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The statistics of linear models: back to basics

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.

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Nelder, J.A. The statistics of linear models: back to basics. Stat Comput 4, 221–234 (1994). https://doi.org/10.1007/BF00156745

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  • DOI: https://doi.org/10.1007/BF00156745

Keywords

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