Including mean-variance relationships in heteroskedastic mixed models:
theory and application
by Jean-Louis Foulley.
Abstract:
In mixed linear models, it is usually assumed that both
residual and random effects have homogeneous components of variance.
This paper presents models and corresponding techniques of estimation
to relax this restrictive assumption. Models proposed include log link
functions linearly relating variance components to explanatory variables
that can be either discrete or continuous. Special emphasis is given to two
aspects of modelling. First, a structural model for residual variances is
considered which incorporates, in addition to classical covariates, a function
of the data expectation to take into account mean-variance relationships.
Secondly, residual and random effect component of variances are linked via a
linear functional relationship. Estimation and testing procedures are based on
restricted maximum likelihood procedures (REML) via the expectation
maximization (EM) algorithm. The procedure is illustrated by the analysis of birth
weight of rats that were used in a toxicology experiment.
Key Words:
Mixed models, Heteroskedasticity, Restricted maximum likelihood,
EM algorithm
Author:
Jean-Louis Foulley, foulley@jouy.inra.fr
Editor:
Avner Bar-Hen,avner@bar-hen.net
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