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## Confidence intervals for variance components

Measuring the source and magnitude of components of variation has important

applications in industrial, environmental and biological studies. This thesis considers

the problem of constructing confidence intervals for variance components in Gaussian

mixed linear models. A number of methods based on the usual ANOVA mean squares

have been proposed for constructing confidence intervals for variance components in

balanced mixed models. Some authors have suggested extending balanced model

procedures to unbalanced models by replacing the ANOVA mean squares with mean

squares from an unweighted means ANOVA. However, the unweighted means

ANOVA is only defined for a few specific mixed models. In Chapter 2 we define a

generalization of the unweighted means ANOVA for the three variance component

mixed linear model and illustrate how the mean squares from this ANOVA may be used

to construct confidence intervals for variance components. Computer simulations

indicate that the proposed procedure gives intervals that are generally consistent with the

stated confidence level, except in the case of extremely unbalanced designs. A set of

statistics that can be used as an alternative to the generalized unweighted mean squares

is developed in Chapter 3. The intervals constructed with these statistics have better

coverage probability and are often narrower than the intervals constructed with the

generalized unweighted mean squares. / Graduation date: 1998

Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/33883 |

Date | 08 May 1998 |

Creators | Purdy, Kathleen G. |

Contributors | Seely, Justus F. |

Source Sets | Oregon State University |

Language | en_US |

Detected Language | English |

Type | Thesis/Dissertation |

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