<abstract xmlns="http://www.w3.org/1999/xhtml"><p> Linear models with variance-covariance components are used in a wide variety of applications. In most situations it is possible to partition the response vector into a set of independent subvectors, such as in longitudinal models where the response is observed repeatedly on a set of sampling units (see, e.g., Laird &amp; Ware 1982). Often the objective of inference is either a test of linear hypotheses about the mean or both, the mean and the variance components. Confidence intervals for parameters of interest can be constructed as an alter- native to a test. These questions have kept many statisticians busy for several decades. Even under the assumption that the response can be modeled by a multivariate normal distribution, it is not clear what test to recommend except in a few settings such as balanced or orthogonal designs. Here we investigate statistical properties, such as accuracy of p-values and powers of exact (Crainiceanu &amp; Ruppert 2004) tests and compare with properties of approximate asymptotic tests. Simultaneous exact confidence regions for variance components and mean parameters are constructed as well.</p></abstract>

Linear models with variance-covariance components are used in a wide variety of applications. In most situations it is possible to partition the response vector into a set of independent subvectors, such as in longitudinal models where the response is observed repeatedly on a set of sampling units (see, e.g., Laird & Ware 1982). Often the objective of inference is either a test of linear hypotheses about the mean or both, the mean and the variance components. Confidence intervals for parameters of interest can be constructed as an alter- native to a test. These questions have kept many statisticians busy for several decades. Even under the assumption that the response can be modeled by a multivariate normal distribution, it is not clear what test to recommend except in a few settings such as balanced or orthogonal designs. Here we investigate statistical properties, such as accuracy of p-values and powers of exact (Crainiceanu & Ruppert 2004) tests and compare with properties of approximate asymptotic tests. Simultaneous exact confidence regions for variance components and mean parameters are constructed as well.

On exact inference in linear models with two variance-covariance components

School of Public Health LSU Health Sciences Center 2020 Gravier Street New Orleans, LA 70112 USA

Institute of Measurement Science Slovak Academy of Sciences D´ubravsk´a cesta 9 SK–841-04 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"On exact inference in linear models with two variance-covariance components"}

Linear models with variance-covariance components are used in a wide variety of applications. In most situations it is possible to partition the response...

On exact inference in linear models with two variance-covariance components

Published Online: Nov 13, 2012

Page range: 173 - 181

DOI: https://doi.org/10.2478/v10127-012-0017-9

Keywords
linear mixed model, variance components, likelihood ratio test, exact test.

This content is open access.

On exact inference in linear models with two variance-covariance components

Published Online: Nov 13, 2012

Page range: 173 - 181

DOI: https://doi.org/10.2478/v10127-012-0017-9

Keywordslinear mixed model, variance components, likelihood ratio test, exact test.

This content is open access.

Keywords
linear mixed model, variance components, likelihood ratio test, exact test.