### 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 language | English (US) |
---|---|

Pages (from-to) | 367-379 |

Number of pages | 13 |

Journal | Biometrika |

Volume | 88 |

Issue number | 2 |

State | Published - 2001 |

### Fingerprint

### 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

*Biometrika*,

*88*(2), 367-379.

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

Research output: Contribution to journal › Article

*Biometrika*, vol. 88, no. 2, pp. 367-379.

}

TY - JOUR

T1 - Counting degrees of freedom in hierarchical and other richly-parameterised models

AU - Hodges, James S.

AU - Sargent, Daniel J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

KW - Complexity

KW - Degrees of freedom

KW - Hierarchical model

KW - Prior distribution

KW - Random-effect model

KW - Smoothing

UR - http://www.scopus.com/inward/record.url?scp=0011691958&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011691958&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0011691958

VL - 88

SP - 367

EP - 379

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -