### Abstract

We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log-likelihood score function. For the variance components model, we obtain the adjusted profile log-likelihood and show that it equals the restricted log-likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.

Original language | English |
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Pages (from-to) | 535-540 |

Number of pages | 6 |

Journal | Scandinavian Journal of Statistics |

Volume | 27 |

Issue number | 3 |

Publication status | Published - Sep 2000 |

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### Keywords

- Competition
- Mixed model
- Profile likelihood
- REML
- Score function
- Variance components

### Cite this

*Scandinavian Journal of Statistics*,

*27*(3), 535-540.

}

*Scandinavian Journal of Statistics*, vol. 27, no. 3, pp. 535-540.

**Adjustment of the profile likelihood for a class of normal regression models.** / Durban, Maria; Currie, Iain D.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Adjustment of the profile likelihood for a class of normal regression models

AU - Durban, Maria

AU - Currie, Iain D.

PY - 2000/9

Y1 - 2000/9

N2 - We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log-likelihood score function. For the variance components model, we obtain the adjusted profile log-likelihood and show that it equals the restricted log-likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.

AB - We apply the method of McCullagh & Tibshirani (1990) to a generalization of the model for variance components in which the parameter of interest can appear in both the mean and variance. We obtain the exact adjusted profile log-likelihood score function. For the variance components model, we obtain the adjusted profile log-likelihood and show that it equals the restricted log-likelihood of Patterson & Thompson (1971). We discuss an example due to Kempton (1982) of a regression model with autoregressive terms in which the parameter of interest appears in both the mean and variance.

KW - Competition

KW - Mixed model

KW - Profile likelihood

KW - REML

KW - Score function

KW - Variance components

UR - http://www.scopus.com/inward/record.url?scp=0034336106&partnerID=8YFLogxK

M3 - Article

VL - 27

SP - 535

EP - 540

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 3

ER -