linear models. Appl. Statist., 30, 125–131.
Wedderburn, R. W. M. (1974) Quasi-likelihood functions, generalised linear models and the Gauss-Newton method. Biometrika, 61, 439–447.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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