### 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 |

### Keywords

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

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## Cite this

Durban, M., & Currie, I. D. (2000). Adjustment of the profile likelihood for a class of normal regression models.

*Scandinavian Journal of Statistics*,*27*(3), 535-540.