Counting degrees of freedom in hierarchical and other richly-parameterised models

James S. Hodges, Daniel J. Sargent

Research output: Contribution to journalArticle

86 Citations (Scopus)

Abstract

Drawing on linear model theory, we rigorously extend the notion of degrees of freedom to richly-parameterised models, including linear hierarchical and random-effect models, some smoothers and spatial models, and combinations of these. The number of degrees of freedom is often much smaller than the number of parameters. Our notion of degrees of freedom is compatible with similar ideas long associated with smoothers, but is applicable to new classes of models and can be interpreted using the projection theory of linear models. We use an example to illustrate the two applications of setting prior distributions for variances and fixing model complexity by fixing degrees of freedom.

Original languageEnglish (US)
Pages (from-to)367-379
Number of pages13
JournalBiometrika
Volume88
Issue number2
StatePublished - 2001

Fingerprint

Counting
Degree of freedom
Linear Models
linear models
Linear Model
Hierarchical Linear Models
Model Complexity
Random Effects Model
Spatial Model
Model Theory
Prior distribution
Model
Projection
Spatial model
Hierarchical linear models
Random effects model

Keywords

  • Complexity
  • Degrees of freedom
  • Hierarchical model
  • Prior distribution
  • Random-effect model
  • Smoothing

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

Cite this

Counting degrees of freedom in hierarchical and other richly-parameterised models. / Hodges, James S.; Sargent, Daniel J.

In: Biometrika, Vol. 88, No. 2, 2001, p. 367-379.

Research output: Contribution to journalArticle

Hodges, JS & Sargent, DJ 2001, 'Counting degrees of freedom in hierarchical and other richly-parameterised models', Biometrika, vol. 88, no. 2, pp. 367-379.
Hodges, James S. ; Sargent, Daniel J. / Counting degrees of freedom in hierarchical and other richly-parameterised models. In: Biometrika. 2001 ; Vol. 88, No. 2. pp. 367-379.
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