Advertisement

Statistics and Computing

, Volume 4, Issue 4, pp 221–234 | Cite as

The statistics of linear models: back to basics

  • J. A. Nelder
Discussion Paper

Abstract

Inference from the fitting of linear models is basic to statistical practice, but the development of strategies for analysis has been hindered by unnecessary complexities in the descriptions of such models. Three false steps are identified and discussed: they concern constraints on parameters, neglect of marginality constraints, and confusion between non-centrality parameters and corresponding hypotheses. Useful primitive statistical steps are discussed, and the need for strategies, rather than tactics, of analysis stressed. The implications for the development of good, fully interactive, computing software are set out, and illustrated with examples.

Keywords

Constraints data structure fixed effect functional marginality linear models marginal homogeneity marginality model selection non-centrality parameter operand operator prediction random effect 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrews, D. F. and Herzberg, A. M. (1985) Data. Springer-Verlag, New York.Google Scholar
  2. Cox, D. R. (1958) The interpretation of the effects of nonadditivity in the Latin square. Biometrika, 45, 67–73.Google Scholar
  3. Cox, D. R. and Snell, E. J. (1981) Applied statistics: principles and examples. Chapman and Hall, London.Google Scholar
  4. Hocking, R. R. and Speed, F. M. (1975) A full rank analysis of some linear model problems. Journal of the American Statistical Association, 70, 706–12.Google Scholar
  5. Lane, P. W. and Nelder, J. A. (1982) Analysis of covariance and standardization as instances of prediction. Biometrics, 38, 613–21.Google Scholar
  6. McCullagh, P. M. and Nelder, J. A. (1989) Generalized linear models, 2nd edn. Chapman and Hall, London.Google Scholar
  7. Nelder, J. A. (1977) A reformulation of linear models. Journal of the Royal Statistical Society, Series A, 140, 48–77.Google Scholar
  8. Neyman, J., Iwaszkiewicz, K. and Kolodziesczyk, St. (1935) Statistical problems in agricultural experimentation. Journal of the Royal Statistical Society, Series B, 2, 107–54.Google Scholar
  9. Payne, C. D. (ed.) (1986) The GLIM manual, Release 3.77. NAG, Oxford.Google Scholar
  10. Payne, R. W. et al. (1987) Genstat 5 reference manual. Clarendon Press, Oxford.Google Scholar
  11. Pignatiello, J. J. and Ramberg, J. S. (1985) Contribution to discussion of off-line quality control, parameter design, and the Taguchi method. Journal of Quality Technology, 17, 198–206.Google Scholar
  12. SAS Institute Inc. (1985) SAS user's guide: statistics, version 5 edition. SAS Institute Inc., Cary, NC.Google Scholar
  13. Searle, S. R. (1987) Linear models for unbalanced data. Wiley, New York.Google Scholar
  14. Ripley, B. D. (1992) Introductory guide to S-Plus. Dept. of Statistics, University of Oxford.Google Scholar
  15. Wolstenholme, D. E., O'Brien, C. M. and Nelder, J. A. (1988) GIMPSE: A knowledge-based front end for statistical analysis. Knowledge-based Systems, 1, 173–8.Google Scholar
  16. Yates, F. (1934) The analysis of multiple classifications with unequal numbers in the different classes. Journal of the American Statistical Association, 29, 51–66.Google Scholar

Copyright information

© Chapman & Hall 1994

Authors and Affiliations

  • J. A. Nelder
    • 1
  1. 1.Department of MathematicsImperial College of Science, Technology, and MedicineLondonUK

Personalised recommendations