Appropriate combined models are discussed for the analysis of complex traits. It is argued that combined models may be necessary for optimally extracting the information from family studies. It is fur

Estimation of variance components in linear models

The Future of Path Analysis, Segregation Analysis, and Combined Models for Genetic Dissection of Complex Traits

The variability among data may have quite complex structure and the splitting of variation into its individual components is important in many areas of applications. In particular, the study of variation through a class of linear models known as random and mixed models is a central topic in statistics with wide ramifications in both theory and applications. Sometimes these models are called components of variance models since the interest in the model lies in investigating the variances of the effects of factor levels which are assumed to be randomly selected from a large population of levels. These variances are also known as variance components since the total variance can be expressed as the sum of these variances and the error variance. Knowledge of the variance components, i.e., the information on the relative importance and magnitude of the sources of variability in the data is of critical importance in many problems since the isolation of the total variance into the individual components of variance would result in the physical elimination of the sources of variability in question.

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A bibliography on variance components an introduction and an update: 1984-2002

On the solutions of the equation A X B = C under Toeplitz-like and Hankel matrices constraint

The paper deals with construction of exact confidence intervals for the variance component σ 1 and ratio θ of variance components σ 2 1 and σ in mixed linear models for the family of normal distributions Nt (0, σ 2 1W + σ It). This problem essentially depends on algebraic structure of the covariance matrix W (see Gnot and Michalski, 1994, Michalski and Zmyślony, 1996). In the paper we give two classes of bayesian interval estimators depending on a prior distribution on (σ 1 , σ ) for: 1) the variance components ratio θ built by using test statistics obtained from the decomposition of a quadratic form y′Ay for the Bayes locally best estimator of σ 1 , Michalski and Zmyślony (1996), 2) the variance component σ 1 constructed using Bayes point estimators from BIQUE class (Best Invariant Quadratic Unbiased Estimators, see Gnot and Kleffe, 1983, and Michalski, 2003). doi:10.7151/dmps.1104 In the paper an idea of construction of confidence intervals using generalized p-values is also presented (Tsui and Weerahandi, 1989, Zhou and Mathew, 1994). Theoretical results for Bayes interval estimators and for some generalized confidence intervals by simulations studies for some experimental layouts are illustrated and compared (cf Arendacká, 2005).

Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models

Estimation for robust control

https://summit.sfu.ca/system/files/iritems1/6446/b16670486.pdf

Estimation of variance components in linear models

Citations

The Future of Path Analysis, Segregation Analysis, and Combined Models for Genetic Dissection of Complex Traits

A bibliography on variance components an introduction and an update: 1984-2002

On the solutions of the equation A X B = C under Toeplitz-like and Hankel matrices constraint

Bayesian and generalized confidence intervals on variance ratio and on the variance component in mixed linear models

Estimation for robust control

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